Mathematical platonism
@frank wanted to discuss this, so here are my initial thoughts:
Do infinitesimals exist (in the platonistic sense)?
1. If they don't exist then any number system that includes them is "wrong". But if we have consistent number systems that use them then a) we must ask how to determine which mathematical entities exist and which don't and b) we must ask why we ought believe that any mathematical entities exist given that we can do maths using mathematical entities that don't exist.
2. If they do exist then any number system that excludes them is "incomplete" (not to be confused with incompleteness in the sense of Gödel). But then to avoid the problems addressed in (1) we must believe that every possible entity that can be included in a consistent system of mathematics exists, e.g. perhaps "superinfinitesimals" that are greater than zero and smaller than any infinitesimal. However, we then run the risk of a mathematical entity in one system being incompatible with another system, e.g. Quine atoms, and so that incompatible mathematical entities exist.
3. Infinitesimals exist according to some number systems but not others. This would be fictionalism, not platonism:
Do infinitesimals exist (in the platonistic sense)?
1. If they don't exist then any number system that includes them is "wrong". But if we have consistent number systems that use them then a) we must ask how to determine which mathematical entities exist and which don't and b) we must ask why we ought believe that any mathematical entities exist given that we can do maths using mathematical entities that don't exist.
2. If they do exist then any number system that excludes them is "incomplete" (not to be confused with incompleteness in the sense of Gödel). But then to avoid the problems addressed in (1) we must believe that every possible entity that can be included in a consistent system of mathematics exists, e.g. perhaps "superinfinitesimals" that are greater than zero and smaller than any infinitesimal. However, we then run the risk of a mathematical entity in one system being incompatible with another system, e.g. Quine atoms, and so that incompatible mathematical entities exist.
3. Infinitesimals exist according to some number systems but not others. This would be fictionalism, not platonism:
Prima facie, it may sound counterintuitive to state that there are infinitely many prime numbers is false. But if numbers do not exist, that's the proper truth-value for that statement (assuming a standard semantics). In response to this concern, Field 1989 introduces a fictional operator, in terms of which verbal agreement can be reached with the platonist. In the case at hand, one would state: According to arithmetic, there are infinitely many prime numbers, which is clearly true. Given the use of a fictional operator, the resulting view is often called mathematical fictionalism.
Comments (704)
When you say 'exist in a platonic sense', what exactly do you mean?
I am inclined to argue that maths do not 'exist' in any objective sense.
Math is a product of the human mind, and a very useful for modeling reality for human purposes. It's a way of describing ratios and relations between things. The actual objective nature of such relations seems inaccessible to humans though.
Platonism in the Philosophy of Mathematics
Why do you think realism is the prevailing view in Phil of math? Why is it found to be a valuable perspective in spite of its drawbacks?
I don't know, I'm not a psychologist.
So platonic mathematics implies someone had a mystical experience and discovered math still exists 'beyond the veil'?
Dude. Really?
It's certainly unclear, and is precisely what gives rise to the epistemological argument against platonism:
1. Human beings exist entirely within spacetime.
2. If there exist any abstract mathematical objects, then they do not exist in spacetime. Therefore, it seems very plausible that:
3. If there exist any abstract mathematical objects, then human beings could not attain knowledge of them. Therefore,
4. If mathematical platonism is correct, then human beings could not attain mathematical knowledge.
5. Human beings have mathematical knowledge. Therefore,
6. Mathematical platonism is not correct.
Tying it back to the OP, who cares if infinitesimals exist objectively, as long as they are useful in creating more accurate models of reality?
I certainly believe so. Given my thoughts in the OP and Occam's razor, I think that mathematical platonism ought be rejected.
I know this isn't your definition, but I would suggest a modification to just:
"Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is not dependent on us and our language, thought, and practices."
"Independent" might suggest that the two don't interact, but it seems obvious that they must for platonism to be an interesting thesis. The whole second part is problematic in that it seems to assume that "statements" are also independent of us (and true or false independent of us), and I am not sure if all mathematical platonists would like to be committed to those implied premises. It seems to require being a platonist about "statements" in order to be a platonist about any mathematical objects. But, at least for me, "threeness exists without humans around" seems a lot more plausible than "sentences exist without humans around."
Well, my turn to ask for a definition: what does "objective" mean here? I've noticed it tends to get used in extremely diverse ways. I assume this is not "objective" in the same sense that news is said to be "more or less objective?"
As a follow-up, I would tend to think that the game of chess does not exist independently from the human mind. Chess depends on us; we created it. However, are the rules of chess thus not objective? Are there no objective facts about what constitutes a valid move in chess?
I suppose this gets at the need for a definition.
But isn't the follow up question: "why is it useful?" Not all of our inventions end up being useful. In virtue of what is mathematics so useful? Depending on our answer, the platonist might be able to appeal to Occam's razor too. A (relatively) straight-forward explanation for "why is math useful?" is "because mathematical objects are real and instantiated in the world."
This also helps to explain mathematics from a naturalist perspective vis-a-vis its causes. What caused us the create math? Being surrounded by mathematical objects. Why do we have the cognitive skills required to do math? Because math is all around the organism, making the ability to do mathematics adaptive.
I think the platonist response would be that premise 2 is false. Mathematical objects exist in spacetime. There is twoness everywhere there are two of something (e.g. in binary solar systems). Premise two seems to imply that any transcendent, Platonic form is absent from what it transcends. Yet this is not how Plato saw things. The Good, for instance, is involved in everything that ever even appears to be good. Plus, my understanding is that many mathematical platonists (lower case p) are immanent realists, along the lines of Aristotle. So, numbers exist precisely where they are instantiated (in space-time). A Hegelian theory would similarly still allow that numbers exist "in history."
At least according to the SEP article here, (2) is platonism:
Quoting Count Timothy von Icarus
This is moderate/immanent realism:
Objective in the platonic sense refers to the reality that underlies our 'reality' of sense experience.
We infer its existence, because we are able to consistently predict outcomes accurately enough for human endeavors. Mathematics and science help us do so.
Quoting Count Timothy von Icarus
Hmm.. I'm inclined to say that there are indeed no objective facts related to chess. Chess tells us nothing about this underlying reality.
Quoting Count Timothy von Icarus
Math is a very useful way of describing relations and ratios between things.
Claiming things are real runs into all sorts of prickly problems, though. Have you peeked beyond the veil and seen it was so?
Quoting Michael
I'm actually kind of curious what passages of Plato this refers to.
3. If there exist any abstract mathematical objects, then human beings could not attain knowledge of them.
If knowledge is justified true belief then this can be rephrased as:
3. If there exist any abstract mathematical objects, then human beings could not attain justified true beliefs of them.
Is this saying that if mathematical objects are abstract then we cannot conceive of an equation, that we cannot believe that the equation is true, or that we cannot be justified in believing that the equation is true?
Or is there some other sense of knowledge, distinct from justified true belief, at play here?
I think knowledge here refers to absolute certainty, or objective knowledge, and the platonists were highly skeptical of that.
There is an 'extended real numbers' that includes infinity. I'm sure we can name a set that includes infinitesimals as well. Still not complete since I think octonians is necessary for that, extended octonians at that.
I did not follow the bit about fictional numbers
The definition you gave in 2nd post about numbers essentially being real, well, the definition seems to identify them being objective: Independently gleaned by isolated groups. This is a good argument against any specific god since isolated groups might all claim divine communication, but none of them come up with the same story. With mathematics, this is not the case.
Still, the sum of 3 and 5 being 8, is that a property of this universe, or does it work anywhere? Is it truly an objective fact? I don't equate objectivity with being real, but the definition you gave seems to equate the two.
Quoting Tzeentch
Cool. An opposing viewpoint. What's the alternaitve?
This distinction seems more Kantian than Platonic to me. I think "noumenal" might be a better tern here, i.e. "a thing that exists independently of human senses." At least, Plato himself would reject such a cleavage in reality, as well as existence without any edios (quiddity, intelligibility, form).
Have you looked on both sides to see if the veil itself is real? I am not sure if you can have a "reality versus appearances" dichotomy if there is only appearances. If there are just appearances, then appearances are reality. But then how do we justify the claim that there is a reality that is completely isolated from appearances?
On the other hand, if we can "infer" the "'reality' behind the veil," then why can't we likewise infer that this reality includes numbers?
This is, BTW, Hegel's critique of Kant. Kant himself is dogmatic. He doesn't justify the assumption that perceptions are of something, that they are in some sense "caused" by noumena (although of course, "cause" itself is phenomenological and so suspect). He just presupposes it and goes from there (and look, he just happens to deduce Aristotle's categories, convenient!). The Logics are pretty much Hegel's attempt to start over without this assumption.
But then wouldn't these objective/noumenal things need to be the sort of things that have ratios? If they don't have ratios, why is it useful to describe them so? If they do, then numbers (multitude and magnitude) seem to apply to the noumena.
But presumably it tells us something about the reality of chess. This is why I don't know about making "objective" and "noumenal" synonyms. For one, it seems likely to me that many people will find a use for the former while rejecting the assumptions that make the latter meaningful. Second, we wouldn't want to have to be committed to the idea that facts about chess, or the game itself, are illusory.
Sort of besides the point though.
Platonism in many areas is lower case "p" platonism, which tends to be only ancillary related to Platonism. For instance, :
This could apply to Plato in some sense, but you'd really need a lot of caveats. Plato's metaphysics works on the idea of "vertical" levels to reality. Forms are "more real" they aren't located in some sort of space out of spacetime. But at the same time, even for Plato and the ancient and medieval Platonists, the Forms aren't absent from the realm of appearances. The reason medieval talk of God can be so sensuous without giving offense is because they thought all good, even the good of what merely appears to be good, is still a participation in/possession of the Good.
So, the world of the senses and spacetime would be deeply related to the Forms, not isolated from them. However, I am not super familiar with platonism in contemporary philosophy of mathematics.
Quoting Count Timothy von Icarus
One can always answer the question of why something is useful by attaching it to a sovereign ground. This works equally well for the true , the good and the numerical. But it may be more illuminating to ask the question of how something is useful, that is, what are the consequences of resorting to a sovereign ground rather than a pragmatic explanation based on subjectively and intersubjectively constructed norms. For instance, the consequence of asserting that mathematical objects are real things in the world is the risk of skepticism and arbitrariness. Why should there be unanimous agreement about the meaning of enumeration when there is disagreement out every other fact of nature?
By contrast, if we were to argue that the concept of number is a conceptual abstraction derived from the selective noticing of individual elements of a collective multiplicity, wherein one deliberately abstracts away everything about those individual elements other than the idea of same thing different time. Same thing different time is not found anywhere in the world, it is an invention which, when applied to real objects, flattens differences in kind in order to accomplish certain useful goals. One consequence of understanding the usefulness of number as a pragmatic tool rather than as a sovereign fact of nature is to bypass the risk of skepticism and arbitrariness. Numeration arises out of the ground of practical human need for relating and keeping track of disparate objects. Its meaning is universal precisely because it is a pure, because empty, idealization and therefore not subject to the intersubjective tribunal that objective facts of nature must undergo.
[quote=What is Math?; https://www.smithsonianmag.com/science-nature/what-math-180975882/] Some scholars feel very strongly that mathematical truths are out there, waiting to be discovereda position known as Platonism. It takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their ownnot a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist. In The Emperors New Mind, he wrote that there appears to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external trutha truth which has a reality of its own...
Many mathematicians seem to support this view. The things theyve discovered over the centuriesthat there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on foreverseem to be eternal truths, independent of the minds that found them. If we were to one day encounter intelligent aliens from another galaxy, they would not share our language or culture, but, the Platonist would argue, they might very well have made these same mathematical discoveries.
I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians, says James Robert Brown, a philosopher of science recently retired from the University of Toronto. Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, its always the Platonistic answer that they give you.
Other scholarsespecially those working in other branches of scienceview Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing outside of space and time makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, has more in common with mystical religions than it does with modern science. The fear is that if mathematicians give Plato an inch, hell take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?
Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonismbut has since come to see it as problematic. If something doesnt have a physical existence, he asks, then what kind of existence could it possibly have? If one goes Platonic with math, writes Pigliucci, empiricism goes out the window. (If the proof of the Pythagorean theorem exists outside of space and time, why not the golden rule, or even the divinity of Jesus Christ?)[/quote]
Why not, indeed? But I think that extended passage brings out the underlying animus against mathematical Platonism, which is mainly that it undermines empiricism. And empiricism is deeply entrenched in our worldview.
[quote=SEP, Platonism in the Philosophy of Mathematics;https://plato.stanford.edu/entries/platonism-mathematics/#PhilSignMathPlat]Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects that arent part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.[/quote]
I resolve the conundrum by saying that numbers (etc) are real but not existent in a phenomenal sense. They are intelligible or noumenal objects (in a Platonic rather than a Kantian sense) and as such are indispensable elements of rational judgement.
Quoting Wayfarer
If Platonism seems to undercut empiricism, it does so only by occupying the opposing pole of the binary implicating both physicalism and platonism within the same tired dualistic subject-object metaphysics. Why not undercut both empiricism and platonism in one fell swoop, and see both numbers and physical things as pragmatic constructions, neither strictly ideal nor empirical, subjective nor objective, inner nor outer, but real nonetheless?
I don't know if I agree with your diagnosis that the opposition to Platonism arises from 'subject-object metaphysics'. I think it goes back to the decline of Aristotelian realism and the ascendancy of nominalism in late medieval Europe. From which comes the oxymoronic notion of mind-independence of the empirical domain, when whatever we know of the empirical domain is dependent on sensory perception and judgement (per Kant). Hence those objections in that passage I quoted, 'The idea of something existing outside of space and time makes empiricists nervous'. Anything real has to be 'out there somewhere' - otherwise it's 'in the mind'. That is the origin of subject-object metaphysics.
Quoting Joshs
But there are imaginary numbers, and also imaginary objects, even imaginary worlds. There are degrees of reality, and there is a such a thing as delusion, and delusions can be very deep indeed, in today's panoptical culture. Agree with the constructivist attitude overall, but still want to honour the epistemology of the Divided Line.
Yeah, why answer a difficult question when we can just engage in question begging? And if everyone just assumes the asserted conclusion is right, this will prevent any skepticism or charges arbitrariness!.
It is inferred that there exists our world of sense experience, and a reality underlies it. Science has gone a long way in confirming this, showing how our senses mislead us, and only show us the tip of the iceberg.
Quoting Count Timothy von Icarus
It is pretty much the central theme of Plato. It's not that reality is cleaved, but that we do not experience reality - only a reflection of it. That's the cave.
Quoting Count Timothy von Icarus
I think the word 'reality' is a misnomer here. Chess is something we made up. Would you accept it if people were arguing for the reality of the flying spaghetti monster?
Quoting Michael
They are convenient and useful descriptive tools to denote and express the small objects and motions in the real world such as the information or movements of particles and atoms.
Ok, but you didn't answer how this "reality" can be [I]inferred[/I] "by science," but numbers absolutely cannot be. It seems to me that the empirical sciences only ever deal with phenomena.
Further, can we do physics, cognitive science, or biology without mathematics? More importantly, you haven't given any answer for [I]why or how[/I] ratios are useful if they don't *really* apply to or exist in your noumenon. If the noumenal isn't the sort of thing that can be accurately described by number and ratio (we have many things like this in the world of phenomena) then why is it "useful" to describe them that way anyhow? Shouldn't the usefulness of mathematics in science lead us to "infer" that it says [I]something[/I] about reality?
It just seems strange to me to appeal to all the ways in which science shows our senses can be misled, when those same sciences often rely on mathematics to point out these illusions, but then to turn around and say that the math you used to discover the illusions (and so to infer their "reality") is itself illusory. And of course any corrections to perception made by "by empirical science" are [I]also[/I] discovered through the senses, so if the senses and intellect "mislead us," they're also responsible for correcting this.
It seems that at best you're arguing for nescience: "we can never know if numbers are *really* in the noumena with total certainty." But your positions seems to require actually demonstrating that there is no good reason to infer that ratios/mathematics apply to "things-in-themselves." Having some avenue for skepticism is not enough, people can also doubt that there is any reality that is distinct from appearances (e.g. solipsism, subjective idealism, etc.), but clearly you don't think this is good grounds for accepting that reality is just appearances yourself.
(Note: both noumena [plural] and things-in-themselves imply plurality, numberthis is why people who want to go along with Kant's distinction normally speak of simply "a noumenon.")
Plato makes a distinction between reality and appearances. He does not make a distinction between appearances as "subjectivity," and reality as the "objective/noumenal"i.e., reality as "things-in-themselves" as set over and against appearances. This Kantian division makes no sense given Plato's philosophy of appearances and images as participation. Kant's view requires the presuppositions of modern representationalism, i.e., that "what we experience" are our own "mental representations of ideas" and that such representations are "what we know" instead of "how we know." The later Platonists allowed that "everything is received in the manner of the receiver," but not that things' appearances are disconnected from what they are (i.e "act follows on being" and "appearing" is an act of the subject of predication).
For instance, Plato's Good is absolute. The absolute is not reality as separated off from appearances. It must encompass all of reality and appearances to be truly absolutely. Thing's appearances are really how they appear. Likewise, the transcendent Good isn't absent from the very finitude it is supposed to transcend. This would make it less than truly transcedent.
It seems like a lot of people, when it comes to philosophy, think "objective" is a synonym for "noumenal." But this is certainly not how the term is employed by many philosophers, and this leads to all sorts of confusions, like the idea that an "objective" goodness or beauty is somehow one that is wholly absent and disconnected from experiences (Sam Harris has this misreading of the Platonic Good in The Moral Landscape for instance). In which case, no wonder such ideas seen farcical. On this misunderstanding they are incoherent, the objective Good must be, by definition, "good for precisely no one." But Platonic eidos (forms), as the term's usual connotations in ancient Greek suggest ("shape," "something seen") are not unrelated to, or absent from, appearancesa reality as set apart from appearance.
Presumably, the latter is an intentional [I]fiction[/I] created to critique religion. It is one thing to claim that Homer's Achilles is a "fictional character." It is another to claim that the Iliad doesn't "really exist" because Homer wrote it. Do airplanes also not exist because they are the invention of man? States? World history? Chess?
I think a view that commits us to claims like: "there are no objective facts about what constitutes a valid move in chess," or "the proposition 'Kasparov is a better chess player than the average preschooler' is one with no truth value because it refers to the "subjective" game of chess," has serious deficits. Does "the Declaration of Independence was signed in 1776" also become subjective because our calendar system is the creation of man? But then temperature would also have to be subjective because it involves both man-made scales and measurement from particular perspectives.
They're both tools for modeling an inferred underlying reality. But they themselves are human creations, accurate enough for our human purposes.
They're useful because they're accurate enough. But it would be a mistake to believe they convey the objective nature of reality.
Quoting Count Timothy von Icarus
Neither am I, as far as I am aware.
Quoting Count Timothy von Icarus
If someone were to create a gigantic effigy of a flying spaghetti monster, would that suddenly make the flying spaghetti monster real?
I'd argue all of those things you named are human creations, and therefore not 'real' in the sense that we are talking about right now.
Obviously, we can make all sorts of practical concessions in what we colloquially refer to as 'real'.
:up: :100:
Yes, the philosophy of Plato does not seem to be commensurate with modern subject-object dualism. It seems even less applicable to later Platonists, such as Plotinus, St. Augustine, or St. Bonaventure.
Nominalism seems to me to be the larger issue and I think it has generally been nominalism that has motivated to errection of subject-object dualism, rather than the other way around (although obviously the influence is bi-directional).
Yes, you seem to be asserting this as a premise and then arguing from there. But this is to assume as true the very thing you're setting out to prove, that platonism is false.
What's the argument for mathematics being a sui generis human creation unaffected by the reality of multitude or magnitude? What caused us to create it? If it's useful, why?
To say that these questions are unanswerable suggests nescience, not one answer re platonism being supported over the other.
You certainly seem to be. Your claim is that, for something to be properly "real" it must exist wholly outside appearances. How is this not defining reality in terms of the noumenal? For all those following Parmenides, Plato included, there is no reality as totally divorced from appearances and intelligibility. Thought and being are two sides of the same non-composite whole.
Do you think making a statue of a fictional character makes them real? I don't. Yet is chess fictional? Is world history fiction? Temperature? Dates?
Scientific theories and paradigms are human creations. Yet if these are thereby fictions, then your appeal to "inferring reality from science" would amount to "inferring what is real from fiction."
That's not what I'm asserting, because how would I know?
The core of what I'm saying is that, as Plato argued, it is very difficult to even access the reality that underlies our world of sense experience, let alone make statements about this reality.
So rather I am expressing skepticism towards those who would claim mathematics is 'objectively real', and also pointing out the contradiction in the term 'mathematical platonism'.
Does that make sense?
Quoting Count Timothy von Icarus
In the context of a philosophical debate, I would argue all of those things are indeed human 'fictions', that serve a purpose for our human needs.
Note that I am not saying that science shows us what is real, rather it seems to heavily suggest the existence of an underlying reality because it is able to make models of how that reality works to a degree that is at least accurate enough for our human endeavors.
It makes sense, but I would also suggest that its based on a common misconception. The idea of a realm of Forms is often misconstrued as an ethereal realm, like a ghostly palace. But consider the domain of natural numbers. That is quite real, but the word domain has a very different sense to that of a place or world - even if there are some numbers inside it and others not. Domains and objects are metaphors or figures of speech which are easily but mistakenly reified as actual domains or objects. But that for which they are metaphors are real nonetheless.
The point about truths of reason is that they can only be grasped by reason. But due to the cultural impact of empiricism we are conditioned to believe that only what is materially existent - what is out there, somewhere - is real. But numbers, and other objects of reason, are real in a different way to sense objects. And that is a stumbling block for a culture in which things are said to either exist or not. There is no conceptual space for different modes of reality (leaving aside dry, academic modal metaphysics). Which is why we can only think of them as kinds of objects, which theyre actually not. Theyre really closer to kinds of acts.
See this post
Well said. Starting with the natural numbers, which are ways to distinguish objects and converse about quantities, mathematics has grown to virtually unimaginable proportions over the millennia. And it has changed character from a descriptive and predictive tool to an enormous game, unbounded in some aspects, with recently formulated foundational rules.
Some compare it to chess, where material pieces are moved around a board rather than the pen or pencil upon paper, or keys and screen of a computer. Where it might differ is in potential: mathematics awaiting discovery or creation versus possible strategies or moves on the chessboard. Chess players might comment on this.
Is a crossword puzzle real? Pondering how to fill in the spaces, then doing so with pencil. Sounds a little like math. Are emerging ideas real? Of course they are. Do mathematical objects exist in some exotic realm, awaiting discovery? I think of them as commonalities of minds, the way in which human brains have evolved.
Quoting Michael
I've always thought of these little critters as part of the metaphysics of mathematics. They now belong to a variation of the game called nonstandard analysis.
As I said, I think exist is problematical in the context. Not that they dont exist, but the way in which theyre real is different to empirical objects. They are objects of mind rather than objects of sense, but I dont think the philosophical lexicon has an appropriate term. I tried this out on ChatGPT recently and it suggested transcendentally objective, although that is hardly an elegant expression.
Quoting jgill
Consider synthetic chemistry and genetic engineering. These too are grounded in traditional chemistry and biology but now have dimensions that would never be found in nature herself. Its analogous in some ways.
Quoting jgill
Maybe they are to natural numbers as viruses are to organisms ;-)
And why would numbers be able to exist in this way, and not flying spaghetti monsters?
I just want to point out that the bolded phrase is what's at stake. You can believe that numbers and other abstracta really and truly exist without being a mathematical platonist. You merely assert that they exist because we have created them, and they will cease to exist if we also cease. Whether you want to say this or not will depend on how you wish to use the word "exist." Clearly, if you are a friend of "existence = spatiotemporal objects or arrangements thereof", then you won't want to claim even a human-made existence for numbers.
I agree. I don't think mathematical platonism is supposed to be some big metaphysical statement. It's just reflecting our experience with math: that it's something we seem to discover, that it's not owned by particular people, in other words, it's not mental or physical.
That leaves the door open to trying to explain it anyway we want, kind of like gravity is a thing, but we're still working on how to explain it.
Quoting jgill
This IS the mistake we do.
We START from natural numbers as it's the natural place to start for counting. It basically a necessity for our situational awereness, hence even animals can have a rudimentary simple "math"-system. Yet simply as mathematics has objects that are not countrable, starting with infinity, infinite sequences and infinitesimals, whole math simply cannot be based on natural numbers. This is the reason why Russell's logicism faced paradoxes. Not everything was discovered. That there exist the uncountable should make it obvious to us that natural numbers and counting isn't the logical ground on which everything mathematical is based upon.
Something really big is missing here. It's up to us, perhaps, to find the answer. Or at least get closer to it
Thanks for you @Michael to start this thread.
What about the laws of logic, like the law of the excluded middle? Does that cease to obtain in the absence of rational sentient beings? Im more inclined to the understanding that it is discovered by rational sentient beings, and with it the realisation that it must be true in all possible worlds. The alternative is to subjectivize such principles, which reduces them to social conventions. Meaning whatever reality they possess is contingent - so they cant really and truly exist.
I tend towards objective idealism - that logical and arithmetical fundamentals are real independently of any particular mind, but can only be grasped by an act of rational thought. I believe thats more in line with classical metaphysics.
See Frege on Knowing the Third Realm, Tyler Burge.
Right, what I was describing as a possible position about numbers was meant to sharpen the question: Are we disputing whether abstracta as such can be said to exist, or is the dispute about whether they can exist independently of us? Like you, I find the "existing, but not independently" position re numbers to be unconvincing. Some abstracta probably have that characteristic -- the rules of chess, perhaps? -- but logic and math do not seem arbitrary in that same way. If personal testimony counts, the two mathematicians I have known well are both committed platonists, and speak fervently about the experience of math as one of discovery, not invention. But that's hardly decisive.
Quoting Wayfarer
It's hard to talk about existence without presupposing a certain use of the term. So I'll just point out that you're wanting "exist" to mean "not depend on something else". Or perhaps it's "really and truly exist" that has the characteristic of non-contingency? I'm not making fun; these are perfectly legitimate lines to draw, it's just that there's no agreement about which terms to assign to the resulting map.
Quoting Wayfarer
I like this too. It suggests a useful map, one which shows some existing things as graspable by reason, others by perception (or however you want to characterize what we do with stuff in space/time). We might also want a third location on the map for imaginary things -- maybe this would be a region of non-existence. Now of course someone is going to come along and say, "Yes but what is existence really? You can't just reduce it to a dispute about terminological conventions!" To which the only reply I know is -- all together now! -- "To be is to be the value of a bound variable." In other words, it all depends what you're talking about. But how you talk about it is not arbitrary at all. There really is privileged metaphysical structure; we're just not sure about the terms to use.
Classical logic uses the law of excluded middle but intuitionistic logic doesn't, allowing for sentences that are neither true nor false.
You seem to be suggesting that one of these logics is correct. Which may be so if platonism is correct, but not if it isn't.
If you mean, I believe that there is a truth to logical laws that is not dependent on one or another philosophical doctrine, then yes, I do believe that. I think the law of the excluded middle, for instance, describes something inherent in the structure of realitynot something contingent on whether anyone happens to conceive of it. It is a 'metaphysical primitive,' i.e., something that can't be reduced further.
There's a subtle point at issue herethe ontological status of such principles that are not created by the human mind but can only be grasped by a rational intellect. These principles, while independent of any particular mind, require the rational intellect to apprehend themhighlighting the unique role of reason in discerning universal truths. Whereas in today's culture there is an inherent tendency to try and account for those principles naturalistically, as a result of evolutionary neurology, etc (i.e. 'naturalised epistemology'). But this again relativizes them or makes them contingent facts. Would you agree with that?
That's why I suggested that essay about Frege. I'm no expert in Frege - in fact that essay is about the sum total of my knowledge - but it explores the idea of a 'third realm', somewhat similar to Popper's idea with the same name. Those kinds of ideas are all generally Platonistic.
Maths as an act of collective intent. Of course there are infinitesimals.
Popper's "Third world" differs from Plato's world of forms in that it is entirely an artefact of language and culture and is thus constantly changing. This is in contrast to the changeless world of Plato's forms. Also, for Popper the first world (the world of lifeless physical matter and energy) is real in its own right. The second world (the world of sensations, perceptions and volitions) is the world of pre-linguistic animals. And the third world is the symbolically mediated world of abstracta of concepts and theories.
True. Although there is considerable debate about what 'Plato's world of forms' actually is or means. In any case, the reason I mentioned it, is because Popper grants a kind of irreducibility to those things that constitute the third world.
It would have to be the way collective intent interacts with the world, right?
Of course, "whole math" is not "based" on natural numbers. But they did come first. It was a start, like a path of a thousand miles, one step at a time. Those simple initial steps may culminate with climbing a thousand meter peak. Get a grip, man.
If platonism is correct then I suppose a "correct" logic is one that includes these mind-independent logical facts and doesn't include any logical "fictions".
For example, if the law of excluded middle is a mind-independent fact then classical logic is more correct that intuitionistic logic, and if the law of noncontradiction is a mind-independent fact then classical logic is more correct than dialetheism, and if truth is mind-independently bivalent then classical logic is more correct than fuzzy logic.
But if platonism isn't correct then no logic is "correct". They can be consistent or useful, but nothing more substantial.
Quoting J
I addressed that in the OP with respect to incompatible mathematical entities, e.g. the Quine atom which is a set that contains itself. New Foundations allows for such a thing but ZFC doesn't.
If platonism is correct then either Quine atoms are mind-independent mathematical entities or they're not.
I don't think it makes any sense to say that they platonistically exist in New Foundations but don't platonistically exist in ZFC. We can only take the approach of mathematical fictionalism and say that they exist according to New Foundations but not according to ZFC.
Which logical laws, and why those? There's classical logic, intuitionistic logic, dialetheism, three-valued logic, fuzzy logic, free logic, and so on.
Especially if we look at this from the viewpoint of Platonism, saying that we have these "games" in mathematics, pick what you want and look how the game goes then, doesn't seem in line with Platonism at all. Either infinitesimals exist or they don't. If they exist, there shouldn't be any problem with something else in mathematics. And why aren't infinitesimals accepted and only belong to "nonstandard analysis"? Because we still have the puzzling problem that Newton and Leibniz faced when giving an explanation for something that is and cannot be devised into anything smaller.
I was thinking about things like the Fibonacci sequence. It shows up in a lot of places that have nothing to do with human consensus. There's something about the structure of math that matches up to the structure of the universe in some ways.
@SophistiCat Could you explain the thing about the number 1/137 in physics?
I see where you're going with this. But I don't think that what you're calling the "only approach" is quite so straightforward.
Suppose I say, "x exists according to Harry." You say, "x does not exist according to Sally." What is the subject of the dispute between Harry and Sally? Are they in disagreement about x, or about what 'exists' means?
Tell me how you'd be inclined to answer that, and I'll develop the thought further.
Quoting frank
And the structure of the universe isnt the product of imaginative construction? Wittgenstein would say youre being tricked by your own grammar, that is, by hidden suppositions that project themselves onto the real world and then seem to arise from that outside.
So you're saying that math can be a community construction without necessarily arising from any activity involving the world. It's that what we call the world conforms to thought a la the Tractatus, so it's no surprise that we find an affinity between our math and the world's shenanigans.
Do you believe that we are also products of analysis? That your individuality arises from reflection on events?
The question is ambiguous. Consider these two claims:
1. According to the Lord of the Rings canon, orcs exist
2. According to crazy folk, fairies exist
Mathematical fictionalists are saying something like (1), not (2).
I don't know what Harry and Sally are saying.
What contradiction? The only one I've seen is that "since math is a sui generis human creation that doesn't exist "objectively " then it doesn't exist objectively." Yet this is just assuming the conclusion. At best you've argued for a sort of nescience on this question, but skepticism and agnosticism are not the same thing as rejecting a thesis.
Ok, why can't this involve numbers, which are essential to modern science? Can we infer what biology and evolution tells us about how our sense organs work in some way corresponds to reality, but not that the math that underpins these finding does? Why is that?
Your position seems far more similar to Locke, Hume, Kant, etc. To be sure, Plato acknowledges a distinction between reality and appearances, but he does not suppose that reality is some sort of noumenal "reality as divorced from all appearances." Indeed, his supposition is that threeness, circles, etc. are more real than the world of sensible appearances because they are more intelligible/necessary/what-they-are. This is, in an important sense, the exact opposite of supposing that reality is the world with all appearances (including intelligibility) somehow pumped out of it or abstracted away.
Didn't I just tell you that what I am doing is expressing skepticism, and not making claims about what does and doesn't objectively exist?
Quoting Count Timothy von Icarus
Our sense organs do not show us the whole picture, and the same thing appears to be true for math and science.
They're tools that help us model reality.
Quoting Count Timothy von Icarus
Plato's objective reality is 'the One' - an indivisible, all-encompassing unity.
Ok, that makes more sense. I had thought these were supposed to be good reasons for rejecting platonism, not simply not affirming it.
However, it does seem like you have made "objective knowledge" apply to essentially nothing. Mathematics, the natural sciences, world history, the rules of chess, presumably metaphysics as well, will not qualify. And it seems to me that even the notion of the existence of any reality "behind the veil of appearances" also falls victim to this lack of objectivity. It too might be something that only appears like a real distinction, but perhaps it isn't e.g. Shankara, there is only Brahma, even maya.
There is "logic" as formal systems of the sort you listed, but also logic as "good reasoning" more generally (rhetoric was long part of logic), "logic" as the "rules of thought," the "discourse of the soul," and "logic" as the logos of the world, its intelligibility and rationality. I would assume platonists often are looking to some of the broader conceptions instead of a narrow, formal one.
You're probably right in many cases, but I have seen the systems themselves proposed as platonic objects. So both can be right because both are really just descriptions of a mathematical object. For instance, Tegmark's Mathematical Universe Hypothesis, which is fairly opaque on some of the more philosophical elements, takes a very broad view of mathematical objects.
Tegmark brings to mind another view, ontic structural realism. Things just are the math that fundamentally describes them. This seems to me to be, if not a type of platonism, then something quite close, and it seems not unpopular in the physics community (although certainly not a majority view or anything like that). The question: "which sorts of mathematical objects exist" is various answered as "all of them" or "just the computable ones" (with efforts to try to justify the latter position being, IMO, unconvincing).
Quoting frank
I was thinking of the later Wittgenstein rather than the Tractatus, but yes, math would be a community construction. Its not that the world isnt involved, its just that the world only reaches us through our constructive interactions with it. We are an intrinsic part of the world, and the Real is the effect of a two-way interaction.
I believe my individual authonomy as a subject is a product of my partially shared interactions with others.
Which is essentially platonic, and that's exactly my objection to people using the term 'mathematical platonism'.
I'm not rejecting platonism. I'm pointing out that it's being misappropriated here.
Harry: According to me, propositions exist.
Sally: According to me, propositions do not exist.
Is their dispute about propositions, or about the meaning of 'exist'? For the moment, let's not worry about which way of seeing it is closer to what mathematical fictionists are saying. What answer would you be inclined to give?
I think Plotinus is informative since he brings up this line of reasoning and uses it to reject truth as simple correspondence. If truth is the correspondence of phenomenal awareness to a sort of noumenal being, then one can never know truth because one can never "step outside of experience," in order to compare the two. But Plotinus (and I see him as following Plato here) simply rejects this notion of truth and substitutes what might be called an identity theory.
I find this to be almost the inversion of the modern supposition that we must be skeptical because we cannot "get outside thought." This is why mathematical knowledge, dianoia, occupies the highest portion on the Divided Line below the Forms themselves. Noesis (immediate intuition, apprehension, or mental 'seeing' of principles) is not "stepping outside thought to thoughtless reality" either.
They need to define their terms. There is a fairly controversial, obvious sense in which propositions exist. "Exist as 'abstract objects?'" Then what said is probably something like what is going on. They might even be agreement and just dealing with ambiguity and equivocation.
"Exist mind-independently" is also unhelpful if undefined, and the same goes for "objective." There is an obvious sense in which propositions cannot be mind-independent (we are speaking and thinking of them) and on the common dictionary usage of "objective" they would seem to exist "objectively," yet often "objective" is used to denote something like "noumenal."
So they might be in disagreement about a great many things. The problem with going off the SEP summary sentence ITT is that it does not define its terms. For instance, I would imagine that many Platonists (capital P) would deny that anything has the sort of "mind-independent" existence that some contemporary philosophers would take them to be arguing for. That is, this "mind-independence" would be a bad definition, since for anything to be anything at all it has to have some intelligible eidos, although surely they also do not mean "rocks disappear when no one is looking at them or thinking about them," either.
Right. That's along the lines of what I was saying. Although, that's just a gesture at explaining why math helps us predict events. It's when we take individual cases, like Fibonacci numbers, that we find we haven't explained anything. Yet.
It is because they believed 'mind' (nous, if memory serves me right) emanates from the One, and it is through participation in this quality that we are able to gain an understanding of matters that goes beyond sense perception. The quality must exist as some form of emanation from the One for us to be able to participate in it.
Plato and certainly Neoplatonists like Plotinus were quite mystical in their beliefs, where they believed experiences of higher realities were possible, but exceedingly difficult to describe because they encompassed qualities that preceded nous or the intellect, and were, literally, unintelligible.
In a nutshell, 'mathematical platonism' would suggest people have experienced these higher realities and found mathematics to be existing within them.
There was a famous confrontation between Wittgenstein and Godel that has been interpreted in different ways. The way I see it, Wittgenstein honed in on the idea that something like an incompleteness theorem could be proved. What is it we are doing when we prove that sort of theorem, or for that matter, any theorem, as true?One thing that we dont think we are doing is changing the subject. That is, we think of mathematical proof as a paradigmatic example of rational thought, which allows us to link premises with outcomes in reliable ways. The source of this reliability is the assumed persistence of meaning of the premises. We depend on the working parts of logical calculation retaining their identity over the course of the calculation.
But what we dont assume is that when working through something like a mathematical or logical proof, we surreptitiously import new assumptions, changing in a very subtle manner the stakes and the sense of our task as we move through its. steps. The production of Fibonacci numbers is one example of what happens when we do different things with numbers, like create rational out of real numbers. All sorts of new surprises ensue. Not because such things are built into number itself, but because we are changing the subject in a subtle way, importing new concepts into our use of numbers. It is what we are constructing and importing that confronts us with unexplainable riddles, because , believing that each new wrinkle belongs to the same system as the old, we are trying to derive our new invention from a previous one. This is what we hope to do when we talk about explaining Fibonacci numbers.
Here is a passage about Augustine which details the Platonist insights that inspired his religious conversion.
Quoting Cambridge Companion to Augustine
How do you apply that to these examples of the Fibonacci sequence?
Bolds added. It is in accordance with my intuitive understanding.
Not sure why the question is addressed to me - did I write something about this before? Anyway, this is more of a counterexample to the point being made (if we consider something like Fibonacci numbers as a paradigmatic supporting example). In the Standard Model of particle physics, there is a fundamental constant known as the fine structure constant. The interesting thing about it is that it is dimensionless, i.e., it is a number that does not depend on units of measurement - nor on anything else for that matter. (Avogadro number is also dimensionless, but unlike the fine structure constant, it depends on some arbitrarily chosen dimensional parameters, such as volume, temperature and pressure.) What was even more intriguing back when that constant was proposed was that, within the accuracy of early measurements, the number looked simple without being trivial: not 1 or 2 or some multiple of pi or e, but as close as permitted by early measurements to the ratio 1/137 (Avogadro number is ~6.023x10[sup]23[/sup]). For that reason, physicists puzzled over the possible significance of that ratio. This led to some unfortunate numerology - long since abandoned - that grew ever more convoluted as later, more accurate measurements no longer quite fit that initial 1/137 estimate.
Such speculation may look silly in retrospect, but it should be understood within its historical context. Physicists, probably more than anyone else in science, are obsessed with simplicity, unification and "naturalness," and not without reason, because this attitude has accompanied spectacular advances in physics over the past two centuries. But how philosophically justified is it? And how sustainable? I suppose that goes to the question of the proverbial "unreasonable effectiveness of mathematics."
Count T's answer -- that Harry and Sally need to define their terms -- is the direction in which I was going. With all respect to Michael, we have no way of knowing whether H & S are disputing platonism until we get an answer to the question I posed. I was hoping to develop this thought in a dialogic fashion, but I'll go ahead and just say what I mean.
Two accounts of the Harry/Sally dispute are possible.
In the first, H & S share a common understanding of how they're going to use the term 'exist'. Either they live in a cultural community in which this is taken for granted, or -- better, for our purposes -- they have a preliminary conversation in which they discover that they do indeed mean the same thing by 'exist'. So if they're having a dispute, as we imagine them doing, it must be over what a proposition is. They're in full agreement about what it means for something to exist, but they differ about what sort of thing a proposition is -- what its characteristics and qualities are. Thus, Harry, using his ideas about propositions, makes the case that they exist; Sally, using hers, that they don't.
In the second, the reverse is the case. H & S share a common understanding of what a proposition is -- again, we can picture them determining this beforehand. So if a dispute is occurring, it must be over what it means for something to exist. They're in full agreement about the "characteristics and qualities" of a proposition -- how to use the word, how to recognize one, what functions it serves -- but they differ about whether existence can be ascribed to that sort of thing.
(Yes, this little story is about the existential quantifier, ?, and quantifier variance, but I'm trying to avoid Logicalese so as to keep it accessible.)
So what does this have to do with platonism, and in particular with the idea that only one type of quantification could be countenanced in a world of mathematical platonism?
Let's look again at Michael's suggestion that, depending upon which version of logic/math you're using, certain items would either exist or not exist:
Quoting Michael
Now apply the "Harry and Sally question": Is the mathematical fictionalist saying that New Foundations and ZFC share the same meaning for 'exist' but differ about whether the items in question qualify? That, I think, is Michael's meaning. But we can now see that it's equally possible for the mathematical fictionalist to claim that New Foundations and ZFC differ about what 'exists' means. They may share the same understanding of, say, what a Quine atom is, but because they don't agree about existence, their conclusions are different.
To simplify, we can either hold X steady and differ about existence, or we can hold 'existence' steady and differ about X.
So what I'm saying is that one version of mathematical platonism will indeed have room for only one correct logic, because it will be a logic that debars certain entities from existing at all. Those other, renegade logics would have to be "man-made." But another, equally reasonable version of math platonism will be liberal or agnostic about different uses of 'exist', so that both New Foundations and ZFC, e.g., may be "found" in the platonic world.
This all circles back to my question about how correctness has a bearing on the plausibility of mathematical platonism -- whether math platonism requires a single correct logic for it to be plausible. It seems that two incompatible logics could both be found as objects of mathematical platonism. For:
Quoting Michael
but if my argument is sound, then it does make sense after all. That's because now we're no longer fooled by seeing the word 'exist' occurring twice and believing it must mean the same thing each time. It may or it may not. But if the use of 'exist' itself is not consistent, then anything goes, platonically. We can't put a fence around it by using an operator like "according to Y" or "to Z" because we don't know Y and Z's account of existence. Either, or both, of them may be claiming that its own version is compatible with quantifier variance.
Of course there is.
Subject of a book by Sabine Hossenfelder, Lost in Math.
(Although from my perspective, embracing reality 'as it is' will entail abandoning the axiom that it is only physical.)
No, it's that you're a reliable source for information about physics.
Quoting SophistiCat
Oh. So it's not really significant? Good to know. :grin: Thank you!
Mathemarical concepts for Husserl are no more real than the spatial objects we interact with in the world. That is to say, their reality is the result of an abstractive idealization on the part of the subject, drawing from encounters with concrete data but imposing on those contents an idealized form. Derrida explains:
And no less.
Rather like objects as permanent possibilities of sensation but here the objects are noumenal.
Quoting Wayfarer
It doesn't sound like your view. since you are always arguing that reality is entirely constructed by consciousness, and that it is meaningless to speak of concrete things having an independent existence. It is clearly stated in this article that they do have an independent existence, and I think the implication there is that the non-arbitrary way in which consciousness models objects is the best evidence we have for their independent existence.
I never have used that expression nor would I put it like that //although on reflection I suppose it is fair//.
What I do say is that material objects are perceived by the senses and so cant be truly mind-independent, because sense data must be interpreted by the mind for any object to be cognised. What interests me about the passage I quoted, is that mathematical functions and the like are not the product of your or my mind, but can only be grasped by a mind. Thats the sense in which theyre what Augustine describes as intelligible objects in the earlier post about that.
The underlying argument is very simple - it is that number is real but not materially existent. And reason Platonism is so strongly resisted is because it is incompatible with [s]materialism[/s] naturalism on those grounds, as per the passage from the Smithsonian article upthread, What is Math?: 'The idea of something existing outside of space and time makes empiricists nervous.'
What might be some examples of the concrete contents or data? Is the implication that there is some level of sense impression which is not mediated by ideas or "abstractive idealization"? This connects with the thread awhile back about scheme/content distinctions, especially this:
Quoting J
So the question I'm posing is whether the "concrete data" are pre-theoretical, which Wang thinks is not possible. Personally, I think it is possible, but I'm wondering how you think Husserl understood this in relation to numbers.
Right, if we focus heavily on the ontology of abstract objects, we overlook the accompanying problem: what's the basis of our confidence in the other two categories: mental and concrete? It's all myth building.
Quoting J
I believe Husserl argues that all perception is conceptually driven. What appears as concrete data of experience are themselves given relative to modes of givenness constituted by a subject.
Husserl's answer seems be that there is no such essence, and each "thing" is indeed always underway (a nice phrase) as a phenomenon to/for our consciousness. I'm wondering, though, whether trying to invoke an essence somewhat prejudices the discussion. My question concerning numbers, for instance, wasn't about whether there was some "essence" of number that is pre-theoretical for us. The question was much more ordinary: What are the concrete contents or data of which Husserl speaks, that allow us to form our idealization of numbers? Can you give an example of how this might work?
Maybe like this? This is probably what a Babylonian (500 BC) abacus looked like. This is where the number zero entered into the human intellectual scene. It was when a merchant would draw a diagram of a certain abacus result that he or she would need a symbol for the blank spots. Zero was born as a symbol: an attempt to stop that which underway and record it for future reference. Phenomenologically, it's like when we say we were arrested by the beauty of the sky. Stopping, exiting time, inhabiting an inner sanctum.
Different people may mean different things by "exist" but I don't think different people mean different things by "mathematical platonism", else there wouldn't be much sense in discussing which of platonism, formalism, intuitionism, fictionalism, nominalism, etc. are correct.
My claim is that it doesn't make sense to argue that both of these are true:
1. Quine atoms exist in the platonistic sense
2. Quine atoms don't exist in the platonistic sense
One of them is true and one of them is false. However, regardless of which of (1) and (2) is true, both of these are true:
3. Quine atoms exist according to New Foundations
4. Quine atoms don't exist according to ZFC
And notice the difference between saying that Quine atoms exist according to New Foundations and saying that New Foundations is correct to claim that Quine atoms exist.
Mathematical fictionalists claim that (1) is false and that (2), (3), and (4) are true.
Perhaps a more helpful phrasing of (3) and (4) is this:
3. There is a set that contains only itself according to New Foundations
4. There is not a set that contains only itself according to ZFC
Is it likewise not sensible to argue that both of these are true?:
1. Sherlock Holmes exists.
2. Sherlock Holmes doesn't exist.
There is more than one way to construe 'exist' here, as I'm sure you'd agree. 1 & 2 can't both be true with the same construal, but that doesn't mean there is no genuine argument about it.
What you're wanting to say is that there is only one way to construe 'exist in the platonistic sense'. As evidence for this, you cite the ongoing disagreements among platonists, nominalists, etc -- they wouldn't make sense, or be to the purpose, without consensus on 'exists'. Indeed! -- and that may be the very problem. What I've tried to argue is that there is another way to understand what these disagreements are about, and why they are so intractable. It may be down to these different construals of 'exist platonically'.
In short, it isn't obvious that mathematical platonism necessitates a commitment to only one construal (one use of ?) of what it means to exist.
From here, "[p]latonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices."
I'm not sure how this can be further distinguished. Either some set is a mind-independent abstract object or it's not.
Heres my long-winded attempt at a Husserlian explanation of the subjective constitution of number:
In Philosophy of Arithmetic(1891), Husserl described a method for understanding the constitution of a multiplicity or plurality composed of independent parts, which he dubbed collective combination'. According to Husserl, the basis of any sort of whole of independently apprehended parts(a whole in the pregnant sense) is the collective combination, which is an abstracting act of consciousness uniting parts.
Collective combination plays a highly significant role in our mental life as a whole. Every complex phenomenon which presupposes parts that are separately and specifically noticed, every higher mental and emotional activity, requires, in order to be able to arise at all, collective combinations of partial phenomena. There could never even be a representation of one of the more simple relations (e.g., identity, similarity, etc.) if a unitary interest and, simultaneously with it, an act of noticing did not pick out the terms of the relation and hold them together as unified. This 'psychical' relation is, thus, an indispensable psychological precondition of every relation and combination whatsoever.
In any such whole the parts are united in a specific manner. Fundamental to the genesis of almost all totalities is that its parts initially appear as a temporal succession.
Succession in time constitutes an insuppressible psychological precondition for the formation of by far the most number concepts and concrete multiplicities - and practically all of the more complicated concepts in general.Almost all representations of multiplicities - and, in any case, all representations of numbers - are results of processes, are wholes originated gradually out of their elements. Insofar as this is so, each element bears in itself a different temporal determination.Temporal succession forms the only common element in all cases of multiplicity, which therefore must constitute the foundation for the abstraction of that concept.
The first step of constitution of a multiplicity is the awareness of the temporal succession of parts, each of which we are made aware of as elements separately and specifically noticed. In the case of numbers, one must abstract away everything else about those elements (color, size, texture) other than that they have been individually noticed as an empty unit. The concept of number is only possible once we invent the idea of identical sameness over time ( same thing, different time). This concept is not derived from the concrete data of experience (i.e. real apples as their appearance is given to us via continually changing perspectives). Rather, it is a concept we impose upon a world in continual flux. It was necessary to invent the concept of identity, and its pure repetition, in order to have the notion of the numeric unit.
The collective combination itself only emerges from a secondary act of consciousness. This higher order constituting sense changes what was originally a temporal succession into a simultaneity by bringing' back the previous parts via reflecting on them in memory. Husserl says that a combination of objects is similar to the continuity of a tone. In both cases, a temporal succession is perceived through reflection as a simultaneity.
For the apprehension of each one of the colligated contents there is required a distinct psychical act. Grasping them together then requires a new act, which obviously includes those distinct acts, and thus forms a psychical act of second order. It is essential that the partial representations united in the representation of the multiplicity or number be present in our consciousness simultaneously [in an act of reflection].
The constitution of an abstract multiplicity is analogous to the creation of any whole, even though the former involves a peculiarly external form of unification in comparison to combinations unified by similarity or continuity.
A key feature of the fact that a totality is a product of a temporally unfolding series of sense acts is that prior elements of the originally apprehended series have already changed by the time we move on to the succeeding elements of that series. In forming the representation of the totality we do not attend to the fact that changes in the contents occur as the colligation progresses. The secondary sense-forming act of the uniting of the pasts into the whole is not, then, faithful' to the original meaning of the parts it colligates, in that they have already changed their original sense via the passage of time at the point where we perform the uniting act of multiplicity. Rather than a being faithful, the sense of the unification act may better be described as a moving beyond the original sense-constituting acts forming the apprehension of the parts. In forming a new dimension of sense from retentional and protentional consciousness, the unifying act of totalization idealizes the parts that it unifies. In addition to the abstractive concept of groupness (collective combination), many kinds of more intimate idealizations are constituted as wholes out of original temporal successions. We can see this clearly in the case of the real object, an ideal totality formed out of a continuous synthetic flow of adumbrations in which what is actually experienced in the present is not the faithful', that is, actual presencing of temporally simultaneous elements but a simultaneity of retentional series, present sense and protentional anticipations.
In a way, the number 5 implies all other numbers, because its meaning is rooted in its place in a sequence. And every thing is like that.
Yes indeed.
Hmmm.
All other natural numbers? Integers? Rationals? Reals? Complex numbers?
I think the answer is:
Quoting frank
But Josh is the one who's actually read Husserl. Take it up with him probably.
"There are abstract mathematical objects whose existence is independent of us" etc.
You simply ask, "What do you mean by 'existence'?" There is no one obvious reply. What are we supposed to say? -- "You know, exist, be. The opposite of not-exist. Case closed." Hopeless, and to make it worse, this so-called definition acts as if it is settling the matter, just by using the word and expecting readers to import their own concept of 'existence'. It looks like it is defining a certain kind of existence -- platonic existence -- but that's not possible without first knowing how existence itself is being construed.
Honestly, this isn't meant to be merely verbal gymnastics. I'm trying to demonstrate what I think is an important and all-pervasive issue, namely that there is no such thing as a sentence using 'exist' which can settle the question within the sentence itself of what 'exist' means. Again, this could be written using quantificational language, but I think it comes up often enough in ordinary discourse. A discussion of platonism is a great example. I'll leave Harry and Sally alone and just say: One person thinks there are abstracta which exist independently of us; another person says there are not. Why should we think they are both working with the same concept of what it means to exist? Indeed, if they were, wouldn't the issue be quickly resolved? The SEP talks about abstracta "whose existence is independent of us." Very well; what does SEP mean by 'existence'? Does it refer to a dimensional embodiment? being the subject of a proposition? being rationally apprehendable? being thinkable? being the value of a bound variable? something non-contingent? etc. etc. Thus the definition of mathematical platonism has told us absolutely nothing about what it means to exist. It cannot, formally.
Right you're saying the cognition of the objects is mind-dependent, and I have no argument with that since it is true by definition. But it doesn't seem to follow that the objects cognized are mind-dependent.
Quoting Wayfarer
Again I have no argument because it is only minds (and in a different sense hands and other implements) that grasp. It seems undeniable that a differentiated and diverse world is given to the senses, and that we experience that world in ways that are unique to the human, just as other animals presumably experience the world in ways unique to them. So, it seems to me that we are presented with number, that is numbers of things, and we abstract from that experience to conceptualize numbers.
Quoting Wayfarer
This is where I disagree; for me number is real and materially instantiated in the diversity of forms given to our perceptions. I don't "resist" platonsim, I simply don't find it plausible. It seems to me you try to dismiss disagreement with platonism by psychologizing it, by assuming it somehow frightens those who don't hold with it.
I think that is to greatly underestimate the intelligence and intellectual honesty of those you disagree with. I could do a similar thing by saying that people believe in platonism because they are afraid to admit and face the fact that this life is all there is. But I don't say that because I respect different opinions, and because dismissing arguments and worldviews on psychological grounds is shallow thinking. I don't claim that all platonists are stupid or afraid.
I think my question gets addressed in this passage:
Quoting Joshs
This helps me imagine the process Husserl is speaking of, but I'm still left wondering what counts as a "part" or "element" (and these would presumably also be the "concrete contents" mentioned earlier). It is from these parts or elements that we must first abstract away qualities like color, size, and texture, and then engage the remainder -- the empty "unit" -- in the multiplicity-constituting process.
So . . . can this process take place with any physical series? Would Husserl countenance using an apple, say, as the starting part or element? Does it matter where we start? I think the answer is, "Sure, anything at all will do, as long as its perception counts as a 'sense act'," but I want to get your take on it.
Quoting J
Im not criticizing individuals but ideas. In this case, empiricist philosophy which cant admit the reality of number because of it being outside time and space. If you take that as any kind of ad hom, its on you.
Quoting Wayfarer
You said "Makes empiricists nervous". Empiricist philosophy can consistently admit the reality of number as instantiated in the things we encounter every day. You know, for example, like ten fingers and ten toes...
The key difference between Frege and Popper here is, as both @Banno and @Janus allude to, whether the 3rd realm exists independently of human thought, or is created by our thought. If Burge is right, then there's no doubt what Frege believed: complete independence. Popper stakes out a middle ground. In Objective Knowledge, Popper says:
And in fact, he chooses natural numbers as his example for how this works:
This is odd (sorry!) at first, but Popper goes on to explain that there are "facts to discover" about our human 3rd-world products. I think his use of "unintended" is key to understanding what he means. Just because I have created or invented something, it doesn't mean that in the act of doing so, I find myself in complete command, or complete awareness, of every single fact about my creation. And this does seem plausible with regard to numbers. If the number series is indeed invented, pace Frege, it's easy enough to imagine that early users would then discover that certain numbers -- invented merely for counting purposes -- had the quality of being either odd or even. This was never intended, but is certainly a fact for all that. Same with multiples, and primes, and on and on.
It's even more intuitively clear with regard to products we tend to agree are human creations. When I write a piece of music, I am very far from "intending" everything the music contains. In the process of (hopefully) improving what I write, I absolutely do discover things that are really there, but that I was not aware of when I wrote the music. Often enough, the discoveries are unpleasant, and I have to revise accordingly. But sometimes I find connections or implications that are fruitful and aesthetically interesting; they feel like genuine, "autonomous" facts about the music. Yes, I created the whole thing, but no, that doesn't mean I understand it completely. Only God, one supposes, creates in that fashion.
So anyway, Popper demonstrates that we can believe in all sorts of abstracta without needing to be platonist about it, and also without giving up the sense of discovery that goes along with exploring the 3rd realm.
If anyone is spending their holiday on TPF, poor devils, then Merry Christmas!
Yes.
But we can go further than Popper. This, and this, and that, all count as one of something. These, and those, as two. That's an intentional act on our part, which is not only concerned with the things in the world but also concerned with ways of talking about those things. We bring one and two into existence, by and intentional act - it's something we do. Some important aspects of this. First, its we who bring this about, collectively; this is not a private act nor something that is just going on in the mind of one individual. Hence there are right and wrong ways to count. Next, the existence had here is that of being the subject of a quantification, as in "Two is an even number". Notice that this is a second-order quantification: Supose we say that there are two marbles and two flowers. We have not thereby created a third thing within the domain of discourse. We still only have two marbles and two flowers. When we say that two is an even number, we are still talking about marbles and flowers.
Quoting Michael
Infinitesimals exist. They are a higher-order quantification that can itself be quantified. Adding "in the Platonic sense" serves only to confuse what is going on.
This s what I tried to explain here:
Quoting Banno
A note on logic. Natural languages are free to range over any topic and to say all sorts of strange things. Logic allows us to tie down what we can say with some level of consistency and coherence. The relation between higher-order logics described here sets out a way of talking about concepts without giving them some mystical "platonicistic sense". That's why the logic is useful, as a guide to language use, not as a replacement for natural languages.
Plato's approach was too muddled to be useful. Higher-order logic and intentionality provide a much clearer picture without the mysticism. It explains how such things as numbers can be said to exist when they are clearly not like chairs and rocks. It explains why mathematicians feel like they are 'discovering' things - they are. It gives precision to Quoting Tzeentch
This is a good question. What the Fibonacci sequence gives us is a way of talking about the things you picture. It doesn't provide an explanation of why the shell follows that sequence. But it's not hard to find one.
All the snail does is to add calcium to the edge of it's shell. Each new shell chamber it grows is built on the previous two shell chambers. If we say the first is size one, then the second is grown on that, and is also size one. The third will be grown on those last two, and so be size two. The fourth is grown on the previous two, and so is size three.... 1,1,2,3,5... and so on.
Think of these as cross-sections of each chamber.
Snails do not have access to a platonic reality. It's not some mystical or divine intervention, but a simple result of a snail adding calcium to the edge of it's shell.
But we have a language that can talk about this growth.
Edt: Here's more than you ever needed to know about mollusc shells:
Compare:
[quote=Tyler Burge]Frege believed that number is real in the sense that it is quite independent of thought: 'thought content exists independently of thinking "in the same way", he says "that a pencil exists independently of grasping it. Thought contents are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." ' Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: they "are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth."[/quote]
Quoting Cambridge Companion to Augustine
Plainly Augustine has theological commitments that Frege lacks, but nevertheless the Platonist elements they have in common are significant. Augustine adds that reason is: a kind of head or eye of our soul ... which does not belong to the nature of animals (lib. arb. 2.6.13).11", clearly a reference to the tripartite soul of Plato, in which reason is a governing faculty, responsible for wisdom and seeking truth. Frege's notion that logical laws are "boundary stones set in an eternal foundation" parallels Plato's Forms and Augustine's intelligible objects as timeless, immutable realities. They are not dependent on human minds, cultures, or contingent physical realities but are 'discernable by reason', where 'reason' represents the faculty that is capable of grasping incorporeal truths.
Quoting Banno
Hence, these MUST be understood as constructions, hence contingent facts, our own creations, in fact, not immutable truths, which still retain a theological undertone that does not sit well with our secular age. Thomas Nagel quotes C S Peirce:
[quote=Evolutionary Naturalism and the Fear of Religion;https://drive.google.com/file/d/1z_IqIxLEwAaRi2ztoP3PIF_6lCSfqm-X/view]The only end of science, as such, is to learn the lesson that the universe has to teach it. In Induction it simply surrenders itself to the force of facts. But it finds . . . that this is not enough. It is driven in desperation to call upon its inward sympathy with nature, its instinct for aid, just as we find Galileo at the dawn of modern science making his appeal to il lume naturale. . . . The value of Facts to it, lies only in this, that they belong to Nature; and nature is something great, and beautiful, and sacred, and eternal, and real - the object of its worship and its aspiration.
The soul's deeper parts can only be reached through its surface. In this way the eternal forms, that mathematics and philosophy and the other sciences make us acquainted with will, by slow percolation, gradually reach the very core of one's being, and will come to influence our lives; and this they will do, not because they involve truths of merely vital importance, but because they [are] ideal and eternal verities.[/quote]
This is part of the preamble in which Nagel then describes the 'fear of religion' as one of the main motivations for the rejection of Platonism and the adoption of evolutionary naturalism:
That's the cultural dynamic that I think is behind the rejection of platonism in mathematics and the subsequent relativisation of reason.
Quoting J
Beats crossword puzzles! And, same to you. :party:
Rather, these CAN be understood as constructs. If you feel you need to include, in addition, a god or a platonic realm or whatever, then that's your choice.
What do you think that might comprise? An ethereal palace, replete with ideal dogs and cats?
I say that 'forms' are much more like 'intelligible principles' than what they are often confused for, which is a kind of ethereal shape. I think much of the dismissal of them is based on centuries of poor schoolroom teaching by those who really hadn't grasped that fact. But there are contemporary sources, such as Rebecca Goldstein's Plato at the Googleplex, and Iris Murdoch's Sovereignty of the Good, which provide a much more nuanced account of their continuing relevance.
It's not a novel account I believe.
I'm not overly interested in defences of Plato or Thomisim, or even Popper or Searle. Thier value is in what they help us understand.
Quoting Banno
Sure. I agree. Josh and I were talking about "constructive interaction" with the environment and how that might be the genesis of universals like numbers. He said:
Quoting Joshs
That led to a little discussion of how that actually works in individual cases. We didn't get very far tho.
Quoting Banno
I agree with the emphasis on the collective creation of counting (if the non-Fregean story is correct). I'm not sure I'd go so far as to say that intersubjective agreement results in the idea of "being right about counting." One can imagine mistakes in math that are widely accepted, but then corrected by reference to some Popperian discovery in the 3rd world. Wouldn't we say that it was that discovery that now made us "right," rather than the fact that everyone now agrees? After all, we agreed before, too.
Quoting Banno
Extremely important. @Michael and I are having a related conversation about what role "existence" plays in descriptions of platonism, and it hinges on a similar point. In the case you describe later in your post, the moral of the story would be: "P" is brought into existence depending upon an interpretation of (ideal logical) language; there are no facts in the world that change as a result of that interpretation. If -- as I do -- I lean toward the quantificational interpretation that allows P to be a "new thing," and if you dispute it, we aren't offering arguments pro and con about the object of the concept "to exist". We are specifying that very concept, rather than assuming it, in our differing interpretations. Or so it seems to me. And I think it's the gist of your comment here:
Quoting Banno
I'm not a best-friend of formalism, but this is the kind of case where formal models really excel.
Which leads to the passages from Peirce and Nagel. History of philosophy isn't my forte, and I defer to Nagel on this, though it does seem a little oversimplified? I suppose there is a generalized "fear of religion," especially in analytic phil., but anti-Platonists seem to be offering genuine justifications for their position, that have to be taken seriously in their own right. And though my own sympathies are with religious modes of life, I don't doubt for a minute that one can be an anti-Platonist and a non-believer without also subscribing to what you're calling "the relativization of reason." Nagel himself is a good example. So is Habermas. And really, so is (most of) analytic phil., which questions various points concerning reason but rarely abandons it to relativism; the questioning is itself usually done using entirely standard assumptions about reason and its grounding.
Which is maybe just to say that evolutionary explanations aren't the only game in town, if one is dubious about platonism.
Not at all. History of ideas is very much my interest - more so that what is taught as philosophy nowadays - and I see the issue in terms of the cultural dialectics sorrounding philosophy, religion and science. The major point I take from it, aside from the often-quoted passage about the fear of religion, which really is a major underlying factor in my view, the bulk of the essay is a defense of reason against attempts to explain it as a product of evolution. The main argument being, to say that it is, is to undermine the sovereignty of reason:
[quote=Thomas Nagel op cit]The only form that genuine reasoning can take consists in seeing the validity of the arguments, in virtue of what they say. As soon as one tries to step outside of such thoughts, one loses contact with their true content. And one cannot be outside and inside them at the same time: If one thinks in logic, one cannot simultaneously regard those thoughts as mere psychological dispositions, however caused or however biologically grounded. If one decides that some of one's psychological dispositions are, as a contingent matter of fact, reliable methods of reaching the truth (as one may with perception, for example), then in doing so one must rely on other thoughts that one actually thinks, without regarding them as mere dispositions. One cannot embed all one's reasoning in a psychological theory, including the reasonings that have led to that psychological theory. The epistemological buck must stop somewhere. By this I mean not that there must be some premises that are forever unrevisable but, rather, that in any process of reasoning or argument there must be some thoughts that one simply thinks from the inside--rather than thinking of them as biologically programmed dispositions.[/quote]
Whereas I'm pretty confident the majority opinion is that reason can only be understood in terms of evolutionary development, because what else is there?
There's also been discussion of another book from time to time, The Eclipse of Reason, Max Horkheimer, which makes the case that the sovereignty of reason as understood in classical philosophy has been progressively subsumed by instrumentalism and pragamatism - the utilitarian ends to which reason can be directed. In fact the whole conception of reason changed with the scientific revolution (per Alexander Koyré). It is no longer understood as a cosmic animating principle, but as a human invention (numbers are invented not discovered). That's what I mean by the relativising of reason (reference).
So - they're the themes I'm exploring. But I agree that it is a different to the subject matter to philosophy per se.
Links of interest:
Does Reason Know what it is Missing? - on Habermas' dialogue with Catholicism.
Join the Ur-Platonist Alliance! - Edward Feser on Lloyd Gerson
I don't entirely agree with this. The characteristics of the natural numbersoddness, evenness, divisibility and primenessare clearly shown in the ways groups of actual things can be divided up. I do agree, though, that once these characteristics are formulated as rules then the characteristics of extremely large numbersnumbers too large to be worked with by arranging actual objects in order to discover such characteristicsfollow logically.
Mathematical platonism originated with Frege. He lived at a point when a scientific outlook was coming to dominate the intellectual scene, but panpsychism and the idea of a world-mind mixed easily with mechanistic thinking at that point. There was no conflict until the 20th Century when eliminatism became fashionable.
It's not as if we must choose and stick to only the quantificational interpretation, or alternately we must only ever use the substitutional interpretation. Which we use depends on what we are doing, on the task in hand.
Quoting J
A misleading phrase, since it implies a background of subjectivity prior to, say, counting; the incoherence of the solipsistic homunculus talking to other homunculi. What is salient is that arithmetic is an interaction between people, and this is so even if one occasionally counts to oneself.
A pity then that did not address the argument of my post directly, but instead could only see it as reactionary 'fear of religion'. But yes, it is circular to reason that evolution is needed in order to explain reason. The relevance of that remains obtuse.
We can take Quine's joke seriously: to be is to be the subject of some quantification; and us that to reply to the OP.
That is a common thread throughout practically all pre-modern philosophy.
Oh, I think he meant it! But more to follow.
This isn't true. It's unfortunate that this wasn't made clear at the outset.. Mathematical platonism, otherwise known as realism, is just the view that mathematical objects are neither mental nor physical. We call them abstract objects. That's it. There's no accompanying doctrine.
Sure. And Nagel is one of my favorites. I was raising a brow at the idea that fear of religion, specifically, accounts for the current interest in naturalized Explanations of Everything. The passage you cited -- and just about all of The Last Word -- articulates a position that I think is broadly correct, but you can hold it and still be an atheist to the core. Likewise, you can find it unconvincing on the merits, not because you're afraid you'll "cross the Tiber" (as they used to say) if you start believing that reason provides a privileged access to the world.
And yes, the Habermas discussion is very interesting. He's still alive, you know -- we could ask him what he thinks now (at 95!).
Quoting Sartwell, The post-linguistic turn
The theme, one that may be becoming prevalent, is that post modernism has noticed that not just any narrative will do. Global warming does not care what narrative you adopt, and relativism works for oligarchs as well as anarchists. The truth doesn't care what you believe. That's for @Joshs.
Well, Nagel says he is. But he's philosophically open to a somewhat religious perspective, the idea expressed in Mind and Cosmos of rational sentient beings as the universe coming to self-awareness. That is a theme that animates many kind-of religious philosophies, like Hermeticism. Besides, I think the missing dimension is not the idea of God, but to the entire category of the sacred.
I did register that Habermas was still with us. He has a massive corpus which again I've barely touched, but I came across his dialogue with then Cardinal Ratzinger. Whilst I am not Catholic, and find much that is disagreeable about that institution, Catholicism is still arguably one of the conduits through which a form of the philosophia perennis has been preserved and transmitted. In my recent (2022) trip to Florence, I was impressed by the frescos showing Aquinas laying down the lore to the assembled gathering of philosophers.
Spanish Chapel of the Church of Santa Maria Novella, Florence.
However it presents an obvious ontological question. As SEP puts it, and as I'm sure I've previously quoted:
God explains everything, and so might be introduced into any topic. But of course in explaining everything he explains nothing.
And of course Wayf is entitled to introduce god, just as others are entitled to point out that he is not necessary.
:grin: The number of experts in phil of math is tiny. You have to be an expert in two fields. Maybe one day such a person will pass our way! That would be cool.
Quoting Sartwell, The post-linguistic turn
You can sense the parodic aspect of the Quinean formula, but I always took him to be saying, essentially, "There is no way to usefully define 'existence' such that all customers will be satisfied, so let's just limit existence-talk to what we do with quantification." And I don't think the resulting ontological "theory" says that existence is dependent on language -- it's dependent on a certain understanding of logical thought, which we're free to maintain is independent of language if we want to. See Frege the platonist.
A very shallow analysis, Banno, although easy to stereotype, which is what you're doing. There's an excellent book mentioned by me and others from time to time, The Theological Origins of Modernity, Michael Allen Gillespie, 2009, which I read when first joining forums, and which gives the deep background to these disputes.
[quote=Reader Review;https://www.goodreads.com/book/show/16896236-the-theological-origins-of-modernity] the apparent rejection or disappearance of religion and theology in fact conceals the continuing relevance of theological issues and commitments for the modern age. Viewed from this perspective, the process of secularization or disenchantment that has come to be seen as identical with modernity was in fact something different than it seemed, not the crushing victory of reason over infamy, to use Voltaires famous term, not the long drawn out death of God that Nietzsche proclaimed, and not the evermore distant withdrawal of the deus absconditus Heidegger points to, but the gradual transference of divine attributes to human beings (an infinite human will), the natural world (universal mechanical causality), social forces (the general will, the hidden hand), and history (the idea of progress, dialectical development, the cunning of reason). [/quote]
A background which is transparently clear in many of your comments.
@Count Timothy von Icarus already referred to the Analogy of the Divided Line upthread, in that, there is an hierarchical ontology, meaning different levels of being or existence. Which has what has been 'flattened out' by modern ontology, and why the ontology of abstract objects is so difficult to account for.
:grin: If you like. You insist on telling us, at great length, about the ineffable. Fair enough. I'll continue to point out that you haven't, thereby, said anything.
He wasn't there again today. Oh, how I wish he'd go away.
Lots to be said about Nagel and religion. Is he really open to religious belief? We know that he doesn't want religion to be true, and that he's provoked (in a good way) by the fact that so many philosophers he respects are deists of one stripe or another. Your distinction between belief in God and belief in a sacred dimension may be relevant here.
I've read a bunch of Habermas but as you say, there's a mega-bunch to read! You'd probably like Between Naturalism and Religion (2008), which addresses a lot of our topics here. His concept of a "detranscendentalized use of reason" is a real contribution. He is absolutely unwilling to give up the Nagelian position that reason is the "last word," and equally unwilling to accept the traditional foundationalist explanations for why this is so. In addition, several of the essays in the book are extremely sympathetic discussions of the role of religious belief -- and religious adherents -- in secular, liberal society.
I bet, looks right up my street, thanks for it.
Quoting J
I sometimes wonder if he's being dragged kicking and screaming......
Quoting Banno
Fine! I have realised the link between Terrence Deacon's absentials and the via negativa. Anyway, as you say, enough for today, thanks all for the comments :pray:
Well, here we are again. That is absolutely one way to employ the terms "being" and "existence," a way with a distinguished history. If you were willing to say that the hierarchical organization may be an actual metaphysical structure but not necessarily described by the terms you've used (being, existence, ontology), I would be inclined to accept that. The map is not the labels.
Quoting J
Yep. And to this I would add that the relation between what exists and what we do is worth considering. Language is one of the things we do. Didn't Habermas reflect on this in his use of unavoidability and irreducibility? That it is action that has import?
:wink: My objections just show that you are right.
Quoting Banno
Given your emphasis on language as use, I want to point out the implication of truth not caring about what one believes, desires, feels or cares about. That is , a notion of truth as pristinely separate from issues of affect, value, power and purpose, as though those factors were at best peripheral to, and at worst repressive of attainment of truth. Pragmatism and hermeneutics, which treat truth as a function of discursive practices, know better than that.
Mathematical platonists distinguish themselves from non-platonists like nominalists. Each group seems to understand what the other means, hence their disagreement. I'm asking if infinitesimals exist in the sense that would satisfy mathematical platonism.
Have you still not answered this question? I think it's very clear that "infinitesimals" do not qualify as Platonic objects, because they do not have the "well-defined", or even "definable" nature which is required of a Platonic object.
This creates a schism in mathematics because calculus requires infinitesimals, while set theory assumes Platonism. So instead of employing infinitesimals, set theory views infinities as well-defined objects.
Of course mathematicians will not admit to an inconsistency between calculus and set theory, they would just claim that one is an extension of the other, just like many physicists would not admit to an inconsistency between Newtonian laws (governing objects) and Einsteinian laws (governing spacetime) . What they do instead, is veil the inconsistency behind a whole lot of extra axioms and principles, designed to smooth out the bumps, and hide the inconsistencies which exist between different applications which use different principles.
Simply put, "infinitesimal" refers to the continuity (like a "dimensional line", or space) which is assumed to lie between discrete objects (which may be infinite in number), as required to maintain separation between the assumed objects, making them discrete.
So the two, infinitesimal space, and infinite objects, require completely different accounting principles. The infinite objects are given by Platonism, but they require a "space" to be, in order to account for them being discrete objects, and since the objects are infinite, the "space' where they exist must be infinitesimal. Notice that "infinitesimal" refers to what is outside the Platonic objects.
I dont recall what Habermas says about unavoidability and irreducibility (of language, I assume), but I have only read sections of the 1,000-page Theory of Communicative Action, along with a lot of secondary criticism, so I may have missed it entirely. I think its fair to say that Habermas sees rationality as procedural, and the procedure necessarily involves language. Anthony Giddens has a good overview of TCA in which he says that for Habermas, rationality presumes communication, because something is rational only if it meets the conditions necessary to forge an understanding with at least one other person. (Reason Without Revolution? in Habermas and Modernity, Richard J. Bernstein, ed.). In general, Habermas sees reason and communication as activities that we do together, which fits the picture of language (perhaps including logical and mathematical languages) as already given in the life-world we find ourselves born into. You can't fly solo.
Do not qualify yet. Once infinity and it's opposite are well defined (and infinity isn't just taken as an axiom), they likely would be Platonic objects. At least I have enough belief in the "logicism" of mathematics that it is so.
Quoting Michael
And that is the question I answered. I gather I need to be more explicit. You gave the following as yout definition...
There are mathematical objects in the sense that we can quantify over mathematical things such as numbers and triangles. There are even numbers, therefore there are numbers. There are isosceles triangles, therefore there are triangles.
These are not independent of "us and our language", since if we were not here there would be no mathematics. Mathematical entities are however independent of any single individual, but built by a community int he way that a language is built. Hence the "us".
We decide the truth or falsity of statements about planets and electrons by experimentation and inference. We use telescopes and potentiometers. We do not use such devices to decide the truth or falsehood of mathematical entities. We do use inference. The truth of mathematical suppositions is agreed in much the same way that the truth of Ohm's Law or Kepler's Law is agreed. If that is what is meant by "objective", then they are objective. We discover things about mathematical entities, in that we find unexpected results in our construction. This is not the same as discovering that the orbit of a planet is elliptical or that electrons have a specific mass.
I take all of this to be saying that infinitesimals exist, but not in the way set out in your quote.
That's it. Nothing has been said, although plenty has been shown. :wink:
Quoting Banno
:lol: Although it's really more like: He wasn't there again today. Oh, how I wish he'd come to stay.
As I understand it, what is unavoidable is our mutual agreement concerning the way the world is, and the language we use to discuss it; and what is irreducible are certain activities we perform, including illocutionary acts and normative assumptions. So "property" unavoidably takes as granted that there is land, that the land can be subdivided into sections, and that we can talk about the land; and it takes as irreducible the idea that I can dispose of this piece of land as I see fit, while you cannot.
While a dumb animal might defend a territory, it does not own it in the way a person owns a piece of land in virtue of deeds and purchases and so on. In this way "property" is dependent on our being embedded in an irreducible social structure that is unavoidable.
Much to the confusion of libertarians everywhere.
Mathematics is presumable also unavoidable and irreducible, in ways that might well be worth setting out.
The point being made in my post is that there is a difference in method between finding the value of ? and the value of the mass of an electron.
I quite agree, and take that to be one of the main themes of the Investigations - that what cannot be said may be shown or done.
Notice that question from Pigliucci - 'what kind of existence does it have?' That's the underlying question in this whole topic. That, and the reflexive association with intelligible objects and religious belief. It's because it's a metaphysical issue, and the metaphysics is hard to reconcile with naturalism. Which is why I keep going back to Platonism (not that I'm any kind of expert in it) - because it allows for levels of knowing and being, and hierarchical ontology. (And this also is being brought up to date e.g. Vervaeke's reconstitution of neoplatonism.)
As far as quantum physics is concerned, one simple point is that made by both Bohr and Heisenberg - physics reveals nature as exposed to our method of question, not as she is in herself. That leaves ample breathing-room for philosophy.
I'd suggest that this is not a good question to ask, becasue it presumes that there are different kinds of existence. But if we take Quine as a guide, then the issue is quite a bit simpler. Prime numbers and electrons can both be subject to existential introduction, a quantification. That is, from "The electron was deflected to the right" we can conclude "There exists an electron"; from "11 is the first prime number greater than 10" we can conclude "There exist prime numbers". And that's where we might pause to ask "what more is there to existence?"
And they both might have continued by saying that the method of questioning that is appropriate is that of physics, not that of philosophy. And I'd agree - much of what is called "philosophy" in this forum is just attempting to do physics, badly, and without the numbers.
Quoting Wayfarer
Of course, but philosophy has no atmosphere to breathe in when it comes to the ineffableit's the realm that myth and poetry and religion attempt to fill, and we do well to remember that our imaginative creations are just that, and refrain from participating in the hubris that leads to fundamentalism.
Quoting Wayfarer
You will say it doesn't have any kind of existence but is nonetheless real. And that just begs the question: 'Real in what way?' which is just a repeat of the question 'What kind of existence does it have?'.
Without any application, it's all just playing with words.
So there are primes.
I am interested in much of what @Wayfarer is interested in too. but not in the fundamentalist way. In other words, I don't believe in the possibility of the direct knowing of transcendent truths, which he does, but I do believe in the possibility of personal transformation, as in altered states of consciousness; I just don't make any assumptions as to what is the significance of altered states in any ontological or metaphysical connection.
Because of that I am labeled a "positivist" and summarily dismissed.
:up:
Perhaps an aside, but I am curious. To what end? What is the point of the personal transformation you are thinking of - where does it lead?
What troubles me is the presumption to knowledge - justified true beliefs - in the absence of a coherent way of providing a justification.
Which of course leads into the discussion of what is to count as a justification...
And @Wayfarerand I apparently have quite divergent views on this.
I agree. It just occurred to me that physics posits items that are just as far fetched as abstract objects, point particles being one of them.
I think we are being transformed all the time by our experiences. We can also take a more conscious hand in that transformation via various practicesthe arts, meditation, spending time in the wilderness, running and even sports. There are many kinds of cultivation.
Quoting Banno
I think when it comes to matters of faith personal experiences may serve as justifications for one's own (but certainly not anyone else's) beliefs (although personally I prefer to draw no conclusions).
Justification of direct knowledge is not intersubjectively possible, in any sense analogous to the way empirical and logical justification is. So, it looks like I'm an empiricist and a logical positivist, which I'm not really in the fullest sense. I'm with Wittgenstein in thinking that the most important aspects of life cannot be definitively spoken aboutthey can only be alluded to. It's handwaving all the way down, but for me there is a great deal of beauty to be found in some hand-waving.
How, pray tell, did we get from a brief comment about Bohr and Heisenberg, first to 'the ineffable', and then 'religious fundamentalism'?
It reinforces the earlier point I keep making - mere mention of the Platonic intuition that 'ideas are real' just automatically pushes these buttons. Everyone involved in this conversation ought to be aware of that. it's cultural conditioning, pure and simple.
The way it must be constructed to satisfy physicalism, is to say that ideas are the product of brains, which are the product of evolution, which is the product of the interaction of physical forces. To question that, is to be called a fundamentalist, because it is itself a kind of disguised fundamentalism.
[quote=Thoughts are Real (Review of Nagel, Mind and Cosmos);https://www.newyorker.com/books/page-turner/thomas-nagel-thoughts-are-real] Physics is the question of what matter is. Metaphysics is the question of what is real. People of a rational, scientific bent tend to think that the two are coextensivethat everything is physical. Many who think differently are inspired by religion to posit the existence of God and souls; Nagel affirms that hes an atheist, but he also asserts that theres an entirely different realm of non-physical stuff that existsnamely, mental stuff. The vast flow of perceptions, ideas, and emotions that arise in each human mind is something that, in his view, actually exists as something other than merely the electrical firings in the brain that gives rise to themand exists as surely as a brain, a chair, an atom, or a gamma ray.
In other words, even if it were possible to map out the exact pattern of brain waves that give rise to a persons momentary complex of awareness, that mapping would only explain the physical correlate of these experiences, but it wouldnt be them. A person doesnt experience patterns, and her experiences are as irreducibly real as her brain waves are, and different from them.
Nagel offers mental activity as a special realm of being and life as a special conditionin the same way that biology is a special realm of science, distinct from physics. His argument is that, if the mental things arising from the minds of living things are a distinct realm of existence, then strictly physical theories about the origins of life, such as Darwinian theory, cannot be entirely correct. Life cannot have arisen solely from a primordial chemical reaction, and the process of natural selection cannot account for the creation of the realm of mind.[/quote]
Back to the Third Realm.
Not my words.
Quoting Wayfarer
Probably, but so what. Any amount of social or psychological explanation for Banno's foibles will not change the veracity and validity of arguments Banno sets out. And by the same token your defence of spirituality beyond what is reasonable might be explained by your Catholic upbringing. All irrelevant, as you know.
For what it's worth I will repeat that physicalism is perhaps as mistaken as spiritualism. That I reject spiritualism and mysticism does not mean that I accept scientism and physicalism.
Quoting Thoughts are Real (Review of Nagel, Mind and Cosmos)
If.
Read what I said about existence, above. The bit about there not being "different kinds of existence".
A pretty common position. I think Robert Sokolowski does a good job explaining the intuitions that support this position, and demonstrating the centrality of the role of language in the "Human Conversation" (our collective pursuit of knowledge), without running into the problem of reducing reason to language alone (or worse something like computation, symbol manipulation, etc.).
At any rate, such a conception of reason would seem to risk loading the dice against mathematical platonism (and Platonism for that matter) to some degree. All the problems of the "linguistic turn" come up. One cannot "get outside language" or "outside the linguistic community." If these are problems that are assumed as essentially axiomatic, then it hardly seems that one can step outside the sensible world and attain a noetic apprehension of mathematical objects when "notetic apprehension" just is something to do with language (which is grounded in communities, etc.).
By comparison:
That is, reason has become merely ratio. And if intellectus survives, it survives as a grasp of simple axioms, the principle of non-contradiction, etc. In fact though, this is still extremely different because the idea was that all wholes could be "grasped as wholes" and that there might be gradations to a sort of noetic understandings (not the understanding had through discursive demonstrations). The sequestering of intellectus to merely the realm of axioms and "hinge propositions" is sort of the flip side of the reduction of reason to ratio.
Anyhow, the following paragraphs are less relevant but I find the application to literature interesting:
Anyhow, a question philosophy of language has generally ignored (often deciding it belongs to some other field) is: "Why do we feel compelled to speak? Why speak at all, and why of this and not that?"
This is the question Umberto Eco puts front in center in Kant and the Platypus. I think it's also the question that comes front and center when it comes to mathematical objects (or at least if one wants to attempt to explain them in terms of language).
There is the historical question of: "why did disparate cultures all come up with terms for magnitude and multitude?" but also the more immediate question of "why do people feel impelled to use these terms so often?" The platonists seems to have some sort of answer. The more compelling rebuttal would seem to require not only showing problems with the platonists' position, but showing how else these questions might be answered.
The point though, is that "infinity" and "infinitesimal" refer to completely different things. That "infinity" refers to a Platonic object does not imply that "infinitesimal" does.
[quote=various sources including Wikipedia] Intellectus is the Latin term adopted by Roman philosophers like Cicero and later by medieval Scholastics to translate nous from Greek philosophical texts. It similarly denotes the capacity for intellectual intuition or understanding of universal principles. Nous (and therefore Intellectus) is a key term for the higher faculty of the soul, distinct from reason (ratio), which operates discursively. In the Aristotelian scheme, nous is the faculty that underwrites the capacity of reason. For Aristotle, nous was distinct from the processing of sensory perception, including the use of imagination and memory, which animals can do. For Aristotle, discussion of nous is connected to discussion of how the human mind sets definitions in a consistent and communicable way (through the grasp of universals) and whether people must be born with some innate potential to understand the same universal categories in the same logical ways. Derived from this it was also sometimes argued, in classical and medieval philosophy, that the individual nous must require help of a spiritual and divine type. By this type of account, it also came to be argued that the human understanding (nous) somehow stems from this cosmic nous, which is however not just a recipient of order, but a creator of it.[/quote]
"Various sources"? What does that mean, that it's an AI generated piece of crap, compiled from cherry picking sites most often visited? Isn't that just internet mob mentality?
And we do have problems in understanding infinity, so how Platonic that is, is a question. Or otherwise I guess the Continuum Hypothesis has been solved.
My thought about this is that infinity exists in the same way 0 does, as an abstraction of the set. Hence the whole "some infinities are larger than others" thing. If 0 is nothing from the set, infinity is everything from the set. But I am not a mathematician.
Quoting Banno
I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified?
Quoting Janus
It seems to me that "I had an experience of God" may be both true and justified, in terms of my own (reasonable) standards. But the degree of justification -- the standards involved -- are quite different from those I would use if someone asked me to justify my belief that my cat is on the mat. Different degrees of certitude, in other words. Arguments for God based on personal experience are arguments to the best hypothesis. That's why it's unreasonable to expect anyone else to treat my belief as knowledge.
Yep. :up:
The intellectus/ratio distinction is something I focused on when I first arrived at TPF, for it seems to me the biggest error that basically everyone here makes, together.
Note too the way that all moderns tend to agree with Hume that no movement from ratio to intellectus is possible. For example:
Quoting J
(The abandonment of intellectus is the abandonment of knowledge in favor of opinion and hypothesis.)
Yes, and I'd also add that there are different generally socially accepted criteria for what counts as "best explanation" in different societies and times and milieus.
How exactly does this differ from any empirical claims?
It depends on what is meant by "justified." Plato, in Letter VII, says of "teaching" metaphysics that: There neither is nor ever will be a treatise of mine on the subject. For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself.
But note, Plato does attempt to convey such things, and to justify them. Indeed, he produces a 2,000+ page corpus of exquisitely crafted dialogues to do so. St. Augustine has a similar view on metaphysics and a more dismal view of man's unaided reason, and yet he produced 35,000 pages of collected works, much of which deals with these same topics. Dante's Divine Comedy might be the greatest example in world literature of the attempt to convey what escapes language in image.
But if justification is taken to be synonymous with demonstration, (which is obviously a temptation if reason is just ratio) then obviously such efforts will involve "speaking where one ought to be silent." Or they would involve "art" primarily enjoyed for amusement, and not philosophy.
This denotes a very particular approach to the tradition Wayfarer is talking about though. One cannot take a Meister Eckhart, a Rumi, or a Dogen as simply conveying "novel and perhaps inspiring experiences" and take their claims seriously. Indeed, since such "experiences" generally involve the apprehension of truth, and so demand to be taken exclusively, this would be sort of a contradiction in terms. (Dante, for his part, doesn't even allow those who won't take a stand the dignity of a place in Hell; they will spend eternity following a banner that moves relentlessly and arbitrarily about the outskirts of Hell).
If these authors are simply conveying novel experiences to be surfed through, then they are, in some deep sense, fundamentally deluded. Which doesn't mean they cannot be interesting, but it does mean they cannot be right.
This is more complicated than I intended. By "justified," I just meant "explained" or "given an account of." Whereas a demonstration would be simply to show that it is the case, without further explanation why.
Example: A singer attempts to hit a high C, but is unable to do so after repeated attempts. She has thus demonstrated that the note is inexpressible by her. But the question "Why?" remains, and would be answered in terms of anatomy and acoustics. Similarly with philosophy. We may demonstrate that a particular thought is inexpressible, either by argument or some other way, as Wittgenstein claimed to do, and in addition offer an "account" (what I called an explanation) of why that is so. Such an account wouldn't merely repeat the demonstration; it would try to tell us why the result makes sense, or was to be expected.
It depends on what you mean by "empirical claim". Direct observations are obviously corroborable, whereas claims to have experienced God are not
Quoting Count Timothy von Icarus
Why not? They are just men speaking about their ideas and experiences. What they say about their experiences, their ideas, their faith cannot be a definitive justification for anyone else to believe anything. Unless you are appealing to authority? I take their words as seriously as I would the words of any poet whose works I believed to be of high quality. I don't have to strictly believe what is being said in order to be affected, even inspired, by it.
Quoting J
I guess it depends on what you mean by "inexpressible". I take Wittgenstein to mean not expressible in a way that what is being said can be confirmed or disconfirmed. He applies this to ethics and aesthetics. For example, I can say that Beethoven was greater than Bach, but there is no determinable truth to that. So, do you think that by "inexpressible" he means "not truth apt"?
.
Others on TPF know the Tractatus a lot better than I do, but I think he meant something more than merely "not truth apt" or "not confirmable." I think it's closer to "incoherent" or "illusory." And he wasn't just thinking of ethics and religion, but also of certain supposedly bedrock metaphysical truths. In any case, what I meant by "inexpressible" was more like "unsayable save by metaphor and indirection."
I took the liberty of adding the bolded phrase, because leaving it out does make it appear that you're asserting that they succeeded in apprehending truth, which would beg the question.
I too think there's more to Eckhart et al. than "inspiring experiences" but again, let's be careful of the difference between "taking a claim seriously" and "believing it to be true on personal authority." I can be very impressed by a mystic's account without accepting it as somehow self-verifying.
That depends on the experience. The most famous theophanies, the Incarnation (and events related to it, such as the Resurrection, Transfiguration, and various miracles) as well as the Pillar of Fire over the Tent of Meeting all involved appearances to multiple individuals (in the latter case, an entire community). Hence, for those involved, they were corroborable.
They aren't corroborable for us, at least not in the direct sense that we can go back in time to the Sinai and see the Pillar of Fire traveling alongside the Hebrews and the Glory of the LORD filling their tent. At the same time, this is also true for virtually all historical facts. One cannot go back to 1492 to see if Columbus really did "sail the ocean blue," and we certainly cannot run multiple independent experiments to confirm this fact. Corroboration always involves piecing together signs and testimony.
Why not what? Read them that way? Well, I suppose that if they are right, then one is missing out on something terribly important if one reads them in that sort of detached manner. Indeed, according to them what is most important.
If the question is: "why can't we take them seriously if we disregard what they are saying as being true in the sense in which they claim it is?" then IDK, that seems like the definition of not taking them seriously. When the Patristics claim that we are deluded and enslaved to sin until we turn our mind to God, that this alone is our true telos, etc. etc., it doesn't seem possible to say "well that's just a sentiment for their times," and still be "taking them seriously."
One need not be a Sufi to take Rumi seriously, but it hardly seems like one can be an atheist. Likewise, an atheist might find much to enjoy in Dante or Plotinus, but they have to at least allow them the courtesy of being deluded and wrong in order to take them seriously.
I am no expert either, but I understood that in the Tractatus Wittgenstein was concerned to make a distinction between what can be propositionally claimed and what cannot. I think that for him a coherent proposition just is a proposition which is truth-apt.
Quoting Count Timothy von Icarus
We don't know if the reports of those events are reliable, so for us they are not corroborable.
Quoting Count Timothy von Icarus
Strictly speaking that is true. But we think the gospels were written many years after the events, which would make them less reliable than many historical documents, especially in cases where there are multiple accounts of, and cross references, to events.
Quoting Count Timothy von Icarus
We can take works seriously as poetry, as allegory, as being revelatory of more or less universal aspects of the human condition, and hence as being inspiring, insightful. Think about Dante's Divine Comedy, for example, or Homer's Odysseycan we not take those works seriously without believing that the events described therein are accurate descriptions of real events? What about the whole Greek mythical pantheon?
Quoting Count Timothy von Icarus
Apart from taking them seriously in terms of their literary merit. we can take such worldviews seriously in acknowledging that they felt real and important for those who held them, without believing them to be true ourselves. I'm not seeing the problem you apparently do.
Quoting Count Timothy von Icarus
The point is that we don't and can't know whether any of these claims are true or false because they are not empirically or logically confirmable. If I feel drawn to such claims and feel in my heart that they are true, that's fine for me, but it's never going to be sort of thing that must be compelling for any unbiased judge.
If something is inexpressible, then by that very fact one cannot say why... Doing so would be to give expression to the inexpressible.
In the end, past all the justification and discussion, there is the act. Any justification becomes besides the point.
And this applies to ritual, ethics and maths:
This is the answer offered to the problems of rule following, and it's the only one that works - that in the end, it's just what we do.
And in so far as it is just what we do, the rationalisations, arguments and justifications are almost irrelevant, mere superstructure or appendix.
So while "it might be important to say why" (@Wayfarer) it remains that "what cannot be said may be shown or done" (Banno)
So we still have, from the Tractatus, "The world is all that is the case" and "What we cannot speak about we must pass over in silence", both quite so. And then we go to the next step, which is that nevertheless, we must act, and be part of that world.
When Moore holds up a hand and says "Here is a hand" he is performing an act, making a declaration; here he cannot be wrong.
I'd like to quote a passage from the book After Finitude, by Quentin Meillassoux. There he says:
What do you folks make of that? Does any of that make sense to you, or not? Not sure if I'm actually helping here, in the sense of being collaborative. If not, then I'll excuse myself out.
That's what I'm not sure about. I don't think I'm asking for the inexpressible itself (call it P) to be expressed; that would indeed be impossible. Rather, I want to know why P is inexpressible. Call that explanation Q. Does it really follow that, if P is inexpressible, Q must be as well?
In a certain sense, I agree with you (and Witt) that justification becomes pointless when what we do is interpreted as rule-following. Nor am I disagreeing that, often, rule-following is a good way to think about what we do. But I'm not convinced that this entire situation is opaque to explanation, or at least to elucidation.
Probably this all depends on whether one considers the Tractatus to be a demonstration or an explanation. Some of both, surely? I know Witt said very austere things about how not-philosophy his approach was, but I see a lot of explaining and justifying going on nonetheless.
Thanks for picking up on that. I was saying, Wittgenstein's famous 'that of which we cannot speak....' is often used as a fireblanket to suppress discussion of the mystical, which I feel is one facet of philosophy. I peruse the Tractatus (which I've never studied formally or read in full), there are aphorisms which ring true, and many others I don't understand at all. The one that I always recall is 6.41:
I'd like to ask, 'Why is that?'
Is the answer 'Shuddup already' :rage: ?
Quoting Banno
But he can be jejune.
Quoting Count Timothy von Icarus
That resonates with the legendary origin of Ch'an Buddhism, namely, the Flower Sermon, wherein the Buddha's insight is transmitted worldlessly to one Mahakasyapa, the only monk to smile when the Buddha gazes at a flower, and the origin of what is thereafter designated a 'special transmission outside the scriptures' - notwithstanding that this tradition also generated a vast corpus of written texts about what supposedly could not be transmitted by them. Something similar is also discernable in the 'doctrine of divine illumination', associated with Augustine, and about which there's an article on SEP.
Having said that, I also understand that the mystical is something which engenders vastly different responses in people. It resonates for some, and not at all for others, and it is also a fertile source of both exploitation and delusion. I've always felt an affinity for it and I do think that properly grasped, there are self-validating elements in such teachings, but only if they are properly grasped. That is what it 'has to be done' refers to: they're dynamic principles that have to realised in both sense of made real, and understood properly.
Quoting J
So we might proceed by looking at examples.
But your high "C" will not do, becasue the singer being unable to reach it is not inexpressible; we know what note they are trying to reach, and that they cannot reach it.
So give an example of something that is inexpressible...
See the problem?
Yep.
But that's not to stop you from doing.
Shut up and calculate. :wink:
One that requires having a hand no doubt.
What and are proposing is important - but it is also just froth.
https://www.geeksforgeeks.org/applications-of-imaginary-numbers-in-real-life/
Just say that something has "a certain, je ne sais quoi. When you say it in French it becomes ineffable!
Agree. But don't you think that the qualifier 'objective' might be inappropriate in the context? But then, what are the alternatives? The point being, 'objective' means 'inherent in the object/s'. But numbers are not objects per se, they're intellectual acts. We use mathematical techniques to determine what is objective. Not that they're subjective, either, but that their truth status is in some sense transcendental (but then, you can't use that, because 'transcendental numbers' are a special case in mathematics.)
Which is what leads me to speculate that the natural numbers are real but not existent. They are, in a sense other than the Kantian, 'noumenal' - objects of intellect (where 'object' is used metaphorically). But they are also indispensable to rational thought. That is part of the version of mathematical Platonism that makes sense to me.
I've seen this done in a few places actually. Normally the metaphor people use is one of a number line. You have 0 in the middle and positive and negative numbers extending in either direction, out to infinity. To get the imaginary numbers, imagine the real numbers as the x axis on a 2D graph. The imaginary numbers are the Y axis of the complex plain, they are pivoted orthogonal to the reals.
Is Platonism in mathematics, as you folks are discussing it, strictly restricted to a specific area, like Arithmetic? Or does it include all areas, like Geometry for example?
Does it make sense to agree with Platonism on some intellectual fronts but not on others?
I'm sure it does. After all, just what Platonism is, over and above the actual dialogues, is always being refined and re-envisioned. My sole philosophical commitment is to what I consider an elementary philosophical fact: that number is real but not material in nature. Of course there are nowadays kinds of neo-pythagorean views, like Tegmark's, but that's not what I have in mind, as Tegmark is, perplexingly enough, still a pretty standard-issue scientific materialist in other ways.
But the point I've been pressing, pretty well ever since joining forums, is that some ideas are real in their own right, not reducible to neural activity or social convention or the musings of experts. We discussed Frege upthread, about whom I know not much, but he is nevertheless instinctively Platonist, in believing that numbers and basic arithmetical operations are metaphysically primitive, i.e. can't be reduced or explained in other terms. In other words, it's a defeater for materialism, and that is why it is so often rejected in the modern academy.
But there are many controversies. Take a look at What is Math? a Smithsonian Magazine article I cited earlier in this thread. I think it lays bare many of the contentious issues. (After reading that article, I purchased a copy of the book by the emeritus professor mentioned in it, James Robert Brown, Platonism, Naturalism, and Mathematical Knowledge, but alas, much of it was beyond my ken. Review here.)
I think I understand. It's like objective idealism, in some sense. But I'm just having a hard time trying to wrap my head around the underlying concept here. Something (i.e. a number) can be real without being material? How can that be? I'm admittedly a scientific materialist. The specific philosophy of mathematics that resonates the most with me is Mario Bunge's specific brand of mathematical fictionalism. He says that the number 3, for example, is just a brain process. And the same hold for every other abstract concept: from a humble number, to a tautology, to a scientific hypothesis, to a scientific theory, all of them are brain processes, but we feign that they exist as "autonomous ideas", as it were. It's like we're "fake Platonists", if only because all of our concepts are sort of like "useful fictions" in Nietzsche's sense of the term, if that makes any sense.
But I'm not so sure that this is true. Unlike Bunge and other mathematical fictionalists, I think that there's a very solid case that can be made for Platonism about, at the very least, the set of Natural numbers. Complex numbers are a more contentious issue, I think. Are they even "numbers", or are they just concepts? Is Infinity really a number, or is it "just as concept", as some folks say? It's a tough thing to argue, either way.
But I'll definitely read the references that you shared, thank you very much.
What we could do is just use the concept of abstract objects as a placeholder. One day we might understand it better. Maybe it will turn out that Bunge is correct. Until we have a testable theory, all we have is biases.
Well, I think we have - no offense or anything - a flawed understanding of what is real. (After all, it's the business of philosophy to make such judgements.)
Quoting Arcane Sandwich
This is 'brain-mind identity theory' which was prominent in the work of a couple of Australian philosophers, J J C Smart and D M Armstrong.
The fly in the ointment here is what exactly is meant by 'the same'. When you say that a brain process is 'the same as' a number then you're already well into the symbolic domain. There's no feasible way to demonstrate that a particular brain process - in fact, there are no particular brain processes, as brains are fiendishly irregular and unpredictable - 'means' or 'is' or 'equates to' anything like a number (or any other discrete idea.) And indeed an argument of this type has an ancient provenance. It appears in Plato's dialogue The Phaedo, in which Socrates makes a vital point about the implication of our ability to perceive the nature of 'equals'. When we see two things that are of equal dimensions, say, two stones or two pieces of wood, we are able to discern that they are equal?-?but only because we innately possess the idea of 'equals':
Socrates: "We say, I presume, that there is something equal, not of wood to wood, or stone to stone, or anything else of that sort, but the equal itself, something different besides all these. May we say that there is such a thing or not?"
Simmias: "Indeed, let us say most certainly that there is. It is amazing, by Zeus."
"And do we know what it is?"
"Certainly," he replied.
"From where did we obtain the knowledge of this? Isn't it as we just said? From seeing pieces of wood or stone or other equals, we have brought that equal to mind from these, and that (i.e. 'the idea of equals') is different from these (i.e. specific things that are equal)".
The Phaedo 74a ff
Another argument is a version of Putnam's multiple realisability - that a number (or any item of information) can be realised in any number of ways by different brains (or in different media or symbolic types, for that matter.) Neuroplasticity demonstrates the brains of injured subjects can be re-configured to grasp language or number with neural areas not usually associated with those functions. That's also a version of multiple realisability.
And in even thinking about these problems, you're all the time making judgements and reasoned inferences ('if this, then that', 'this must be the same as that' etc.) You can't even define what is physical without relying on those rational faculties, yet brain-mind identity claims that they are somehow the same.
So my view would be that, wherever rational sentient beings exist, there must be a core of real ideas that they are able to grasp, and these are discovered, not invented.
OK. I can understand that (I think?). It's something that I can agree with, if only for the sake of argument. Numbers are real, and they're not material. My follow-up question would be, are they physical? Like, are they somewhere, in spacetime? Are they in our head, in some sense? Not necessarily in the brain, but then where? In "the mind", assuming that "the mind" is something other than the brain? Are they outside the brain? Where are they? In the things, themselves? I think that might be true of Natural numbers, I can agree with Aristotle's notion that "quantity" is a real accident, a real property of "substances" themselves. Is that what you are saying? Or are you saying something different?
In typical philosophical parlance, I find "objective idealism" pretty close to a contradiction in terms.
Subjective ? existentially mind-dependent
· Objective is not
Idealism ? mental monism
· Realism is not
· An analysis of the rationale leads toward solipsism
But, hey, in the rabbit hole of metaphysics, one can come up with whatever. :)
Never mind me, carry on.
I'll mind, I'll take that bet. I think you have an excellent point when you say that "objective idealism" is a contradiction in terms. Plato would not be an objective idealist, then. He would be a "metaphysical realist". But that sounds somewhat "odd", at least to my ear.
Yep.
Quoting Banno
If someone believes something to be inexpressible, then they have a reason why. The ones who are willing to say why are the philosophers.
(And if the object of inexpressibility cannot be referenced in any way whatsoever, then there is nothing which is inexpressible in the first place.)
True, that's an excellent point. I agree.
Quoting Banno
I'm not sure. The adjective "real", as far as I'm concerned, has an external referent: it refers to the quality of being real. And what is that quality, exactly? It's hard to say, and it's a contentious issue in the literature. Should we define "real" as a concept, as that which exists outside the mind? Outside the brain? Is it instead that which belongs to a res, a thing? Would weight be a real property? Perhaps mass would be a better candidate. Or even energy. You could say that the difference between real things and mere concepts is that the former have energy while the latter don't. But how can they not? Can there exist real things without energy? Do numbers, as you understand them (as real but not material) entities, have energy in the physical sense of term? I prefer to define "real" as anything that has spatiotemporality (in other words, that it is somewhere in space and "somewhere" in time, even if such locations are not entirely clear-cut). But all of this is up for debate I think, at least inside the "Ontology Room".
I think that is due to the cultural impact of empiricism. Because of this we are enculturated to believe that what is real can only be in located in space-time. Notice in that Smithsonian essay:
But there's another approach - that of phenomenology. @Joshs is adept at explaining that (see this post.) My take is that numbers and logical principles are necessary structures of consciousness. That doesn't mean they're the product of the mind i.e. they're not neurobiological structures but intentional structures in Husserl's sense.
That may well be the case.
Quoting Wayfarer
That may well be the case, as well.
But then I have another follow-up question. There are four apples on the table. I claim (I might be wrong, of course) that those four apples are still four apples even when no one is looking at them (i.e., "intending" them in any way, as in Husserl's concept of intentionality as a subject-object relation). I would say, the number "one" exists, like an "Aristotelian accident", in each of the four apples. And that "one-ness", if you want to call it that, doesn't somehow "dissipate", or "cease to be", when no one is contemplating the apples, or thinking about them in any sort of way. It's just a brute fact that there are four apples on the table instead of five or three.
Not sure if I'm being collaborative here, Philosophy of Math is quite arguably the toughest branch of philosophy.
What's that, then? See
However, it does make sense to trace a distinction between real fruit and non-real fruit, as in, plastic fruit, not actual parts that were collected from a living plant.
If Mathematical Platonism is right, numbers are more like real fruits than plastic fruit, if that makes any sense. If, on the other hand, Mathematical Fictionalism is right, numbers are more like fake plastic fruit instead of real fruit from an actual plant.
Does that make sense?
What you're referring to is 'brute fact' is actually just direct realism, the view that the world is perceived exactly as it is. But that fails to account for the role of the mind in shaping our perception of order and numerical concepts. It fails to grasp the fact that the order we perceive in the world, numerical and other, arises as a consequence of the interaction of mind and world. I acknowledge that in practical, everyday terms, it may seem straightforward to assert the existence of four apples, but this perception is itself mediated by observation and verification, verifying that they're real apples and not fakes or holographs, etc, of which requires observation. This is the subject of another OP The Mind-Created World, also discussed here, a defense of a form of phenomenological idealism.
Ok. I'll leave you to that.
Nice. That catches something of the drift.
I can't see that saying ? is a fiction is any better than saying it is the subject of a quantification. Indeed, that ? is the ratio of the diameter of a circle to it's circumference isn't in any useful way like saying Frodo walked into Mordor.
I can imagine Frodo walking into Mordor. I can imagine the number Pi (up to a certain point).
Is there a small, barefooted humanoid in the world, walking into a territory somewhere in Europe or some other place on planet Earth, that is a scorched landscape with a tower that has a supernatural Eye at the top (the Eye of Sauron)? I would say no. Is there a thing or property in the world, that "answers" in such a way to the number Pi that I can imagine (up to a certain point)? I think there might be. That would be the difference between Pi and Frodo. Unlike Bunge, who actually compares linear equations to Donald Duck as far as their ontology goes, I believe that natural numbers might indeed have a one-to-one correspondence with the "one-ness" of each ordinary object. Natural numbers could well exist really, outside the mind, in the things themselves. Our intellect merely "reflects" them or "abstracts" them or "represents" them in some way. We pick up on them, we become aware that they are there, just as we become aware that these four apples still exist -as four apples, not merely as a non-numerical bunch of fruit-, when no one is in the house.
?(x)(x=r/c)
:meh:
How is that salient?
Quoting Arcane Sandwich
I agree. Free logic. Not used here.
Quoting Arcane Sandwich
Sure. Quine's point being that treating that ? exists is just to say it is the value of a bound variable has no ontological import. That was kinda the joke.
Later.
Hmmm...
Note to Self: Well the irony here, of course, is that such way of speaking sounds "non-human", if that's even a thing. But if it is, then it would have a de-personalizing effect on the listener. Is that true? Do I even agree with this idea myself? But how couldn't I? I'm the one that has thought it. However, it is a thought experiment. Anyone can perform it, at least potentially. Thought experiments, that is. They are objective, though cerebral, and hence, physical.
Apples are a good example, but cats or whole apple trees might be a better. Are there no discrete individual, whole plants or animals in the world such that they make up a multitude? Organisms are only organic unities as ens ratonis - in our minds? This sounds pretty implausible. And likewise, we have our own thoughts and sensations, not other people's, and so, barring solipsism, this is a fairly obvious instance of multiplicity.
In a debate with Richard Rorty, Umberto Eco tried to press the point that things cannot be pragmatism and convention "all the way down." A screwdriver, in some sense, shapes what we choose to do with it. Rorty disagreed and gave the unfortunate counter example that we could just as well scratch our ear with a screwdriver. Except we wouldn't, because of what a screwdriver is and what we are (or, if the point isn't clear enough, consider a razor sharp hunting knife). The world, and truth, imposes itself on how we deal with things.
Of course. What a sound thing to say. Brilliant, I would say. I'm not trying to be funny here, I believe in good common sense myself.
Quoting Count Timothy von Icarus
Absolutely. I agree with this. It's funny that I should agree with Eco and not Rorty on this point, but I'm a metaphysical realist before being a pragmatist. That being said, I'm also a materialist, an atheist, a literalist (in some sense of the term), and a staunch defender of scientism. Not just of science as a body of knowledge and what have you, but of scientism itself as a mentality. I'd put it like this: I'm a simple person interested in complicated ideas.
Eco is pretty interesting on this point, although I don't know if I'd totally recommend Kant and the Platypus. He starts off by granting the advocates of the linguistic turn and post-moderns most of their premises, and TBH I found the recap of all their points a bit tedious, particularly since some of these premises seem fairly dubious.
It is one thing to say the philosophizing is primarily done with language, it is another to simply assume that language is posterior to being because all talk of being involves language. The assumption seems to require that those without language simply cannot think, which seems a bit much. This is the old reduction of reason to ratio I mentioned earlier, except now ratio is confined to language (and perhaps to isolated, sui generis "language games").
I wouldn't be willing to cede these points. Similarly, one could argue that the senses are that through which we know not what we know. So too do it seem plausible that language is that through which we articulate thought (which is not to say that we don't sometimes use language to think) and another means through which we know, not thought itself and what we know. In the semiotic tradition Eco is advocating for, the sign vehicle is what joins the object and interpretant in an irreducibly triadic relationship (a gestalt perhaps), it is the mediator of a union, and it's a bit tedious to allow it to instead become an inscrutable and insurmountable barrier, only to try to work one's way back from this assumption.
Likewise, it seems unwise to me to leave unchallenged the presumption that truth is primarily in sentences, in syllables and symbols, and not primarily something that relates to the intellect.
Plus, some of the modeling exercise stuff he does could certainly benefit from advances in information theory and the philosophy of information. Although there is certainly still good stuff there. Perhaps the exercise is worthwhile. It is worth pointing out that in the "continua," (his term for "bare" experience prior to language/naming) there are limits. One can suppose that we can go about naming things in many different ways, but we cannot proceed arbitrarily on pain of being corrected on our errors. That there might be many ways to say things need not entail that all are equally correct. One might challenge the notion of genus and species, but if one tries to mate a cat to a dog one shall find a limit on how our conventions might develop.
Still, to me this smacks of the old empiricist view you find in Locke. A sort of atomization at odds with how learning actually occurs. Even brutes have a grasp on wholes. Sheep need not be exposed to many wolves in order to piece together "bundles of sensation" into an "abstracted image" of some whole. The sheep sees or smells their first wolf a bolts, and it is quite good for it that it has this capacity (St. Thomas makes this point in the commentary on De Anima).
Quoting Banno
OK, the challenge is to come up with something that is both a) inexpressible, and b) whose inexpressibility can be explained. It also ought to be something worth worrying about, I would add.
How about starting from the quoted Witt passage?:
.
Would it follow from this that the sense of the world is inexpressible, because it lies outside the world? I know what Witt means, more or less: sense, values, interpretation, none of these things are items in the physical world, which is only a collection of happenings, probably accidental. We import these items. So the question is, in doing so have we rendered the sense of the world expressible, or is it still inexpressible?
This is just a preliminary question. If you think we can express the sense of the world in this fashion, then my example wont serve.
As far as semiotics are concerned, especially philosophical semiotics, and especially philosophical semiotics that lean towards scientism, I gravitate towards Charles Sanders Peirce's philosophy of the tripartite sign and its corresponding areas of study and application: semantics, syntax, and pragmatics.
Quoting J
I'm just going on intuition here:
In response to the first point, my table is not expressible. It's literally inexpressible. It cannot express anything by itself (because it's an inorganic object), and I cannot express it (because I cannot speak for it, since it's an inorganic object). What I can do is talk about the table, I can tell you about it. I can describe its features, I can explain why it has them, factually. I can speak highly of it, in the manner of a poet or a wine salesperson. But, technically speaking, I cannot "express" it. Therefore, it's inexpressible.
In response to the second point: I have already explained its inexpressibility in the preceding paragraph.
If Wittgenstein or anyone else claims that X is inexpressible, then they have already expressed the inexpressible. If X were truly inexpressible then it could not be identified and deemed inexpressible.
And if Wittgenstein or anyone else claims that X is inexpressible, then they have reasons why they think it is inexpressible, and thus the putative grounds for its inexpressibility are already contained within the claim that it is inexpressible. After all, we don't claim that X is Y for no reason at all.
I'll take that bet. I claim that my table is inexpressible. And in saying that, I have not expressed the inexpressible. If you disagree with me on these two points, then I kindly ask you to define, for the purpose of this conversation, what the word "inexpressible" literally means, and I would like a credible source for the definition of that word.
Quoting Leontiskos
I believe that proposition is false. "Truly inexpressible". What do you mean by "Truly" here? Your argument sounds like the "No True Scotsman" fallacy.
Quoting Leontiskos
False. The antecedent of that conditional statement is true, while its consequent is false. I claim that my table is inexpressible, but I have no reason why I think it is inexpressible: I'm just going on intuition, not reason.
Quoting Leontiskos
That is false, as I have just demonstrated.
Quoting Leontiskos
It depends on the case. Sometimes we do, sometimes we don't. The conditions and the circumstances of the case matter in such instances.
See:
Quoting Inexpressible Definition | Merriam Webster
Note how erroneous your definition is:
Quoting Arcane Sandwich
...."Unable to express itself; unable to be spoken for." You won't find your definition in any dictionary. "X is inexpressible" does not mean "X is unable to speak."
Point taken. Granted.
Quoting Inexpressible Definition | Merriam Webster
"Indescribable". I claim that my table is "indescribable", and by that I mean, whatever the Merriam Webster Dictionary defines as "indescribable".
The example of my table still stands, @Leontiskos
"Table" is a common noun, so when you talk about your table you have already given a description. When you talk about your table we all know what sort of thing you are describing.
I think not, and allow me to tell you why I think that. The word "table" is a common noun, but the table in my living room is not a common noun, it's an ordinary object made of wood. And the noun "table" does not literally describe my table, it just defines what the world "table" means. And the Merriam Webster Dictionary definition of the common noun "table" makes no reference to my table, the one in my living room, so how could it describe it? It can't, therefore my table, the one that's in my living room, is indescribable by definition, if by "definition" we understand whatever the Merriam Webster Dictionary has to offer in relation to that word.
EDIT:
Quoting Leontiskos
But that's my point: you only know what sort of thing I'm describing, but you don't know what thing it is specifically, because it's my table.
Sure it does. That's why you used the word "table" to represent the object in your living room. If you had said "chair" we would have known that we are talking about a different object.
Quoting Arcane Sandwich
When you say, "This object in my living room is a table," you are appealing to the definition of 'table'. The definition of a table describes tables. That's what a definition does.
Quoting Arcane Sandwich
Of course it's not. You already described the object: it's a table. You could further describe it by giving its color or its material or its height. In no way is your table indescribable or inexpressible.
I think you're wrong. I would like you to quote the Merriam Webster Dictionary definition of the word "definition".
Quoting Leontiskos
I disagree, from a metaphysical standpoint, with what you just said there. I described my table, but I did not fully describe it (you agree with me up to here, yes?), I could indeed further describe it by giving its color (you just said so yourself), but I disagree with the following thing that you said. My table is in some way indescribable or inexpressible, because I cannot describe it forever. At some point, I will die. The table will still exist. At some point, humanity will become extinct. Tables will still exist, at least for some time. No one will be alive to describe them. So, they are indescribable and inexpressible in such a scenario (which, by all accounts, will actually, physically, happen in the future). The table becomes indescribable and inexpressible in the absence of beings capable of expressing what it is, in the sense of describing it, because such beings have effectively ceased to exist. One hand waving does indeed make a sound, a tree that falls in the forest when no one is there to listen does indeed make a sound, but there is no meaning in the latter scenario, while there is indeed meaning in the former: someone who waves a hand, and in the manner of Moore says "here is one hand, here is another hand, there are two things, thus solipsism is false" is arguing in a valid, sound way.
Bunge doesn't sound like the brightest bulb in the pack.
He was a stubborn man, from what I gather. And he had a great sense of humor. But yeah, he put no stock in modal logic. I'm not sure that I do myself either, but I do take the concept of "modality" somewhat seriously from a philosophical standpoint. I mean, how could I not? Contingency and necessity are modal notions, by definition. This is what Bunge struggled with, I believe. Or maybe he just didnt "buy it", he wasn't "persuaded" by it (again, it seems that he was a stubborn man).
What do I make of his intellect? I think he was a genius, really. At the level of Jorge Luis Borges. At the level of Willard van Orman Quine. I don't think we can deny him that prestige. Did he earn that prestige? I think he did. Is he right about everything? Of course not. There's even theorems that lead to contradictions in some of his more analytical works (like the eight volume of his Treatise on Basic Philosophy). But what I like about Bunge is that he believed, at the same time, in good common sense and scientism. He actually used the very word "scientism" in a positive, unabashed, unapologetic way. And that, quite frankly, is awe-inspiring.
"Indescribable" does not mean "unable to be described forever." If that's what it meant then, by your own criteria, everything would be indescribable, and at that point the word would mean nothing at all.
Then, for the sake of argument, I would say that there are only two logical options here.
1) Option one: you want to solve this problem (the dilemmas of Mathematical Platonism) in a purely "philosophical" way, or
2) Option two: you want to solve this problem (the dilemmas of Mathematical Platonism) in a purely non-philosophical way, i.e., with the language of mathematics alone. Perhaps even with the language of first-order symbolic logic (or perhaps something more exotic, like second-order logic, though I agree with Quine here, second-order logic is just "set theory in wolves' clothing").
Or you can just quote the definition of the word "indescribable", as the Merriam Webster Dictionary defines that word.
EDIT: Note to self: what Quine actually said is "in sheep's clothing", not "in wolves' clothing".
I could keep quoting the dictionary for you. You keep asking me to. But better that you learn to fish. Use the dictionary yourself. Before writing a post claiming that "indescribable" means something like, "unable to be described forever," go check your claim against a dictionary. Too much of this exchange has been you giving highly inaccurate definitions and me correcting these inaccuracies. If you use words in an accurate way people will be much more keen to engage your thought.
Just sell me the damn fish, mate. I'll "teach you to fish" some other sort of "fish" in return.
Quoting Leontiskos
Fair enough, but you're the one that chose Merriam Webster, not another dictionary. I myself would have made a different choice of dictionary, for example. Is that allowed, or do we have to refer to Merriam Webster in this Thread?
Quoting Leontiskos
That's actually a very solid thing to say. Point taken, lesson learned.
Quoting Leontiskos
Well... that's debatable. Again, in what "Room" are we? Is this "the Ontology Room", is it the "Linguistics Room", is the "Mathematics Room"? At what "level" of awareness are we currently discussing when you say something like that?
Quoting Leontiskos
I agree. So, take the lead. What words should we use to reach a general agreement as far as the topic of Mathematical Platonism goes?
Was he gainfully employed?
My understanding is that he was. He taught Epistemology and Metaphysics at McGill University in Canada, if I'm not mistaken.
The Merriam Webster Dictionary definition for the word "definition"
And I quote:
1) "a statement of the meaning of a word or word group or a sign or symbol."
2) "a statement expressing the essential nature of something."
3) "a product of defining."
4) "the action or process of stating the meaning of a word or word group."
5) "the action or the power of describing, explaining, or making definite and clear."
6) "clarity of visual presentation: distinctness of outline or detail."
7) "clarity especially of musical sound in reproduction."
8) "sharp demarcation of outlines or limits."
9) "an act of determining. Specifically: the formal proclamation of a Roman Catholic dogma."
These are all options, mate. And they're collectively incompatible with each other, that is, they lead to contradictions if you accept all of them at the same time. Choose at least one. Which one of these Merriam Webster definitions is the one that is equivalent to your own definition of the word "definition"? You said "That's what a definition does". Does it? Refer to the previous list of nine options and choose at least one, then. I can't make that choice for you, mate.
Here is your claim:
Quoting Arcane Sandwich
The word "table" presumably describes the object in your living room, given the fact that you used the predication. Most of the definitions of 'definition' will suffice to show that the word 'table' describes the object in your living room.
No it does not, since my table is arguably a rigid designator in the Kripkean sense of the term. I don't think it is, but you could in principle argue in a Kripkean way about this point.
Quoting Leontiskos
Rigid designators are not predicates, mate. They're individual constants.
Quoting Leontiskos
No, none of them will suffice. And that's my point. If you wish to argue that point with me, then make an actual argument. I'll "teach you how to fish" in that sense, if that's what you need. If not, do it yourself, I'm not going to make the argument for your.
A rule of thumb for you: don't argue for things you don't believe are true.
Why not? That's what science does. You argue things that you don't believe in, to see if they hold up. It's called putting a hypothesis to the test, mate. Again, what "Room" is this? At what "level of awareness" do you want to reach an agreement on the issue of Mathematical Platonism? You're being uncooperative and trying to put the blame of un-cooperativeness on me. Well, I'm laying the blame right at your feet. Explain your POV on Mathematical Platonism, tell me why it's better than mine, and be done with it, mate.
Quoting Mario Bunge
Mario Bunge,"In Praise of Intolerance to Charlatanism in Academia", page 96.
I wonder whether you have a response to this, or have you lost interest.
The date Bunge gives there seems imprecise, since much of the philosophy he is higly critical of, such as existentialism and phenomenology, considerably predated 1960.
Right. That's why he says that before the 60's, you would have been ostracized if you were an existentialist or a phenomenologist. And rightly so. That's his entire point.
Bunge hated Hegel, and he hated him publicly as well as privately. That's no secret to anyone. He said that Hegel was a charlatan. He said it in lectures, in books, in press conferences, in the context of a coffee with friends, etc. Do I myself think that Hegel was a charlatan? Not necessarily. I don't agree with Bunge on everything.
As for Husserl and Heidegger, Bunge is speaking from the Analytic tradition. He defends people the likes of Rudolf Carnap, for example. Not Karl Popper, mind you. He thought that Popper was a fraud and a charlatan.
Thanks for checking -- I was sort of assuming you were right. It makes it easier to get a grip on what Witt meant, anyway. Talking about objects being "expressible" doesn't seem on target. I think Witt wanted to say something about what can and can't be said, sensibly. I'm not sure whether, for him, "sensibly" means "using truth-apt propositions," but it seems plausible. And there's the whole self-reflexive question about demonstration versus expression -- when Witt says that certain things can't be said, does he go on to show this or give it propositional expression?
EDIT - I meant, "give propositional expression to the impossibility of something being said."
Fair enough, point taken. Let me try something else instead. Quine famously said that the very reason why Pegasus does not exist is because there is no object or creature in the world that "Pegasizes". In the 50's, someone wrote a paper, asking Quine if President Truman exists because "something Trumanizes", there is an object or creature in the world (i.e., Truman himself) who "Trumanizes".
Those types of words, "Pegasizes", "Trumanizes". What do they mean? What do they express?
That is indeed what he meant. But that is also what Frege meant, and what Russell meant, though each of them had different reasons for it. What are Quine's reasons for even translating this discussion into common parlance when he speaks of "Pegasizing"?
Quoting J
It has to do with this. The existential quantifier, ?, does not have ontological import. Quine is averse to it because he thinks that it does have ontological import. But he's just plain wrong. Deluded, even. Frege and Russell had the same problem. If the universal quantifier, "?", has no ontological import, there is no reason to believe that the existential quantifier has ontological import either, because you can switch these symbols under certain conditions, so what would you make of that, in ontological terms? Nothing, there is no ontology to symbols such as ? and ?. They are not types of predication, they are types of quantification.
I haven't followed Bung, and you provide no reference, so I've no clear idea what he might be saying, but that sounds like a variation on free logic.
That mathematics is "pleasing" looks to be besides the point.
Let me craft an example for you, then. Consider the following statement: "Pegasus conceptually exists in the context of Greek mythology, but it does not really exist in the actual world."
That statement (I've argued this on paper, in an article that I published in a Bungean journal), is troublesome for someone the likes of Frege, Russell, and Quine. All of them would treat the term "Pegasus" as a predicate, no matter what differences they might later have (i.e., regarding the very concept of "Pegasizing").
Bunge's existence predicate manages to symbolize that statement in a very neat way. Like so:
?x((x= p) ? E(gp) ? ¬E(rp)
That formula should be parsed like so: For some particular x, it is identical to Pegasus, and it exists conceptually in the context of Greek mythology, and it does not exist really in the actual world.
Notice that the existence predicate, "E", is a two-place predicate. It binds an individual constant, such as "p" (which stands for Pegasus), and it binds it to a context (i.e., Greek mythology, the actual world, etc.)
I played with your idea of a high C for a while. The supposition was that the high C could be understood - perhaps C6, two ledger lines above the treble clef; but unachievable by a certain musician. We have a clear idea of what that is, even if it cannot be sung by our soprano. Is there a note that no soprano might sing? Apparently the highest achieved is F#8, truly awesome. But again, we know what it would mean for someone to say, sing C9, even if this is never achieved. These are tied to our use of this sort of language.
But is there a highest C? Here we start to leave firm ground. Is there a C higher than any other C? A first approach might be to claim that since for any given C there is a higher C, one octave above, that there can not be a highest "high C". In theses terms the term "Highest high C" doesn't have any referent, and very little sense.
But taking a step further, a high C must travel through a medium, and at frequencies above around 10 Ghz, the separation of air molecules is such that sound fails ton be transmitted. There will presumably then be a particular high C, far beyond anything we might hear, that is the highest C that can be transmitted via air. Higher frequencies might be achieved in other mediums.
Hopefully this digression shows that the context sets limits on the terms being used. Until we have a clear idea of what we mean by "high C" we don't have an answer to questions about what is the highest high C. Similarly, perhaps until we have a clear idea of what sorts of things are ineffable, we don't have a clear answer to the issues being discussed around ineffability. Trouble is, we don't have a way of saying what it is that is ineffable without the danger of thereby contradicting ourselves.
Put in more Wittgensteinian terms, we don't have a clear language game around ineffability. So we end up making one up. And that is fraught with the potential for contradiction.
Anyway, a bit off topic, I supose. Thanks for the reply.
Well, I'm glad we've got that straightened out! :smile:
You might be interested in a recent thread on quantifier variance that tackles this question from number of perspectives.
It's a very small step, though. I'm not sure that it brings us any closer to reaching a general agreement on the status of Mathematical Platonism. It's just a tough debate to have, no matter if you've read all of the literature (well, all of the relevant documents, anyway).
EDIT: But thanks for the link to the Thread on quantifier variance, I'm a fan of Eli Hirsch, but more for his contributions to the Metaphysics of Ordinary Objects (i.e., his concepts of "incars" and "outcars". I don't believe in such things myself, but it's a fascinating debate nonetheless).
By way of continuing the example, here's how I might parse the same sort of thing.
Pegasus is an individual in the domain we are discussing. So not a predicate. We can write ?(x)(x=a) were "a" is a constant that refers to Pegasus. It says very little.
Since it is true that Bellerophon rode Pegasus to Mount Helicon, there is something that was ridden to Mount Helicon, by existential introduction.
Something like "Pegasus exists in the context of Greek mythology, but it does not exist in the actual world" says little more than that Pegasus is an individual in the domain of Greek Myth, but perhaps not in the domain of chairs and rocks. Do you see a problem with such a simple and direct approach?
Note the dropping of the words "conceptually" and "really". They do not appear to be doing anything.
If needed, we could well put Pegasus and Mount Helicon into the same domain, and add a predicate something like "real", and say that Mount Helicon is real, but Pegasus is not real. But that has no implications for Pegasus' existence, as set out. It remains that Pegasus exists, but this amounts to little more than that Pegasus is one of the things about which we can talk - it is an item in the domain.
What I've said here will be misunderstood and augmented by others, but to my eye it dissolves the issue of the OP. Infinitesimals exist, since they can be the subject of a quantification. Pegasus exists, since it can be the subject of a quantification. But neither are the sort of thing you might run into in the street.
And what is going on here is a clarification of what we mean by saying that something exists, made by looking at how a formal language can deal coherently with the problem.
That doesn't chime with my understanding. Did you mean ?! ? But that's not a quantifier.
Quine certainly used quantification, to the extent that questions of existence and reality are for Quine to be answered using quantification. While I think this a but too tight, he's not wrong.
No, I meant the good old, classic ? from first-order logic. Let me show you what the problem is, with the notion that this quantifier has ontological import:
(1) ?x(x = x) - Principle of Identity.
(2) p = p. From (1), by universal elimination.
(3) ?x(x = p). From (2), by existential introduction.
Now, what does that mean? It means this:
(1) Everything is identical to itself.
(2) So, Pegasus is identical to Pegasus.
(3) So, Pegasus exists.
You arrive at the odd result that Pegasus exists. So what's the solution? To treat Pegasus like a predicate? Not at all. You can treat it as an individual constant, as I showed in my last example, while also claiming that it exists only in a conceptual sense, and in a specific context (Greek mythology instead of Aztec mythology, for example), and you can also say that it doesn't exist really, in the actual world. And you can say all of that at once, in the same breath, and with classic first-order logic.
Quoting Banno
And I humbly think he's wrong. Better intellectuals than me have argued this point, I take my cue from them, but I don't simply take their word as one does in a fallacy of authority. I can see the actual reason why he's wrong. Then again, I should be humble, so perhaps I'm wrong.
Becasue I don't think it is.
I must have misunderstood you. You appeared to be saying that Quine had a problem with quantification. He didn't, he had a problem with individual constants, replacing them entirely with quantified variables.
The solution I offered makes use of them, contra Quine, and in accord with Kripke's answer to the sort of problem you presented. Pegasus does exist, which is to say no more than that he is an individual in the domain of discourse.
Quine didn't have a problem with quantification. If that's how what I said came across, then I apologize for the confusion, I did not intend it like that. He did have a problem with individual constants, and I have a bit of a problem with them myself, actually. But Bunge had no problem at all with individual constants, as I hope to have shown.
If I have not responded to this , it's because I'm thinking about what you said, and I want to take my time. You're not exactly asking me a triviality like "What time of the day / night is it over there in Argentina?"
Thanks for clarifying re Quine.
Quoting Banno
Agreed.
Quoting Banno
Agreed. But only for the sake of argument. I've been experimenting with the possibility of treating the term "Pegasus" as a predicate, but in a different manner than Frege, Russell, and Quine. Just an anecdote, mate. Nothing substantial.
Quoting Banno
Right, but it leads to the problem of literally saying that "Pegasus exists", if by that you mean that there is an "x", such that "x" is identical to some individual constant "p", such that "p" stands for "Pegasus". As in: ?(x)(x=p). To me, all that means is that there is an "x", such that "x" is identical to "Pegasus". That's all it means to me. It has no ontological import as far as I'm concerned. It doesn't literally say "Pegasus exists in the real world, as a living horse that has the wings of a bird." It doesn't even say "Pegasus exists". That's not what existence is, in the context of Ontology. At least not how Bunge understands Ontology. And here I take his side. And he's not alone here. Graham Priest, for example, might argue something along those lines as well, I believe. Not that such appeals to authority mean anything, what I'm saying in my last sentences is a fallacy, granted. But I'm just saying, mate. It's possible to make a valid, sound case for it.
Quoting Banno
Of course. But you see, that's what I'm arguing here: semantics. That rule is fine. It's legit, innit. All I'm saying is that it shouldn't be called "existential" introduction. It has nothing to do with the concept of existence, which is something that concerns Ontology, not Logic, and certainly not Mathematics. That's all I'm saying, mate. And some people sometimes make it seem like I'm saying something brutal or whatnot. You know what I'd call it? The "particularizing rule of introduction", or simply "particularizing introduction".
Quoting Banno
You're 100% correct in your interpretation of that statement. And yes, I do indeed see a problem with Bunge's simple and direct approach here. I'm just going on guts, instinct and intuition here, but I think that we should distrust individual constants for some reason. Quine distrusted them. And he was a smart man. I don't care if my argument here is a fallacy. I'm thinking this from the perspective of sound common sense now. Which is not to say that I'm right, but my suspicions aren't unfounded.
Quoting Banno
See, here's where I'm on the fence. I go back and forth on this one. Sometimes I think they do nothing. Sometimes it seems to me that they perform different functions, which, by "existential introduction", as you call it, there would be at least two "things", "x" and "y" such that they are performing different functions. I know this sounds cryptic, I can try to clarify it, if that sounds like something that might add anything positive to this Thread.
Quoting Banno
My only suggestion on this, is that you should be able to say, in first-order language, that Pegasus exists (is an item of) the domain of Greek mythology, to use your vocabulary, and that at the same time it does not exist (it is not an item of) the domain of Aztec mythology. In other words, you need to be able to say that Pegasus is neither in the domain of Reality nor Aztec mythology, etc. Bunge's approach allows you to say exactly that, since his existence predicate is a two-place predicate. But, as I've told you, I'm leaning towards Quine's approach here: like Quine, I simply don't "trust" individual constants like Bunge does. Not that such manner of speaking demonstrates anything at this level of the conversation, mind you.
Quoting Banno
Well I don't know if I would phrase it like that, but for the purposes of the OP, yes, I think you are correct: Pegasus exists if and only if Infinitesimals exist in the exact same sense. Now, if that sense is being "the subject of a quantification", that's where you and me personally begin to disagree. But that is not to say that you have not answered the question in the OP: in my eyes, you have.
Quoting Banno
Exactly, but it can't. No formal language can deal coherently with the problem of the meaning of existence. The concept of existence is not a concept of a formal language. It's a concept of ontology. And ontology is not a formal language. Now, there are some very smart people out there, who work in a place called "The Ontology Room", and they will tell you that there is such a thing as "Ontologese", which is a formal language, comparable to Portuguese as far as the poetics go. Those people, I believe, are wrong. And I take my cue here from someone smarter than me. Whatever the case may be, Ontologese is not a formal language, and there cannot be such language. You either get a formal language (like first-order logic) or a language with ontological import built into it from the get-go (i.e., "Ontologese"), you can't have both. You can't have your cake and eat it too, I would say. You have to choose one or the other, sadly.
"Pegasus exists (is an item of) the domain of Greek mythology" looks to be a round about way to say that Pegasus is a myth. But we can do that without using any notion of existence. I just did. We can add that if something is a Greek Myth, then it is not an Aztec myth, and conclude that Pegasus is not an Aztec myth. All well and good and done without introducing two-placed existential predicates.
Greek myth(Pegasus)
For all x, Greek Myth(x) ? Aztec myth(x)
Hence
~ Aztec myth(Pegasus)
So I'm still not seeing the need for Bung's approach.
I could not follow that last paragraph, my apologies.
But here's the problem. Let's try to translate that to first-order language. You can't. You literally can't. Why not? Well, the closest you could get is the following:
First premise: G(p)
Second premise ?x((Gx) ? (Ax))
Conclusion: ¬A(p)
The second premise is where the problem is at. You can state that premise in higher logics, but not in first-order logic. You can't declare that there's no identity between the variable "x" as the subject of a predication (Greek Myth), and that very same variable "x" as the subject of another predication (Aztec myth). It just makes no sense in the context of first-order logic, it's an error at the level of syntax. It's not a well-formed formula. And I specifically said the following:
Quoting Arcane Sandwich
But we're just squabbling over details at this point. Fascinating conversation, I don't mind it, in fact I love it, but for the purpose of the OP, I already conceded and acknowledged that you have effectively solved the problem: Infinitesimals exist if and only if Pegaus exists in the exact same sense. So, you're right. Now, what that sense might be, is where our disagreement is to be found. But that's insubstantial for the purpose of this Thread and its main objective.
is just
U(x)~((Gx?Ax) & (Ax?Gx))
Looks fine.
Cheers. Good chat.
I don't think it does. It seems to have a missing operator. Take a look:
https://www.umsu.de/trees/#U(x)~3((Gx~5Ax)~1(Ax~5Gx))
Im going to assume you meant the meaning of ?existence as in what the term means, as opposed to the meaning of existence in the more existential, what-is-my-life about? sense. If thats right, can you explain how existence could be anything other than a concept of a formal language? The question connects, surprisingly, with my convo with @Banno about inexpressibility, which Im about to try to continue.
Sure. Existence is an ontological, or metaphysical concept, if you will. It's what analytic philosophers working in the field known as "Metaphysics of ordinary objects" study and discuss. In doing so, they use formal languages, most notably second-order predicate logic, and I'm averse to it for personal reasons (which are theoretical in nature), which is why I prefer to translate anything that is said in second-order language into first-order language. But that's beside the point. The point is that existence itself, not the concept, but existence itself, is a physical "thing", if you will. And in being a physical "thing", it cannot be formal. Now, there are some metaphysicians who dispute that last claim that I made, but they do it for metaphysical reasons. They will argue that forms are really out there in the world, that they're not just "in your mind" or "in your formal language". So it's a metaphysical debate. It's the same debate, more or less, about the literal existence of quantities in the objects themselves, which is the same debate regarding Natural numbers: do they exist in Nature, in some sense? Are they "out there", like apples and trees are? That's the actual "existence debate", as opposed to the debate that people have regarding the concept of "does the existential quantifier have ontological import or not?"
Not sure if anything that I said there was of any help. I can quote some books by smarter people than me, if not.
Thanks, I see where you're coming from now. I think equating "existence" with "physical 'thingness'," no matter how many scare-quotes we use, is debatable, though not for the reasons you suggest. I don't know whether forms or concepts are really "out there," but I'm pretty sure that the term "existence" only takes on meaning when given the sort of contexts you and @Banno are discussing. But what about Existence?!, we of course want to know. Yes, well . . . that takes us out of the Philosophy Room entirely.
Does it? It just takes us out of the Math & Logic Room. We're in the Ontology Room when we discuss the topic of existence from an ontological POV instead of the limited POV of formal languages in general (as in, both math and logic). Ontology, simply put, is done in ordinary language. Literally. You are of course within your epistemic rights to utilize formal languages as tools, just as the professional physicist uses math and logic merely as formal tools.
Your exploration of the high-C example is helpful. I know it was my own example, but I'm no longer happy with it because I don't think it's to the point of what Witt meant. What you write above puts it quite well -- words like "inexpressible" and "ineffable" and "indescribable" run a double risk. Not only are they like fly-paper for the flies of ambiguity, but there's a legitimate question whether even merely indicating or pointing to the inexpressible makes it no longer inexpressible.
Staying with that last point (which was the one I originally indicated doubt about), we still want an example. Two possible paths to take: We could try to state (try to!) what Witt himself had in mind when he referred to "that which cannot be spoken." I do not believe he was only making a formal point. I think he had a large range of such items in mind, having to do with values, God, and bedrock metaphysics. We could also take your suggestion about how such expressions are used in ordinary language. This dovetails with a theme that @Arcane Sandwich has taken up: whether ontology can be sensibly expressed in ordinary language.
I'd like to hear your thoughts about what might be "inexpressible in Wittgensteinese." And as an example of common usage, how about this: "We have a sense that life has a purpose, a meaning, that there is more to my existence than birth and death. But what that deeper sense may be, we find impossible to express -- not because it is incoherent, but because we don't know how to conceptualize what it is we are intuiting when we speak of 'the meaning of life.'" Might this be an example of something that's more or less describable, yet remains inexpressible?
My own view on that topic is actually far more extreme that what you said, and that's precisely why I'm suspicious of my own view. I shouldn't feel so strongly about this issue, but I do, and that makes me suspicious of myself, if that makes any sense. Anyways, here's what I would say: ordinary language is the only language in which ontology can be sensibly expressed. In other words, ontology cannot be done within the context of a formal language alone, be it math, logic, or a combination of both. You can utilize math and logic, you are free to do so because formal languages are mere tools, that's what they are to the professional physicist. Mathematicians and logicians do not automatically get the last word in matters of ontology "just because", without any reason.
What we are using a thing for shapes how we perceive the constraints and affordances offered by that thing. If we understand what a computer is for , then we perceive the properties of that computer and how those properties shape what we can do with it in terms of speed, memory, screen brightness, quality of manufacturing, etc. If we have never heard of a computer, and find one on the side of the road, we will not consider the tower, screen, mouse and printer as even belonging to the same thing. We may then use the tower as a doorstop, and then its properties will appear to us in terms of its weight, ability to grip the surface its placed on, and other considerations relevant to effective doorstops.
A series of connected lines and curves made out of sticks doesnt shape what we do with the this object all by itself. What we do with it may involve interpreting it as a string of letters that form a meaningful sentence, if we read that language. Or if we dont recognize that language, the stick objects may appear as random collection of shapes. In either case, what the object is and how it shapes us is a function of the role it plays for us a system of meaningful references tied to useful purposes. In order to decide that a screwdriver drives screws better than it scratches ears, we have to already know about not only the role of a screwdriver , but that of screws and the surfaces that screws fit together, the role of these fitted surfaces in a construction project, the role of the construction project in relation to a finished building or machine, the role of that building or machine in our activities, and so on. What makes the screwdriver a screwdriver for us is not inherent in the object all by itself but in this totality of chains of in order tos that belongs to and on the base of which it was invented.
Do the world, and truth, impose themselves on how we deal with things? Yes, but only in and through how we deal with things.
I believe that @Banno has solved it. Infinitesimals exist if and only if Pegasus exists in the exact same sense. What we're debating now, at page 11 of this Thread, is what that "exact same sense" is. And my wager is that it cannot be solved in the language of first-order logic, or any other formal language, including mathematics.
The case I'm making here, folks, is a simple one. It's what's known in the literature as a "parity argument":
First Premise) There is no epistemic difference between the epistemic rights of professional physicists and the epistemic rights of professional philosophers.
Second Premise) If so, then: if professional physicists are within their epistemic rights to claim that math and logic are just mere tools, then professional philosophers are also within their epistemic rights to claim that math and logic are just mere tools.
Third Premise) Professional physicists are within their epistemic rights to claim that math and logic are just mere tools.
Conclusion) So, professional philosophers are also within their epistemic rights to claim that math and logic are just mere tools.
I claim that the preceding is a logically valid argument. I also claim that all of the premises are true, which means that the conclusion is necessarily true as well.
Does anyone wish to resist this argument, or do you agree with it?
EDIT: Here is the logical form of my argument, using Propositional Logic:
1) p
2) p ? (q ? r)
3) q
4) r
There are no restrictions on what a person can claim unless it's a religious environment and people are executed for saying the wrong thing.
What do you mean by that, @frank? I mean, in relation to the topic of Mathematical Platonism, formalism, and ontology? I don't get it. Can you explain it to me like I'm simple-minded?
This needs a lot of expansion. What exactly is at stake with this premise?
I just meant physicists and philosophers can claim whatever they like. The idea of rights isn't needed.
It means that it's an "all or nothing" deal, whatever we mean when we speak of "epistemic rights". Whatever they may be (the epistemic rights), there are only two options:
Option 1) Physicists and philosophers both have them, or
Option 2) Neither physicists nor philosophers have them.
There is no Option 3. At least not to my mind. And if you wish to deny the premise that you asked for expansion, you would have to argue that there is indeed an Option 3. What would that be? That there is an epistemic difference between physicists and philosophers.
(edited for clarity's sake)
It is for my argument, frank. I would like to have a better argument, but I don't. I'm all ears, though, if you have a better idea.
They're meant to be rights. Letter of the Law versus Spirit of the Law and all that. Define them however you want. They're something that physicists and philosophers have in common, and it's what allows them both, to say, at the same time and in the same sense, that math and logic are just tools. They have no ontology built into them as formal languages. The existential quantifier doesn't really say anything about existence, just as the universal quantifier doesn't say anything about existence. You can even switch one for the other under certain conditions, as I've shown in my example about the "existence" of Pegasus.
just means (it seems to me)
"To avoid rabbit holes, do this: read 'there exists some x such that' as 'at least one of the x among the set of all that exist is such that' ".
I.e. the sentence (following) isn't about whether some particular thing exists but about some particular existent thing.
This might not be a perfect method of staying above ground, but replacing 'the set of all that exist' with anything else isn't following the method.
E.g. replacing it with 'the set of all elements of this or that fiction' is trashing the method.
Try
https://www.umsu.de/trees/#~6x~3((Gx~5Ax)~1(Ax~5Gx))
But then you reach a problem, mate. You can't deduce ¬Ga from ?x¬((Gx?Ax)?(Ax?Gx)). Here's your argument:
First premise: Gp
Second premise: ?x¬((Gx?Ax)?(Ax?Gx))
Conclusion: ¬Ga
But your two premises do not entail your conclusion. See for yourself: https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ga
EDIT: Whoops, sorry, you do ineed reach your conclusion, which is not ¬Ga, but ¬Ap instead. Yep, you have a valid argument, mate: https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ap
Quoting Banno
It'd be
https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ap
So, as I think you agreed, the answer to 's question is that infinitesimals can be the subject of a quantifier, and in that way, they exist; they can be in the domain of discourse. If there is something more to their existence, some "platonic" existence, then it's up to the advocates to set out what that amounts to.
Indeed you have. I had been harboring suspicions about that part of Bunge's work myself (and about other parts of his work, but those are beside the point being discussed here). I'm not sure if I'm sold on the Kripkean-esque part of your proposal, though. I just don't know. I've done some experiments with treating individual constants (i.e., "p" for "Pegasus") as predicates (i.e. "P" for "is Pegasus"). If I say that there is an x, such that x "is Pegasus" in a predicative sense, like so:
?xPx
what would I be committed to, exactly? Does that formula commit me to the claim that the symbol
? has ontological import? I don't think it does. All it means is "a particular thing, x, is Pegasus in a predicative sense). Now what does the predicate "is Pegasus" mean? Does it mean that x performs the act of "pegasizing"? I don't think that's a sound thing to say, so Quinenians will have to excuse me here.
Quoting Banno
But I disagree with that for metaphysical reasons. To exist, in my opinion, is to have a spatiotemporal location. Pegasus does not have a spatiotemporal location. Where is it? Where is it located? Or, you could say that to exist is to have some kind or type of energy, such as potential energy or kinetic energy. Or thermal energy, or nuclear energy, or what have you. What kind of energy does Pegasus have, being a fictional object? I don't think it has any. So, I don't agree that existence is somehow a matter of words or even language more broadly. It's independent of language.
Quoting Banno
Exactly, 100%, couldn't agree with you more on that point.
You'd like me to set out what sort of things re inexpressible? To give reasons for the ineffable? To answer for Wittgenstein the question I asked you? :wink:
Well, why not. Trouble is, it'd be a thesis, not a post. Indeed, a series of theses.
I read the Tractatus as saying that things can't be said - It's propositions that are said, "the world is what is the case"; there are things only in so far as they are the subject of a proposition - a view few others seem to hold nowdays, but it fits his notion of logical atomism. Hence the extended discussion of proper names in the earlier part of the last century. That's probably salient to the nascent discussion of Bung and Kripke.
And values are not said, so much as enacted. Ethics is about what we do, which is why he has so little to say about it. Instead he worked as a hospital orderly and watched cheap crime thrillers.
Hinge propositions are said, but never quite rightly. "Here is a hand" isn't justified, at least not by other propositions. It's shown. "If you do know that here is one hand, we'll grant you all the rest".
So I keep coming back to PI §201. What's not expressible may nevertheless be enacted. Not just in following a rule, but in using language, deciding what to do, and generally in what he called a "form of life". You don't say it, you do it.
Any comments, @Sam26? I suspect this is an older reading of Wittgenstein than is popular now.
That's good, as far as it goes. But the other kind of "more" that some philosophers (I think including @Arcane Sandwich?) want to claim is physical or spatio-temporal existence. I think we agree that quantification is agnostic about that, as it is about platonic existence. So is there a case that can be made for preserving the term "existence" for that sort of thing? I'm saying no -- that this is still trying to privilege a particular word and make it do something we don't need it to do. We understand the concept of "something in space-time" -- isn't that good enough? Why do we need to praise it by additionally saying it "exists" in some superior way -- so superior that it casts doubt on whether other non-spatio-temporal items exist at all?
Quoting Banno
Let's lean into that a little. "Here is a hand" is certainly expressible. It's a proposition that states a fact about the world. You now say of it, "But it isn't justified by other propositions." Fair enough. Have we reached inexpressibility -- what "can't be spoken"? How, exactly? Is it the alleged justification that is supposed to be inexpressible? That doesn't sound quite right. I would have thought the (propositional) justification was simply absent or non-existent, rather than inexpressible.
Or is this a blind alley? I may not yet be quite seeing the expressibility problem here.
Yes, that is indeed the case. And I will say something even more extreme: there is no other existence than spatiotemporal existence. To exist is to exist at some place, and at some time. Does it have to be a precise, clear-cut spatiotemporal location? No, not at all, since you need to take tiny quantum objects into consideration, and it's a bit of a tough thing to do to pinpoint the exact location of those tiny "jiggly-things".
But yeah, to exist is to be somewhere at some time, like this rock on the floor. Is that a fallacy of appealing to a rock? To me that's just good common sense.
@Arcane Sandwich has agreed with a part of what I had to say. He focused on that we can treat them as individuals in virtue of being able to quantify over them. I also suggested that numbers are more something we do rather than individuals, although we can treat them as individuals. See . So I agree that they are not physical, and add that we can show how they nevertheless come to be treated as individuals by quantification. It's a "counts as..." thing, an act performed in language. These are of course things that exist but are not physical. Money and property and so on.
Quoting J
Asking someone to justify "Here is a hand" is inane in that it misunderstands what is going on in the illocution. In a way "This is a hand" is like "This counts as a hand", it's not part of the language game so much as setting up the language game. But Moore wanted to go a step further, wanting to use the illocution to demonstrate that the world exists. This is the step too far that Wittgenstein examines. Moore takes himself to having proved that there is a world, but rather, that there is a world is already supposed by his demonstration. It's not that Moore has proved the existence of a hand, but that treating this as a hand is what we do. And that doing is not expressible, but, to paraphrase PI§201, "What this shews is that there is a way to grasp that this is a hand which is not a conclusion, but which is exhibited in what we do in actual cases"
And that is not expressed, but performed. Ineffable, yet understood.
How's that?
And he succeeded, in my honest opinion. Like, what more do you want? Good common sense is suddenly not a respectable epistemic framework? Well I mean you should take a look a the amount of bullshit that passes around these days as far as "respectable" epistemic frameworks go, and they're nowhere nearly as good, as sound, and as reasonable as common sense. Like, philosophers begin with a completely demented question (i.e., "How do you know that you're not a disembodied brain in a vat that is hallucinating?") but they expect, nay, demand a reasonable answer to their demented question. Like, here's a hand mate, what are you talking about? Why should I take your nonsense seriously to begin with?
Well, he wasn't wrong.
Then what are we even arguing about? I mean, let's keep this on track, we're talking about quantities and numbers. Do they exist? As in, did you learn this stuff in school? Sure mate, they exist in that sense. I can imagine the number 3. That doesn't mean that they exist in the same sense that this rock on the floor does, and if the fallacy of appealing to a stone is such a sin, then by God send me straight to Hell for all Eternity, because what you call "appeal to the stone" I call good common sense.
Phew... I really should chill out.
Are we arguing? I thought we were agreeing.
Quoting Arcane Sandwich
Numbers exist. 2 is a number, therefore there are numbers. But it is difficult to make sense of the idea of 2 existing only at some place and some time.
I'll grant, at least provisionally, that to be physical is to exist at some place and some time. As good a definition as any. But there is a difference between existing and being physical.
Quoting J
I'd be inclined to say yes. You? I suppose we could quibble about whether your account, above, really counts as an explanation, but I think it does. It's certainly an elucidation. Nor do I see us falling into the contradiction dilemma; we're not saying "ineffable" with one mouth while making it effable (is that a word?!) with the other.
What? Let's formalize the argument a bit:
First Premise: Numbers exist.
Second Premise: 2 is a number.
Conclusion: Therefore, there are numbers.
What? I'm not buying it. I'm not even sure that's valid, deductive reasoning. But let's suppose that your argument is somehow valid. Then I'll just deny the First Premise, mate. Technically speaking, numbers don't exit. You can pretend that they do, but they don't. If you say something insane and wild from an ontological POV, a statement like "Numbers exist", I'll tell you one of two things:
1) That no, numbers don't exist. Or:
2) That they exist in the same sense as Pegasus, or any other fictional entity. As in, they don't exist. So here's where Bunge would step in and he would say "Right, but people need to believe in something. So, let's talk about "conceptual existence" and "real existence". To exist conceptually is to be a part of a conceptual context, such as Greek mythology, or Euclidean geometry. And to exist really, is to be a mereological part of the world. This is where I disagree with Bunge. I believe that to exist is to have a spatiotemporal location. But I'll just quote you my favorite quote of his, to see what you make of it:
Quoting Banno
In that spirit, we haven't explained its inexpressibility as much as exhibited it.
There will be plenty of folk who say Moore has proven that there is a hand, and others who say he has done no such thing, just as there are folk who see the duck but no the rabbit.
Me either. It should be
2 is a number
Therefore there are numbers.
Hence numbers exist.
Which is an instance of f(a) ? ?x(f(x))
I thought we'd agreed on this.
But like, mate, you know what we're arguing right now? As in, right now at page 'effin 12 of this thing? Here's how I would describe it: we are debating the semantics of the rules. Like, I told you what I think, I gave you the example of Pegasus:
(1) ?x(x = x) - Principle of Identity.
(2) p = p. From (1), by universal elimination.
(3) ?x(x = p). From (2), by existential introduction.
Now, what does that mean? It means this:
(1) Everything is identical to itself.
(2) So, Pegasus is identical to Pegasus.
(3) So, Pegasus exists.
So, I ask you, have you seen a flying horse somewhere, mate? Of course you haven't. And that's my whole point. Like, here's a hand mate, here's a Moore-like argument that refutes solipsism. Now, that's not a particularly difficult thing to do, ey. To refute solipsism, that is. Again, here's a hand, mate. It's not a big deal. There are more important things to discuss. For example, do mathematical entities exist? Like, literally, outside of space and time themselves, structuring Reality itself? That's what a fan of Max Tegmark would say and I think he's wrong. Tegmark is wrong about that, and anyone who agrees with Tegmark about that is just plain wrong. And I have the right to say that. Nay, I have the epistemic right to say that, just as much as any professional physicist. That's how I would phrase it.
If folk want to say that, in addition, Pegasus is in the stables down the road, it's up to them to present their case. If they want to say that primes have physicality, it's over to them to show how. If they claim that infinitesimals exist in the "Platonic"sense, then they can explain what they mean.
But we can all affirm and agree that there are numbers.
But if they want to point out that, literally and unequivocally, Pegasus and numbers don't exist, it's up to you to explain how this
Quoting Banno
isn't equivocal.
"Apples and trees"a number of apples and treeshow many? So of course, number is out there if apples and trees are. So, number is out thereare numbers out there? That's a different question, no? Is 5 out there over and above all the collections of five objects? Is 5 out there in the sense that digits and numerals areas written or spken?
No, I would say that you have argued well for the existence of natural numbers, like 1, 2, 3, 4, etc.
But then we need to talk about fractions, and then, the number Pi, and then, the square root of minus one, etc. I would draw the line somewhere, but I don't know where. Maybe there is no line to draw, as in, maybe it's an "all or nothing" deal.
Are we in agreement? Might be a first!
I don't knowI could be talking shit.
No.
What bit of your post is where you think we differ?
That was my impression.
Quoting Banno
Oh, you!
Quoting Banno
About you equivocating between fact and fiction. I suppose that does sound like us.
Where?
Quoting Banno
So, is that the same as admitting that Pegasus is fiction, and doesn't literally exist? Or not?
Quoting J
The posts on the last couple of pages make an excellent argument for my case. What would happen if we tried to reframe the "existence" question in terms of structure, grounding, and quantification, retaining full rights to claim metaphysical truth, but did so without once using the term "exist"?
But, my perhaps ignorant question would be, why would you do that? The concept of existence should be retired from the field of mathematics and logic, I can agree with that (and I actually do). It does not follow, however, that it should be retired from metaphysics, to say nothing of ordinary language.
The words "exist" and "existence" cause nothing but trouble, because they call like Sirens to philosophers, inviting us to argue about which use of the word is correct. "My use is correct!" says one group, "because when I use it, I mean concept A." "No, my use is correct!" says another group, "because when I use it, I mean concept B." "Well, Plato used it for concept A." "Well, Kant used it for concept B."
Oh dear, which concept is the right one to be called "existence"? The answer is, Neither, none, because the word doesn't matter. What matters -- and it matters a great deal, if you believe metaphysics is worthwhile -- is getting straight on the conceptual territory, on concepts A, B . . . n. But you can do that with any vocabulary you please. So pick one that doesn't bring 2,000 years of ambiguity and dispute along with it.
But, you see, this is my argument. Ordinary people philosophize from time to time. How could they not? Everyone does. But we, as philosophers, have a responsibility towards them, because, like it or not, they are indeed our colleagues when they philosophize. We have the moral responsibility to vindicate their use of the very "word" existence like they mean it in ordinary language, as something that rocks have and that winged horses from Greek mythology don't. That's on us, philosophers. We have to explain why appealing to a rock is not a fallacy, why it's not fallacious to rely on good common sense in all matters, not just the ones involved in ordinary life.
That said . . . is it genuinely helpful? A great deal of damaging nonsense on this subject is spoken in the name of "good common sense," which too often means "ways of thinking that are common to me and the people who share my views." People who think only physical stuff exists -- materialists, in other words -- are the same people who often want to say that "rights" and "truth" and "justice" also don't exist. What they believe exists may influence them on issues from abortion to contract law. I know, it looks very unproblematic to point to Pegasus vs. rocks, and if that's all one ever needs the concept for, I guess no sweat. But if we really have an obligation to help clarify thought when it gets difficult, then we can't stop there.
My other response also refers back to what's "good common sense." I dunno, is it really your experience that the average non-philosopher you know is quite settled in the opinion that rocks exist but numbers don't? I get into a fair number of semi-philosophical discussions with friends and acquaintances, for obvious reasons, and when they're not ordering me a cup of hemlock, they seem to be very alive to why this question of what exists is not cut and dried. They also seem to move quite quickly to noticing that it looks like a terminological dispute. So again, I think we should be really wary of invoking a notion of common sense that may not stand up under inspection.
So wouldn't what you say provide reason for going in the other direction - for showing that rights and truth and justice do exist?
He's wrong about that, in my humble opinion, Banno. He's right when he says that most materialists are like that, but not all of us (materialists, that is) deny emergence in an ontological sense.
Quoting J
I'm a proponent of Emergent Materialism, more or less how Bunge has articulated it throughout his publications. And, as a materialist, I can confidently say the existence of rights, truth and justice is not incompatible with the materialist premises and conclusions of my philosophy.
EDIT:
Quoting Banno
My thoughts exactly.
Good! But that must mean that "existence" is being given a much broader interpretation than "made of material stuff." So here we go again . . .
Existence, in my philosophy, is what has a spatiotemporal location. It has nothing to do with the concept of "being made of material stuff". To be material, in my philosophy, is to be able to change, at least with regards to position in space and moment in time. So you see, existence and matter are not the same thing. True, I hold that material objects, and only they, are the ones that exist. But that does not mean that existence is the same thing as the plurality of material objects that we call "the Universe".
EDIT: In other words, I believe that existence is a property of material objects. And it just so happens that only material objects have that property. Fictional entities like Pegasus do not have that property.
I've had years of dispute on this forum about the meaning of the term 'ontology'. At one point in the past, etymologyonline.com had the etymology of the word derived from the present participle of the Greek verb 'to be' - which is, of course, 'I AM'. (Regrettably that detail is now no longer extant at the source.) I seized on that detail to argue for the distinction between ontology qua probing the nature of being, and natural science, qua probing the nature of what exists. I used this as a kind of wedge to distinguish 'being' from 'existence', which I think is a fundamental but generally forgotten or neglected distinction (although C S Peirce recognised it, as he held to a form of scholastic realism and insisted that universals are real.)
One of the previous mods, also a very active contributor, disagreed violently with me about this (although he had a tendency towards violent disagreement with many people which eventually led to his being banned.) Anyway, he posted a link to an article which is apparently a classic in respect of that question, The Greek Verb to Be and the Problem of Being , Charles Kahn, which I've read very carefully a number of times. And I think it supports my general contention about this distinction. Which leads to:
Quoting Arcane Sandwich
The generally Platonist objection to that would be, what, then, of numbers, logical and scientific principles, and so on and so forth? In what sense to these exist? That has been the subject of this thread the last couple of weeks, and I think it's by no means settled.
My heuristic, and it is only that, is that numbers, laws, etc, are real but not existent as phenomena. They do not appear amongst phenomena, but can only be discerned by the intellect (nous). So they are, in the Platonic sense, but not the Kantian, noumenal objects, object of nous. Of course, we rely on them automatically, transparently, and continuously, in the operations of discursive thought, whenever we make inferences or judgements. But the elements of those judgements do not, themselves, exist in the way that tables and chairs and Banno's beloved crockery exists. Without them, though, we could not even converse, let alone pursue philosophy.
This, to me, is starting to step in the right direction, because with this distinction we're at least no longer asking "existence" to do more work than it can handle.
OK.
Quoting Arcane Sandwich
OK.
Quoting Arcane Sandwich
But now you've lost me. Is this a coincidence? You've said there's no definitional relation, so how and why does this relation obtain?
Only that the sense of 'is' implicit in 'A=A' seems of a different order to that conveyed in 'The cat is on the mat' or 'that apple is red'. In mathematics, "is" (or the equals sign) denotes a relationship of equivalence or identity with absolute precision (e.g., A=A) reflecting the necessary and universal nature of mathematical truths, which are immune to the vagaries of empirical or contextual variation.
Such expressions are intelligible objects belonging to the domain of the noumenal.
In natural language, "is" has a broader and often less precise function. It can indicate:
Predication: "The apple is red."
Existence: "The cat is on the mat."
Identity: "Hesperus is Phosphorus."
These uses depend are context-dependent, and the precision of "is" in natural language is correspondingly far less than in mathematics. Empirical judgements are always in some sense approximations.
The apodictic nature of mathematicsits reliance on axioms, proofs, and logical necessitywas seen as a model for how scientific knowledge should be pursued.
(For that matter, isn't a large part of the astonishing success of science since Galileo owed to the way in which science learned to harness empirical observations to mathematical logic, through the quantification of primary qualities?)
Polysemy of 'being' - At the beginning of the Metaphysics. Aristotles recognises that "being" is said in many ways. Disambiguating and differentiating these meanings becomes foundational to his metaphysics and has had a major influence on the Western philosophical tradition.
The fact that this nuanced understanding of "being" is often overlooked today, except in the formalized context of analytic modal metaphysics, is a significant commentary on the state of contemporary philosophy.
In the Metaphysics, Aristotle identifies multiple senses of "being," which include:
* Substance (ousia): The primary sense of being, referring to what a thing fundamentally is.
* Qualitative Attributes: Being in the sense of having certain properties (e.g., "the apple is red").
* Existence: Being in the sense of "being there" or existing in time and space (e.g. "the apple is on the table")
* Potentiality and Actuality: Being as a dynamic process, involving what something can become versus what it is. (Heisenberg, in his interpretation of quantum mechanics, recognized Aristotle's concept of 'potentia' as a useful way to describe the indeterminate states of subatomic particles before measurement.)
Now on this understanding, the question is not "Is there something that is not covered by these but is available in being or existing?" We've stipulated that the conceptual ground is indeed covered. Rather, the question is "Will it ever be helpful to use the words 'being' and 'existing' to talk about this ground?" Again, notice how much depends on separating term from concept. We want maximum fidelity as to concept and maximum flexibility as to term. So, to my amended version of your question, I would reply, "Sure, it's quite possible. Let's find out. Let's read Heidegger. But what we mustn't do is mistake the question as being about additional conceptual territory. If we do that, we fall once again into the endless battle about what counts as Existence. No, we are asking a terminological question."
Final thought: This is all based on: "for the sake of argument, the three first-order translations, taken together, describe the conceptual territory covered by 'exist' in loose talk." They may not, in which case an entirely different conversation will occur. Here the friends of Existence and Being have the task of convincing us that the issue is conceptual, not terminological.
If by "coincidence" you mean something like an atheist version of occasionalism, then I would say no. It's not a co-incidence, as if two "things" were "inciding" with each other somehow. Let me just go back to my definitions (as in, the context of my personal philosophy):
Existence: it is a property. It is something that material objects have. It is the property of having a spatiotemporal location (which can be fuzzy or clear-cut, it doesn't matter).
Matter: it is not a "stuff", and it is not a single object (i.e., a universal "blob"). Let me explain it like so: to exist is to have a spatiotemporal location, and to be material is to be able to change. I need the concept of matter (in my philosophy) in order to be able to explain why things can change (at the very least, their current spatiotemporal location). Otherwise, you end up with a Parmediean universe. Someone from the school of Parmenides (like Einstein, arguably) will tell you that there is no movement, no change. In other words, a Parmenidean would agree with my definition of existence: it is the property of being in a place and at a time. But then she would disagree with my definition of matter: she would say that nothing changes, that spatiotemporality is in some sense eternal, we are not really moving in our ordinary lives, we just can't see the truth of the immobile, Parmenidean Being, etc.
My response to the Platonist there is that numbers, logical and scientific principles, and so forth, have the same ontology: they are all just concepts, which means that they are fictions, which means that they are brain processes occurring inside the living brain of a member of the biological species homo sapiens. And I mean that as a metaphysical and scientific statement at the same time. This is textbook Bunge. Which doesn't mean that he's right, since he could be wrong. I'm just saying, I didn't invent this part of my personal philosophy, I simply take this part from Bunge. I'm willing to discuss it rationally and scientifically to see if I have to abandon it, not doubt about that. But anyways, in Bunge's ontology there is a difference between what he calls "conceptual existence" and "real existence". Conceptual existence, according to him, is what the number 3 and Pegasus have in common: they only exist as fictions, which is to say, as brain processes. On the other hand, this stone on the floor and this table in my living room both have the property of real existence, even though the former is a natural object and the latter is an artificial object. How does Bunge define "real existence"? He thinks that real existence is a mereological property. One of his Postulates is that the Universe itself is identical to Reality itself, and that it is the Largest Thing of all. It is the largest Individual in a metaphysical sense, and it is the largest Whole in a mereological sense. To have real existence, he then says, is to be a mereological part of the Universe, because the Universe is Reality itself. And that is where I disagree with him (I also disagree with him on other topics): I don't think that the Universe is a single object, I think it's a plurality that composes no further object. So, my definition of existence, unlike Bunge's, can't be mereological. I agree with Bunge when he says that existence is a property. But I claim that it's the property of having physical spatiotemporality, not the mereological property of being a part of the largest whole.
Quoting Arcane Sandwich
I like what you, and Bunge, have to say about numbers being fictions created by the brain (idealizations a might be a better word than fictions). But how can we assign a reality to the universe independent of such brain processes consisting of spatiotemporal localizability? Isnt the notion of spatiotemporal localization based on a mathematical
abstraction?
Well I mean, if you want to get technical about it, it has a lot of math to it, but it's ultimately within the domain of what physicists study. To them, math and logic are just tools, they have no ontology. Physics is the academic discipline that deals with the ontology of the world, not math. I don't expect you to agree with that idea, I'm not so sure that I agree with it myself, but that would be the "Bungean" answer to your question, I suppose. It sounds like a fallacy to me, but that's the best I got in relation to your question.
Quoting Arcane Sandwich
I think math is more than a tool for physics. Physics deals only with those aspects of the world which are mathemetizable. The objects of physics are based on geometric idealizations such as space and time. These are presuppositions imposed on the world by physics rather than emanating from the ontology of the world. Forgetting the role such presuppositions play leads to such confusions as Wigners famous paper on the unreasonable effectiveness of mathematics in the natural sciences.
But that's my point: there are aspects of the world which are not mathematizable. They're called objects, in the literal sense of the term. They are "out there", outside of our brains, they are what Descartes called res extensa. We ourselves are a res extensa. But it does not follow that we are not also a res cogitans in the Cartesian sense. We are both. Our body in general, and our brain more speciffically, is a Cartesian res exstensa and res cogitans at the same time. So, by grammatical simplification, you can remove the word "res" from both of those terms. What that leaves you with, is two "disembodied" predicates: just extensa, and just cogitans. And the argument here, is that there is something to which the predicates extensa and cogitans apply. So, there is something. That something is the brain as a res extensa, and as a physical body more generally, which is physically related to other physical bodies, some of them containing human brains just like yours, just like mine. And the brain is the object to which the predicate cogitans applies as well. One thing (the brain), two predicates (extena and cogitans). The brain is a thing, but the mind is not a thing, the mind is simply what the brain does, in the same sense that digestion is what your gut does. Your gut is the object (the res extensa) in that case, but your digestion is not: your digestion is a process that your gut undergoes (it's more complicated than that, biologically, but that's "how this works" at the basic level of ontology)
Quoting Arcane Sandwich
Res extensa forces onto objects the concept of persisting identity, which is also the basis of enumeration.
Heidegger explains:
Heidegger argues that the fundamentally undiscussed ontological foundations of empirical science since Descartes are based on his formulation of objective presence. Just like number, the notion of pure self-persistence is a fiction applied to the world.
Do I agree with this? I'm not so sure. Let's see what Heidegger has to say, in those passages that you quoted.
Quoting Joshs
Does he argue that? I'm no so sure that he does. But let's continue. You then say:
Quoting Joshs
I don't think so. I think it's an objective feature of the world. The world was already like this, before I was born. And it will continue to be this way, after I die. And currently, it is that way, the fact that I'm alive has nothing to do with it, and since my mind does not live by itself (it requires my living brain), the world simply is that way tout court, so to speak. So, Heidegger (and you) are simply wrong about that. At least that's my opinion. I could be wrong, of course, but I don't see how anyone could possibly make a convincing case for it, let alone state it as an argument (i.e., an exclusive series of true premises that deductively entail a conclusion).
What is Heidegger saying there, in your honest opinion?
Or just explain this part to me, @Joshs, what does Heidegger even mean by that? I genuinely don't get it. And I studied Classical Latin at the Uni for one semester. "Remanens capax mutationem"? What does that even mean? Is there any textual evidence to back this sort of claim up? Like, is that an actual phrase from ancient Roman times, yes or no? I think Heidegger wants to imply that it is, but I'm arguing for the opposite point of view here.
EDIT: According to Google Translate, "Remanens capax mutationem" means "remaining capable of change" in English, and "Siendo capaz de cambiar", in Spanish. That doesn't make any conceptual sense to me, so I doubt that it many sense for anyone other than Heidegger himself.
Quoting Arcane Sandwich
I assume he means , that which truly is is that which remains self-identical in its substantive qualities as it undergoes quantitative change in spatial or temporal location. Im with Heidegger here. I dont believe there is anything in the world which retains its exact qualitative identity over time. It just appears to us as if this is the case because things can remain SIMILAR to themselves over time, and thats why we invented number (same thing, different time).
Yeah sorry, I genuinely don't understand that. It sounds like Heidegger and you are on to something there, but I don't know what it is. That's always been the case with Heidegger and I. It was even like that for himself, since the literal reason why he didn't write the conclusion for Being and Time is because he didn't have the language to do such a thing.
And his point was, that no one does. However -what follows is extremely important, if you're a Heideggerian (which I'm not)- that situation has historical limits. It's not a static thing. It changes. Think of it like Hegel's Absolute Spirit marching through History, think of it more like that. At least that's how I read it, but I could be wrong, of course.
I baulk at your distinguishing "conceptual" from "terminological". Our terminology sets out our "conceptual framework" as it were.
"A is at (x,y,x,t)".
Therefore something is at (x,y,x,t).
But ? is not at (x,y,x,t); are you willing to conclude that ? does not exist?
There are genuine problems with treating existence as a property, some brought out in free logic, some accounted for in ordinary first-order logic. There are reasons that quantification is different to predication. Reasons first order logic works with "?(x)" and not ?!x. Foremost are perhaps the difficulties in applying extensionality to existence if it is treated as a predicate.
Extensionality is simply the idea that if two predicates range over the same individuals, they are the smae predicate. If f={a,b,c} and g={a.b.c} then f=g. If we allow ?! to be a predicate of this sort, then does it includes everything? What things are not in ?!? The elements of ?! are the domain of discourse.
I don't know how Bung deals with this, but in free logic is leads to there being two domains, one of things that exist and one of things that do not. And it gets a bit weird.
So if ?! is a property, it is not like (f,g,h...) and the other properties of first order logic.
There's a simple argument to show that this is not so.
If ? is a brain process in your brain, and also a brain process in my brain, then it is two different things.
But if that were so, when I talk about ? I am talking about a quite different thing to you, when you talk about ?.
This is a cut-down version of the private language argument. ? is not private thin in each of our heads, but a public thing that is used openly to make calculations and settle disagreements.
Right, but that's what I'm saying. Explain this phrase to me: "remanens capax mutationem". Those are Heidegger's literal words, they make no sense in the English language nor in the Spanish language (not if we're being charitable towards them). And those are the only languages that I speak as an individual. I don't speak Classical Latin. But that's how Heidegger "means it", that's the intent of those words. But that phrase itself, never appears in classical documents. Better classicists than me have argued this point quite strongly, and historians back up such claims. So what's Heidegger saying? It's incomprehensible to me. What it means, according to Google Translate, is "remaining capable of change" in English, and "Siendo capaz de cambiar", in Spanish.
And that doesn't make any conceptual sense to me, but it does make grammatical sense. What he's saying is grammatically correct, but semantically meaningless.
Quoting Banno
Pi is like any other word. It is communicated in partially shared circumstances. This circumstance includes your brain processes and my brains processes , along with their embodiment in each of our organisms and the embeddedness of our brains and bodies in a partially shared social environment. None of these aspects
can be neatly disentangled from the others, but the fact that the meaning of pi is only partially shared between us explains why its use by either of us can always be contested by the other.
But that brings back @Count Timothy von Icarus's point about the debate between Rorty and Eco. Things cannot be pragmatism and convention all the way own. That's what Eco said to Rorty. And it's an excellent, sound, reasonable thing to say. Why? Because it's true, that's why.
Quoting Joshs
But that's not quite right - ? refers to the ratio of the diameter to the circumference of a circle; that's it.
Moreover, the idea of meaning as shared is decrepit. Meaning is something we do. Or better, stop looking at meaning and look instead at use.
Quoting Banno
Apparently you dont have much use for practice-based accounts of discursive normativity either.
Quoting Banno
Use determines the sense of meaning , and use is a function of partially shared discursive practices within a community of language users. The definition of pi doesnt determine its sense any more than any rule determines its use.
Quoting Arcane Sandwich
In case you didnt see it , I responded to Count Timothy this way:
https://thephilosophyforum.com/discussion/comment/956726
What Im trying to say is that a description of what pi refers to cannot guarantee that what I do with it is the same as what you do with it. Witt goes over this in his account of rule following.
OK. So is it like a literal "game"? Like, if Wittgenstein speaks of "Language Games", are they really games, from a scientific standpoint? Because there is a science called Game Theory.
Sure.
So what.
I use ? to work out the volume of a water tank. You use it to lay out the design for your garden. We are not here making use of a different thing. You could also use it to work out the volume of the tank.
That you do something different with ? does not suggest that you are using a different ?.
Edit: But this seems to be the implication of your approach. You can disavow that, if you like. It would be good if I were wrong here, since it might lead to some agreement between us.
I don't quite follow your argument. Again, I don't see what I'm arguing as exceptionally obtuse or difficult. The element of Platonism that I appeal to, is the rational faculty - that which grasps real ideas such as number, ratio, etc ('real' I use to distinguish such ideas from the momentary content of individual minds.) This is the basis on which I argue that numbers are real but not phenomenally existent.
Consider a number 7. I ask you: does it exist? Well, yes, you say, you just wrote it on this screen, there it is. But that's a symbol. What is denoted by the symbol is an intellectual act, namely, an act of counting. And that act is not an existent, in the sense that objects are existents. This is where the distinction can be made between the kinds of existence of numbers (etc) and sensory particulars. This distinction is 'Platonic' in that it mirrors the division between sensory (pistis, doxa) and mathematical (dianoia) knowledge in Plato's thought.
This is an heuristic, as I say, not a developed theory. It provides a conceptual framework for distinguishing the phenomenal (the domain of existents) from the noumenal (the intelligible domain). These two are intertwined in our thought, yet the distinction is discernible.
As Brennan explains in Thomistic Psychology, 'the process of knowledge is immediately concerned with the separation of form from matter, since a thing is known precisely because its form is received in the knower. Sense knowledge retains particularity, while intellectual knowledge universalizes. This is why, as Brennan notes, 'to understand is to free form completely from matter. In the same way, the reality of numbers, as universal forms, is grasped immaterially by the intellect. They are real but do not exist in the same way as physical objects.
Quoting Arcane Sandwich
'Mind is what brain does' is lumpen materialism. But while there is a plausible and comprehensive account of how the gut digests nutrients, along with many other basic functions of metabolism, there is no corresponding account for the relationship of brain and mind, of how and in what sense the brain produces mind, any more than how, or if, matter has produced life. As Liebniz said, if you could make the brain the size of a mill and walk through it, and nowhere in it would you find a thought. In order to even examine the brain and to begin to raise questions about how it does this, the very faculties which you wish to explain, namely, those of reasoned inference, must already be deployed in the pursuit of that question. And you can't see the elements of rational inference from the outside, so to speak. They are internal to thought. See this post.
:rofl: Why are you being so mean to me when you say something like that?
Quoting Wayfarer
I'll make you a deal. I'll respond to what you said there, but you first have to explain how and why "lumpen materialism" is even a thing to begin with. Deal or no deal?
Is digestion also lumpen materialism?
Yeah, I took that from Bunge, actually, and Bunge took it from Searle, surprisingly. I mean, if you read Bunge's Matter and Mind, he has some really scathing things to say about Searle. But regarding the brain-stomach analogy, he agrees, again quite surprisingly. At least that's how I read that part.
Both numbers and chairs exist.
Where they differ is not in their existence, but in the other properties they have. The chair has a time and place, the seven, no so much.
It would be an error to think of this as a difference in the way in which they exist, or as a difference in their being (whatever that is).
But this seems to be an error Wayfarer is prone to.
Well, I mean, not to get overtly political or anything, but he just said that Searle's and Bunge's opinion on the brain-stomach metaphor is "lumpen materialism". I mean... :lol:
Sure. There was a famous expression which circulated in Enlightenment Europe, that 'the brain secretes thought as the liver secretes bile', spoken by one Pierre Cabanis. That characterises a particular strain of enlightenment materialism which attempts to account for everything that exists in terms of the motions of bodies, which is basically what is described as physicalist reductionism. The expression 'lumpen materialism' an allusion to the Marxist 'lumpenproletariat' which is characterised by a kind of false consciousness. Materialism is similarily a kind of false consciousness, in that it assumes that the base level of existence can account for everything that exists. An expression can also be found in the writings of one D M Armstrong, one of the 'Australian Realists' you mentioned in another thread:
[hide="Reveal"]Quoting Arthur Schopenhauer, World as Will and Representation[/hide]
The way I read that, and I might be wrong, is that it's essentially a demonstration that the determinism-freedom continuum exists. Freedom is indeed an actual "thing", like, it's an objective feature of Reality itself because it allows the subject to arise from the objective in a completely different ontological sense, even though they are ontologically "on a par", so to speak. In other words, the brain is a res extensa and a res cogitans at the same time, it's no big deal. Why is that "lumpen materialism"?
@Wayfarer has a point - you will not find seven by dissecting a brain.
One might conclude that there must be two sorts of things, the mental and the physical. But there are alternatives.
Wayfarer sometimes says that there are only mental things, but when the problems with this are pointed out, he quickly retracts such a view.
So? Bunge's point (and Searle's point, perhaps) is that you won't find "hungry" by dissecting a stomach either. It's no big deal. The mind is a series of events, which compose series of processes. In that sense (metaphysically, ontologically) it does not differ from what the stomach (the digestive system, actually) does when you digest something.
Quoting Banno
:chin:
Quoting Banno
This is your congenital misrepresentation of what I actually say, but no matter how many times I try and set it straight, you never get it.
What I say is that objects exist for a subject - for an observer, for a mind. The mind, observer or subject is not itself within the field of objective analysis, as per Husserl. When you conjecture a world before you were born, or before h.sapiens came to exist, this conjecture still contains an implicit perspective, within which the terms 'prior to' and 'before' are meaningful.
"Hungry" isn't something stomaches do. Being hungry takes an organism.
So does the act of thinking, being aware, and being conscious of something. All of them require a living organism. Intentional consciousness as Husserl understands it is necessarily (in a modal sense) dependent upon the factual world in which the Living Subject in the phenomenological sense is immersed. And that factual world, most of the time, is the world of ordinary life. The "Lifeworld" of Phenomenology is just ordinary life. So why is it morally wrong to be a lumpen?
And my reply is that yes, saying (believing, doubting) that something exists does indeed require a mind.
But not existing. There is gold in those hills, even if it remains unsaid (unbelieved, undoubted).
I didn't even know that Australian Paraguayans even existed before I joined this Forum a few days ago. Why not? Why didn't I know that? Well, the Peircian inference-to-best-hypothesis here is simply that Realism is true: objects exist outside of your own brain, "out there", along with all of the other res extensa of the Universe. And some of those, are also res cogitans, because they are living brains inside the bodies of individual homo sapiens just like you. So, Realism is true. That's not to say that materialism is true, it only means that realism is true.
So far.
He wasn't a good writer, that's an Aesthetic defect that Husserl had. Peirce had the same problem.
See this excerpt from some lecture notes on Wittgenstein:
This is entirely in keeping with the phenomenological analysis. Again, it does not call into question the empirical facts of existence. It is about the conditions within which they're meaningful. Can you not see this distinction, even after all this debate?
I'd suggest that "I am my world" is itself something that can only be maintained as part of a community - so "I" has a sense only against "you". If language is not private, neither is the world. I am my world, in relation to others. The sense of isolation or separation associated with solipsism arises from misunderstanding how language works.
I think we're in agreement, actually, and if you don't follow, the fault is likely mine. We're both saying that there is a conceptual division that we want to acknowledge; in your words, it's "'Platonic' in that it mirrors the division between sensory (pistis, doxa) and mathematical (dianoia) knowledge in Plato's thought." I think that's exactly right, as far as this particular debate about "existence" goes.
Quoting Wayfarer
The difference in what we want to say about this division, however, is this: You want to use the term "existents" for the phenomenal domain, and I'm recommending we stop doing that, as the word is so fraught and unsatisfactory. I'm simply urging us to notice that "the distinction is discernible" no matter what terms we use, and that is what counts. On the important point -- pistis and dianoia as picking out two different areas on the conceptual map -- we agree. And when we examine the various relations between the objects of pistis and dianoia, we may find yet further agreement. So we shouldn't let logomachy get in the way!
Yeah but it's like, I hate to play the role of Devil's Advocate here, but Plato's theory of the mind (i.e., pistis, dianoia, episteme) is outdated. Was it scientific when Plato first discussed it? Yes, it was, and it remained scientific for some time afterwards as well. But, today, that's not a respectable scientific theory, because it's no longer a scientific theory to begin with.
You've happened on the forums at a time when the fashion is towards mediaeval thinking.
That's a bunch of nonsense, as far as I'm concerned. Medieval thinking, that is. It has no ontological relevance, nor does it have any ethical relevance, nor any moral relevance. It's not important.
By that's just my honest opinion. I could be wrong.
This too will pass.
They are. Those appeals, I mean. Technically speaking (since we love debating "the semantics of the rules" so much). They're fallacies.
Quoting Banno
I'm not a Thomist myself, since I'm an atheist. But the mere fact that I'm an atheist doesn't mean, by itself, that I won't comprehend religious philosophers when I read what they wrote. That's just not being charitable to my own intellect.
That's an essay question. I cribbed some of the lecture notes but never sat the exam. Regardless, hope the point is clear.
Quoting Banno
It's not that. I've explained I'm not Catholic (although I'm also not atheist), but that Thomas preserves an element of the philosophia perennis which has elsewhere been forgotten. Similar points are made by Max Horkheimer in The Eclipse of Reason, and he's no friend to theism.
Quoting J
I'm very pleased to hear that. And, I've learned a new word!
Quoting Arcane Sandwich
Post-realist approaches would agree with you. Realism is indeed true, but thats just a circular statement. Realism is that way of thinking which thinks truth in terms of adequation and correctness of fit. Post-realist approaches, by contrast, understand truth as correctness to be a secondary form of truth. For instance, for Wittgenstein, within the norms provided by a language game , one can determine truth and falsity. But this notion of truth is irrelevant to the comparison between different language games. The life transitions that take us from
one language game to another cant be made sense of in terms of truth as adequation.
Again, you express a tractatian view, that is not carried forward.
Quoting Wayfarer
Forgotten or bypassed? I remain unconvinced.
Phenomenology is lumpen idealism.
If you could make lumps from air.... :rofl:
We are using more or less the same sense of meaning of pi if we are proceeding within the same language game. This form of life is not strictly defined by the description of pi as the ratio of a circle's diameter to its circumference. It is rather a larger network of interconnected references that forms the basis of intelligibility of that description, as well as a potentially unlimited variety of similar but not identical descriptions. If the language game were different, the meaning of pi could change even if the description remained the same.
But you see, this is something else that I've been "secretly" arguing about, in other Threads. You know what it feels like? It feels exactly like this:
[hide]The "Pepe Silvia" Meme[/hide]
You have it exactly backwards. It is the factual world which is dependent on the processes of transcendental consciousness. Husserl was not a realist. The factual world was for him a product of the natural attitude, which concealed its own basis in subjective processes.
You're not doing your case any favour by citing cartoons.
You talk as if there were a discrete entity that is the "meaning" of ?.
That's the bit to which I am objecting.
Whether you use ? to find the volume of tanks or the orbital period of a planet, the extension of "?" is the very same. That much is clear.
That we are doing something different with ? does not imply that we are using a different ?.
If in your novel language game the value of ? is different, then that is simply not a use of ?.
So extension is clear. Meaning, not so much.
If @Wayfarer can say that the brain-stomach metaphor is lumpen materialism, then I can say that what you just said in that quote is lumpen idealism.
@Joshs and I have our differences, but I'm entirely on board with that quote he provided from and about Husserl. That Mario Bunge thinks Husserl is obscure is not an argument, but again, an attitude. He simply takes it for granted that anything that sounds like idealism is wrong, because any sensible person would think so. But Husserl is making a case. Tackle that case.
And yet not just any "processes of transcendental consciousness" will do; the "processes of transcendental consciousness" is itself restricted by the "factual world"...
It's not either realism or idealism, We construct the facts, from the world.
Quoting Banno
Taking this step by step:
I should say sense of meaning rather than meaning.
When I talk about the use of pi I dont mean applying it to different problems, I mean that every time I hear or think the word pi I am using pi. This goes back to Witts claim that words only existence in their use. The point is that we dont first learn to understand a word or mathematical symbol and then draw on that understanding like a static picture stored in our memory every time we hear or think the word or symbol. Instead, something new happens when we connect our memory of prior understanding with the actual context we are faced with when we hear or think the word again. This is why we dont simply recall a learned word, we use it.
So what happens when we use a word in a new context, but within a stable language game? If that word is pi, then there is little likelihood of any dispute arising over whether one of us is following the rule specified by pi correctly. That stability is not the consequence of the description of pi as the ratio of a circle's diameter to its circumference. There is a much richer network of significations underlying that seeming simple and straightforward description making it possible for us to agree on what it means to apply pi correctly. Put differently, the bedrock belief alleviating the need for doubt in the case of applying pi is in the underlying language game , not the extension.
How do you know that "There is no way" here? Overstretching yourself, again, it seems. The best you might conclude is that it hasn't been done yet; that's not to say it cannot be done.
The neuroscience is in a state of rapid development.
Quoting Wayfarer
You just described my attitude as "lumpen materialist". So if I'm literally a lumpen materialist, why should I even tackle that case? I am a lumpen after all (you just said so, by calling me a lumpen materialist), so why would I put in the work to being with?
I know what you're getting at, but discussing the Divided Line is a different matter, no? Surely we can adapt the ideas of pistis and dianoia into our modern debates. And very interesting contemporary philosophers like Kimhi and Rödl are using Aristotle in new ways.
What is "medieval" to me -- and this has nothing to do with Thomism as such -- is the appeals to authority. It's not so much "X is correct because Plato said so" but rather "X is incomprehensible to modern thought unless we agree with how Plato viewed X."
Quoting Joshs
What is your point of disagreement, if there is one?
Yes, neither realism nor idealism. But for Husserl, the factual world only has its intelligibility on the basis of acts of coordination and correlation between events and schemes which assimilate them. Just as for Wittgenstein, there is never a norm-free basis for understanding the world.
I think not, pistis and dianoia are pseudo-scientific concepts. They had their day, let them rest. When a science lives long enough, it turns into a pseudo-science, unfortunately. Oddly enough, it never begins as one. As a pseudoscience, I mean. Pseudosciences never turn into sciences. Only protosciences do. But when a science is living past "its heyday", so to speak, then it turns into a pseudoscience.
This is all just Theory though, that part might be wrong.
I apologize, it was careless of me to use that term and I will not do so again. But then, as I explained, the view that 'mind is to brain as digestion is to the stomach' is a materialist attitude. Mario Bunge, whom you introduced into the conversation, is an avowed materialist. And the kinds of criticisms of phenomenology of his which you've referenced so far, hardly amount to arguments, so much as declarations.
Quoting Banno
Agree! I've said this many times - that self and world co-arise. There is not one without the other. But that is much nearer to phenomenology and transcendental idealism than it is to direct realism. And it's also very near to Buddhist philosophy.
Quoting J
But notice that nowadays even reason is relativised; it is social convention, it is a useful tool, it has nothing to do with the way the world is. To even appeal to reason is nowadays covertly regarded as an appeal to authority.
Quoting Banno
Ive forgotten now.
Sure. That does not make the world only the result of those "acts of coordination and correlation between events and schemes which assimilate them". Not just any "acts of coordination and correlation between events and schemes which assimilate them" will do. There remains novelty, agreement and error, embedding us in a world that does not care what we believe. Quoting Joshs
Me too.
Thanks -- but if we can't distinguish "conceptual" from "terminological," then what I'm saying wouldn't make sense. How about this? We likely construct our conceptual maps using language, the language we're taught as children and the further technical language, if any, that we acquire as philosophers. At a certain point we can realize that we now have a pretty adequate conceptual map -- we see where the pieces ought to go, more or less -- but there's a problem with the words we were taught. So we can abandon some of the terms, while retaining the map. This is what I mean by "conceptual" versus "terminological." Another way to describe it would be "structural" versus "labeling". We all know what it's like to view a structure, note the various pieces, but find the names (if any) for the pieces to be confusing or silly.
The contrary view -- that language goes all the way down, that thinking or conceptualizing is irreducibly linguistic -- I think is wrong. The path may depend on language, but what we find there has got to be independent, because otherwise the problem will metamorphose into Everything Is Language -- cats and so forth. I'm too much of a realist for that.
So what? Who cares? It's not a big deal, to anyone. Not even to Bungeans, and I'm one of them myself.
Quoting Wayfarer
And so am I. And, I am not Mario Bunge. I'm allowed to have my own thoughts. That is a basic ontological right that I have. It implies nothing.
Quoting Wayfarer
And I told you that I agree with you on that point: Bunge is wrong, and you, Sir., are right. Like, what more do you want, mate? I'm not going to give you a Medal of Honor for that.
So what's your point? You sound like you don't need me, from a philosophical point of view. But we're philosophizing. So what is that you need from me specifically in philosophical terms, mate? I mean, am I even allowed to call you "mate"? Have you somehow allowed it? Must you allow it? What do you think of it? Is your opinion as valid as mine? Do we both believe in good common sense? What is good common sense, anyway? Should it be trusted? Good common sense I mean, should it be trusted as if it were "a thing"? Etc., and so on, and so forth, down the Rabbit Hole we go, but for what? That's what I call "lumpen idealism": chasing the experience of imaginary Rabbit Holes. Like, mate, you have an intellectual addiction, you need more materialism in your life.
I'm following your other thread on Rödl and also reading the text.
Quoting Arcane Sandwich
I don't need or expect anything from anyone. We're here to discuss ideas, and these discussions do push buttons from time to time.
Yeah, the button that says "lumpen materialism", and you lay that down on Bunge, on me, and on Searle. What did Searle ever do to phenomenology?
:wink: No. It is direct realism, in that there can be no gap between the talk and what we talk about.
That's why i haven't participated in @Srap Tasmaner's new thread - there is no model.
Edit: Quoting J
There it is again. I have to go with Davidson here and deny that a map sits between us and the territory.
But real life calls. Later.
Is it justice that shows up or merely actions that are deemed to be just or not? It is common parlance to speak of injustices, but we don't generally speak of justices, which is itself a little strange, and speaks to the inconsistency of language usages.
In any case instances of both justice and injustice do appear, and that seems somewhat disanalogous with rocks since we don't speak of instances of rock showing up. Language is not a thoroughbred, though, but a mongrel.
I'm comfortable with saying that rocks exist and that ideas and instances of justice exist.
Ok... Can you explain that? I'm willing to be charitable to your intentions if you're willing to be charitable towards my intentions. Deal or no deal?
Quoting Arcane Sandwich
I mean language usage has evolved not in an ordered and planned (selective breeding) way, but in an ad hoc (free for all mating) manner.
Quoting Banno
Thats right. We dont simply fabricate the world according to our wishes. And yet, the only access we have to the world is through our aims and purposes. Care is indispensible to the connection between us and world, in the form of relevance , mattering and significance. Isnt this the basis of the normative power of language games? No matter how strange and surprising things can strike us , they are always, at a more fundamental level, already familiar to us thanks to the fact that even the most unanticipated event is recognizable on the basis of a background intelligibility. This is what precludes radical skepticism and doubt.
But that is literally the same for biological evolution. Scientifically speaking, evolution, in the biological sense of the term, is purposeless.
Yes, but the response doesn't really act as a good counterpoint. We might very well use a PC desktop as a doorstop. However, we wouldn't turn into into a soup and serve it for dinner, wear it as an earring, attempt to drink it if we are thirsty (seeing as how it is not a liquid), use it as a sledgehammer to replace our sidewalk, ask it out on a date, hire it as our attorney, take it home as a pet, etc. Just as we wouldn't use a hunting knife to clean our ear and just as, while there are pastoral societies all over the world that raise animals for their meat and milk, none raise animals to consume their feces.Nor do any pastoralists mate sheep to cattle, goats to horses, etc.
Obviously. What's the assumption here, either things determine what we do with them or we decide how to interact with them? But that's simply a false dichotomy. "Everything is received in the manner of the receiver," nothing is read without a reader or eaten without an eater, etc.
A screwdriver is an artifact. It's built to purpose. Rorty's point, aside from being a bad one (one he expunged from the transcript he published of the debate), also gets things backwards. Of course you can do many things with a screwdriver, open boxes, etc. But try loosing a Torx screw with anything but a Torx screwdriver and you will be in for some frustration. You can use a computer as a doorstop, but good luck trying to use a doorstop, or anything but a digital computer to run Windows. There can be many ways to be right and still always very many more ways to be wrong.
If it's impossible to be wrong, philosophy/science is worthless (another point Eco makes, echoing Socrates in the Theatetus).
Right, how else would it work? Sort of like: "does the shape of my feet impose itself on how I walk. Yes, but only in how I walk."
Re: the whole quantification thing, this just seems like equivocation.
Consider:
Brutus: Wow Cassius. I saw your results to my survey. I had always thought you were an atheist and a materialist, but I see here that you marked down that you think that both God and ghosts exist.
Cassius: Well of course they do Brutus. Both can be the subjects of existential quantification! But no, I am an atheist and I don't believe in ghosts.
Well, does Brutus have a right to be miffed over what seems to be sophistic equivocation here?
It's a red herring at best. It would be like if the thesis under consideration was: "do subjects determine what can be meaningfully predicated of them?"
Brutus: I think this is so. Consider, only numbers can be prime.
Cassius: Au contraire! I ate a "prime" rib just the other day.
:wink: Quite the opposite. It's the clearest definition hereabouts. Your Cassius is being a prat.
Edit: I should add, quantification is only one part of the explanation offered - it includes predication and equivalence and domains of discourse. Quantification tells Brutus and Cassius that we can talk about ghosts. Predication might be used to further say that ghosts are immaterial, imaginary or superstition. Cassius is mistaking quantification for predication.
All of this can be explained from the POV of Object Oriented Ontology, IMHO.
Quoting Count Timothy von Icarus
Yes, indeed, it is an equivocation, and to equivocate, in that sense, is an informal fallacy.
Really, it should be explainable by any metaphysics worth its salt. Explaining why we don't drink rocks when we are thirsty or give our babies razor blades to play with shouldn't exactly be a big hurdle. Once one removes any notion of "human nature" or of the "essence/quiddity" of objects, however this becomes a much more difficult task.
Which is precisely why OOO doesn't even remove it to begin with. It just declares that such essences or quiddities are unknowable, and necessarily so. Every object has an essence. It does not follow from there that the essence of an object is knowable by any human being or animal. In fact, it's not even directly accessible for inorganic objects. A meteor has an essence. The Moon has an essence. When the meteor impacts the Moon and forms an impact crater, it does not follow that the meteor has any more access to the essence of the Moon any more than we do when we look at it in the night sky, or when we look at pictures of it, or when we theorize about its physical properties in a peer-reviewed journal or a web Forum like this one.
So platonism is the idea abstractions exist.
I don't see how abstractions as non-physicals can exist. If they are non-physical they don't exist. What is the alternative?
If abstractions are mental content that's different and it should be acknowledged. And the infinitesimal as mental content is one possibility out of many.
Brain; ( number system 1 )
Brain; ( number system 2 )
Brain; ( number system 3 )
And so on.
Good luck. Beware of serious babble on this thread. :roll:
Call these your axioms:
[b]Existence is a property.
All material objects have this property.
To exist is to have a spatio-temporal location.
All material objects have the potential to change their spatio-temporal location.[/b]
So my question is, Is this further statement:
Only material objects have the property of existence.
a conclusion drawn from some subset of the above axiomatic statements, or is it a separate axiomatic statement itself? If the latter, its what I was referring to as a coincidence. It seems to demand further explanation.
Yes. That is correct. Only material objects have the property of existence. Ideal objects do not have that property. So, ideal objects do not exist. Again, what's the big deal here? No one care.
Quoting J
Indeed. Again, I'm not going to give you a "Medal of Honor" for something so trivial.
Quoting J
No mate, it's a theorem. You just said so yourself, because a theorem is literally what you deduce from some set of axioms. You make me angry when you ask that sort of question.
Quoting J
But it's not the latter mate, it's the former. Again, you're making me angry.
Granted, there are many versions of an appeal to authority, including the argumentum ad baculum (check your Thomas)! Those who regard an appeal to reason as illegitimate on that ground are wrong, I think, but so are those who want to say that the ancients nailed down the meaning of all our key philosophical terms.
Then I challenge the latter camp to explain to me, in Plain and Simple English, what this phrase means (these are Heidegger's literal words BTW): remanens capax mutationem. I know for a fact that Heidegger made that up. And I'm not even sure that's even correct from the POV of the syntax of Medieval or Classical Latin.
I apologize. These discussions have to do with my profession (philosophy), and I studied at Academia, and I work in Academia. It is only natural for me to be passionate about such things (philosophy). And, since I'm aware that I might be wrong (in addition to being ignorant in general), I have joined this forum seeking wisdom, a greater intellect, and a terrain for philosophical discussions.
In other words, I would wish to hear the explanation of language, from your own First-Person Perspective. Or, tell me what your philosophy is, as a set of axioms, and highlight any particularly important theorems, please. Thanks in advance.
EDIT: What is an apology? Did Plato apologize for Socrates? Like, literally?
I hadn't thought about a conceptual scheme of the sort that Davidson denies when I articulated this idea. But you raise a good point. Let me think on it.
This subthread shouldn't get left behind. Some of this was sounding familiar to me, and I thought it might have jogged a memory from Nozick's Philosophical Explanations. So I spent a little time searching (it's a big effing book) but couldn't find anything that specifically addressed explanation versus exhibition/illustration/waving-at a la Wittgenstein. But Nozick's idea of what an explanation is in general might be relevant. He thinks a good philosophical explanation addresses the question of modality, of how some given X is either possible, or necessary, or would be the case if, etc. He contrasts this with proof, which is non-modal (given the premises). And he points out that transcendental arguments are an admixture of both approaches. He's in favor of what he calls philosophical pluralism, because he thinks that while explanations can be ranked in order of plausibility (hence not relativistic), they usually can't settle a given question.
That's an interesting OP in itself, but the relevance here might be: Nozick seems to draw a clear distinction between explanans and explanandum. He doesn't think that p is necessarily going to be explained in terms that derive from or relate to p. So -- and again, he doesn't say this directly -- if p is "Why is q ineffable?", we can talk about p without needing to talk about q.
I still want a good example of this. Was my "meaning of life" example any help? I feel like there's some obvious way we handle this in ordinary life that I'm not thinking of . . .
Quoting Count Timothy von Icarus
We are not disagreeing that the world poses constrains on what we can do with objects, so I have no problem with your laundry list of all the things we can or cannot do with specific things. What I am arguing is that our perception of of what we can or cannot do with a thing is based on HOW we understand what that thing is, how it works, and that understanding is not static, it evolves
over time. When our understanding of a thing changes, due to shifts in scientific and technological knowledge, it is not simply a matter of reconfiguring our knowledge of the external causal associations between objects. What also changes is the core concept of object as center of properties and attributes. The reason that this core concept of objectness does mot remain stable in the face of changes in under is that it is an abstraction derived from a system of relations not only between us and the world we interact with, but between one part of the world and another.
:grimace:
Quoting Mark Nyquist
It seems the thread has drifted well away from the main topic. I'm more interested in that.
This approach doesn't work, I think for at least two reasons.
If numbers are just abstractions, how do you distinguish "3" from "The second even prime". The first "exists", the second doesn't. What distinguishes these two abstractions?
Second, how do you account for numeric laws? If numbers were all in the head, how are laws discovered that were most certainly not in anyone's head until they were discovered?
The "All in one's head" model is a thing known to physically exist.
Brain; (Numbers)
Brain; (Numerical laws)
And numbers just as non-physical abstractions doesn't have an explanation.
Give it a try if that's your position.
Prove it.
Of course - but there's another 'sub-theme' here which is deeply connected to this whole debate. That is the belief in the pre-modern world that the Cosmos was animated by reason. The Logos was in some sense the reason for everything, and in that view, everything existed for a reason (also the belief behind the principle of sufficient reason.) Aristotle's fourfold causation was an expression of this. Over the course of history, though, as Greek philosophy became incorporated into Christian theology, the logos became identified simply with 'God's word' and finally with the Bible simpliciter. The idea of natural or scientific law itself is called into question, or said to be human inventions superimposed on an indifferent universe. Mathematical Platonism is intrinsically connected to this issue, as it seems to suggest that the Universe is itself mathematical, which empiricism generally will reject as a matter of course.
The reduction of reason to a consequence of natural selection is a whole other set of arguments, including Platinga's EAAN, Lewis/Rapport's 'argument from reason' and Nagel's 'Evolutionary Naturalism and the Fear of Religion'.
Quoting hypericin
:clap:
Right, I wasn't asking the second question. I don't think in terms of superior ways of existenceI am not a fan of hierarchical notions of being.
Rocks and justice exist in different waysrocks are spatiotemproally existent and justice like goodness is conceptually existent. So, depending on circumstance you could have good and bad rocksif you are trying to build a certain kind of ashlar wall, for example.
Quoting hypericin
Primeness, evenness and oddness can be observed in the ways that groups of objects can and cannort be divided up.
However, one has to grasp the concept to make such distinctions, so it is not something that can be ascertained by observation alone. It is deduced.
Sure, in some sense. I've long held that, just as Hegel has institutions (e.g. the justice system, family, state, etc.) objectifying morality for a people, we also have science, educational institutions, technology, and the productive arts/trades, serving to objectify certain aspects of the natural world. Positive and negative charge is objectified for us every-time we change a battery or rewire an outlet.
Terminologically though, I would rather say this is a refinement of our intentions, as opposed to our concepts. This is because otherwise, we would be forced to say that "wetness" or "human" is changing, but it seems to be an important distinction that are intentions are changing (and hopefully becoming more perfect). I did not experience a different water when I went swimming before I came to know that water was H2O, a polar solvent, etc.
Plus, to speak only of (presumably efficient) causal associations leaves out the phenomenological whatness of things, their quiddity. I suppose that, on the conception of reason as primarily/wholly ratio, that's all there is, sets of propositions formed from empirical atoms that get shifted around. But I would tend to say that objects are present and grasped/apprehended in a way that transcends this.
Now, something like water does indeed change in some sense when we come to discover that it is a "polar solvent" or "H2O." Being known is a relation after all, and things are, in some sense, defined by their relations. Yet at the same time, there is a more obvious sense in which water today is the same water the dinosaurs swam in, and wetness today the same wetness experienced by a medieval peasant every time it rained. I am not really sure how to capture this distinction outside of an appeal to per se predication.
I am not sure I really understood this. It seems to me that anything involving "us and the world" necessarily involves "one part of the world and another," so I am not sure what the difference is supposed to be. Nor do I think I wholly understand what changes in the core concept of an object, or abstractions being derived from a system of relations entails.
You offered as a way forward for the different approaches adopted by @Wayfarer and I. offers the Aristotelian account as paradigmatic, which we might come back to later.
You phrased the question as about what the three parsings of "is" in a first order language are able to account for in terms of being and existence, and whether there is more to being and existence than these can be grounded in predication, equivalence and quantification. The issue is now "Will it ever be helpful to use the words 'being' and 'existing' to talk about this ground?" but where the issue is one of terminology rather than concept. I have two issues with this. Firstly that we can't long maintain a distinction between concept and terminology, and secondly that our words and actions work directly in the world and not on our model of the world.
It is difficult to maintain a distinction between what is conceptual and what is terminological, between the structure we accept of how things are and the labels we apply to that structure. This because using a term just is using a concept. This follows immediately from not accepting that there is some thing we can call the "meaning" of the term that is distinct from it's use, but instead looking just to their use.
Two caveats here. Firstly I put this in terms of use, as per Wittgenstein, but it can equally well be put in terms of truth functionality, so as to more closely approach Davidson.
And secondly, the use of "terminology" may mislead folk into supposing that that this view takes concepts to be only linguistic, that it is "language all the way down". That's not what is proposed; rather the concept is the doing.That a cat has a concept of "food bowl" is shown by the behaviour it exhibits, by what it does, by how it uses the food bowl. In this regard, language is just more doing, more behaviour. But - and it is an important but - once language comes into play, there is no going back. The rational structures developed on language cannot be rescinded. Concepts are displayed in our actions, including those actions that involve language. Indeed, our concepts are our actions.
Davidson has shown how trying to explain our behaviour, especially our linguistic behaviour, in terms of conceptual schema leads to irredeemable difficulties. Specifically, that we understand what someone else is doing and why implies that their supposedly different conceptual schema is subsumed by our own. We could not recognise their behaviour as consistent and coherent without thereby making sense of their supposed conceptual scheme. But what this shows is not a similarity in conceptual schemes but that they and we have the same beliefs and act within the very same world. It's not the conceptual schemes that are similar but the world in which we are embedded. Our actions, including our language, are in direct contact with that world.
This post compresses two very large ideas into a very few words. But it might give someone with the right background in Wittgenstein and Davidson an idea of the direction in which this conversation might head. Others will misunderstand. I can't help that.
I mean, for a Thread called "Mathematical platonism", this just went to shite.
EDIT: And it appears that we haven't gotten out of that Rabbit Hole yet, on page 17 of this thing.
Humans seem to have evolved to the point of both constructing and exploring mathematics. The counting numbers arise from observations and abilities to distinguish. In my opinion none of math exists in some Platonic realm independent of human brains. These are ideas, not physical objects.
Modern math is concerned more with overseeing the multitude of mathematical ideas and discovering how they relate to one another, than the classical approach to conjuring up problems to solve in the individual areas of the subject (there are about 30,000 Wikipedia pages on math topics, e.g.)
On the other hand, I can't say these ongoing philosophical arguments are of less importance than much of the math being produced. My own areas of exploration are "pure" mathematics and have little to any connections to physical realities. Nevertheless, the results are documented in simple exercises of logic on a set of symbols that are well defined. I don't get the impression that is the case in Platonics. But I could be wrong.
I realize that, sorry if I implied otherwise. I was just using your question to compare with a type of question that I think others have been asking.
The irony in all this is that I sort of am a fan of hierarchical notions of "being," if by hierarchy we just mean structure or grounding. My idea, not to belabor it to death, is that we'll do a better job by dropping the word "being" to the extent that we can.
I'm sorry, I can't resist a good typo. Yes, I too find small numbers to be prim, even reticent. But then there's ?, which is small but goes on and on forever . . .
@Joshs Hi, I'm not sure if I understood this part correctly. I don't know if you're saying what it seems to me that you're effectively saying there. Can I ask for some clarification there? Specifically: what do you mean, and what do you intend, when you say something like that? Does that question make sense? Let's start with that, I think that could put this Thread back on track.
I'm somewhat familiar with Nozick's politics, which have not inspired me to read his wider philosophical work.
Speaking from this ignorance, if we are going to take philosophical pluralism seriously, shouldn't we avoid the sort of over-arching story found in Philosophical Explanations? Shouldn't we avoid saying that philosophical explanations are thus-and-so?
But to this:
Again, this is from the Tractatus, which I take PI to supersede. Roughly, post-PI the "sense of the world" remains unstated, but can be either enacted and shown, or left in silence. In neither case is the sense of the world said.
So this comes down to what we might mean by "expressible" in "is the sense of the world expressible".
Yes, everything you say is a nice concise view of the problematic territory here. I'm more comfortable with Davidson than Witt on this topic but that's just me.
As I wrote earlier, I need to rethink what I want to say in a way that would be a reply to Davidson, which ain't easy. Maybe the place to start is "Using a term just is using a concept". What if we reply, "Yes, but is using a concept just using a term?" So the question is still, "How, and to what extent, can we dissolve that metaphysical Superglue that seems to bind term to concept?" but reverses the grounding. The Davidson/Witt position would, I think, be that there can't be any grounding because "concept" is parasitic on our terms.
Now you may want to say, "It's not metaphysical Superglue at all, it's the opposite of what metaphysics proposes" and/or "If there is no conceptual scheme, no appeal to shared meanings, but merely a congruence of beliefs, acts, and worlds . . . then what's left for 'concept' to be about?" Those would be meta-challenges, for sure. I need to think more about how I in fact use concepts, and find a couple of paradigm cases of terminological changes that really do hold a concept steady. Then I might be in a better position to restate my case. Should take about a year . . . :smile:
You and others might find this essay interesting Aristotle was Right After All, James Franklin. (I don't agree with his depiction of the 'other world' of Platonic forms, but it is still pretty much on topic for this thread.)
I'm not sure what led you to think I was saying anything like that. It seems to me that arithmetic has its genesis in playing around with groups of actual things and inducing the basic concepts of adding dividing, subtracting and multiplying. Once we have generalized and abstracted those notions and represented them symbolically and formulated the rules that govern them, then all of the elaboraqtions of mathematics become possible.,
Quoting jgill
Totally agree.
Quoting J
I also am fine with the notion of hierarchy in the sense of structure or groundingI just reject the spiritualist notion of degrees of beingyou know, the idea that humans are at a higher degree of being than animals, and angels at a higher degree of being than humans, and so on. The "great chain of being" idea I reject.
For me the word 'being' just means, if taken as a noun 'existent' or 'existence' and if taken as a verb, 'existing'.
Quoting J
:lol: Nice!
:up: I like the article, since it is saying just what I have been. It's the middle ground between Platonism and nominalism.
.
Yeah, I know, unfortunate. But he's a good meta-philosopher for all that.
Quoting Banno
Pretty sure Nozick would agree with that. The tone of the book is discursive and investigative, not didactic. It contains one of my favorite passages about doing philosophy:
Quoting Banno
True, but evidently it can be referred to. That may be all we need.
But why should that stop us? :wink:
Quoting J
Here I'll reach to my other pet philosopher, Austin.
The concept "seven" just is being able to buy seven apples, adding three and four, taking nine from sixteen. There is not a something in addition to these that is the concept of seven. So yes, using a term just is using a concept, but we can do stuff without terms, so using a concept is not just using a term. But better than any of these, just drop the use of "concept" altogether. Drop the concept seven and just add three and four.
The implicit picture is of a "concept of seven" in someone's head that are called when one does things with seven. But if we can add three and four, what further explanatory work is done by the concept?That's why this is muddled:
Quoting Mark Nyquist
But I'm not sure if Mark is advocating or laughing at the suggestion.
Quoting J
Waved at, perhaps.
Indeed. But also note
Quoting Banno
As I understand platonism, neither would it. This would be a reification, objectification of the act of act of counting. But it doesn't vitiate the fact that the number is independent of any particular mind, but can only be grasped by a mind.
The last three can be parsed as predications.
The first is ambiguous, partly about placing something in the domain of discourse and hence making it subject to quantification, and partly about essences, which are more trouble than they are worth.
I don't get that. What is it for a mind to grasp a number, apart from being able to count to it, add it, or halve it?
Numbers are not things in the head, not mental furniture.
Just looking at what I wrote, maybe multiple forms of mental content are nessecary to deal with numbers.
The number 7 could be a pure number, or a unit of something, like a length, area or volume on and on.
So numbers as mental content are dynamic and modified as needed by mental process.
That exists by observation so why does some secondary Platonic form need to exist?
One form isn't enough?
I'm afraid this does not do the work you need it to do, nor can you bat the ball back to my court so easily. How do you respond to my reasons that numbers can't just be "all in one's head"?
Quoting Mark Nyquist
Think of chess. This is an arbitrary game, with arbitrary rules that exist in our collective heads. It is well known in chess that a bishop is worth 3x a pawn and 1/3 a queen. Impressively, this was known well before computers made it conclusive. Yet, you will never find this in the rules of chess, it was never in anyone's head before it was discovered. How can this be? I think of the rules of chess as creating a "logical landscape", and facts can be discovered in such a landscape that were never in anyone's head. This, despite the rules of chess being 100% arbitrary, having no connection to the actual universe.
Numbers are such a thing. They also have rules which create a logical landscape, about which things can be discovered which were never in anyone's head. But unlike chess, the rules of numbers are intimately tied to the way things actually work in the universe. If you have one unit, and combine it with another unit, you get two units, no matter how you define what a unit consists of. So long as the definition of unit is consistent, this works for anything across space and time.
I don't think this is an answer in itself, and I'm no mathematician. I'm just trying to convey my intuition on how the problem can be thought about, without resorting to "all in the head", and without resorting to mystical Platonic essences...
This is an excellent point. I would even add: when someone plays a game of chess, it would be wrong to think that the chess-player is executing monarchic politics when he moves the piece called "the King". I mean, come on, have you ever thought such a demented thing while playing an actual game of chess? Of course not. But you see, this is what I'm humbly saying: philosophers step in at this point of the dialogue, and they say: "How do you know that you're not really executing monarchic politics when you're playing a real game of chess at the park with a bunch of random people?" And the appropriate response to that sort of question, is a Moorean response.
Such is my sentiment on that issue.
Were talking about the faculty of reason. I think we take it for granted without noticing how significant it is. Consider what it enables.
It might just be that our mental process is so effortless that we ignore it.
So existing or not existing is one question.
Platonism as an abstraction doesn't exist.
Mental content does physically exist.
Rules that exist in mental content can be valid or invalid. But as mental content they both physically exist.
It's Quoting Wayfarer
that is problematic. Again, what might it be for a mind to grasp a number, apart from being able to count to it, add it, or halve it?
If you can count out seven things, do additions that result in or use seven, double and halve seven... what more is there that you are missing, that is needed before you can be said to have grasped seven?
I don't think there is anything more to grasping seven than being able to use it. Hence concepts are no more than being able to work with whatever is in question, and thinking of them as mental items in one's head is fraught with complications.
There is evidently an elephant in the room, and no one is clearly addressing it. Perhaps because you find it somehow awkward (I don't actually know what that would take in a Thread called "Mathematical platonism", but I digress).
The "elephant in the room" here, so to speak, presents itself as "pack". A "multiple", if you will. A nice, shiny-looking Pandora's Box of philosophical problems.
So let's be simple about this, in a methodological sense. Let's simply, as engineers would. Let us address one specific "part" of that so-called "Elephant in the Room":
Geopolitics, but from the "point of view", so to speak (i.e., the "conceptual framework") of Game Theory.
This is what is now under discussion in this Thread, it seems. In some way or another. Perhaps you had a simpler picture in mind. Perhaps it was instead more complicated than mine. But that is more or less the "tone", if you will, that is being "played" (as in, "Playing the Classical Harp") here. As in, "Oh, Aristotelian Realism, how Romantic, it is so Lovely, and Yet So Troubled".
And what I'm saying, "mates", is that the solution is very, very simple:
Australian Realism (is greater than, in the mathematical sense) Aristotelian Realism.
So, let us simplify that, shall we?
Australian Realism -> Aristotelian Realism.
Which one of you would like to throw yourselves over that metaphorical grenade of a thesis? I'll tell you one thing: it certainly won't be me.
(I, Arcane Sandwich, have edited this thread for Clarity's Sake. And here's the joke: who is "Clarity"? What is her sake in all this?)
One can account for this by understanding commissive speech acts. These are speech acts that bring something about. An example would be "I name this ship the King Charles", performed by the designated dignitary at the proper time and place - before that act, the ship has another, or even no, name. After, and in virtue of, that act, the ship comes to be named the "King Charles".
The act counts as naming the ship.
The bishop on a chess board can be moved in any direction, along a row, along a diagonal, picked up and put in the place of the opposing queen, and so on. But only a move along a diagonal counts as a move in a game of chess.
That "logical landscape" of which you speak is constructed using this sort of structure - taking something and making it count as something new. So yes, "If you have one unit, and combine it with another unit, you get two units, no matter how you define what a unit consists of" because that now counts as two units.
Yes, IF you have one unit. It does not follow that you do have one unit to begin with.
Think of it like the three positions in the Analytic Metaphysics of Ordinary Objects.
There, in that context (the metaphysics of ordinary objects), there are three (and only three) logical answers to van Inwagen's Special Composition Question, or SCQ for short:
1) Never (nihilism)
2) Sometimes (particularism)
3) Always (universalism)
Why is this important? Because it is itself undercut by (or perhaps is parallel to) a similar distinction, this one entirely metaphysical, not mereological like the previous one:
1) Eliminativism: there are no ordinary objects, nor extraordinary objects.
2) Conservatism: there are only ordinary objects, and there are no extraordinary objects.
3) Permissivism: there are both ordinary objects as well as extraordinary objects.
From a purely Pragmatic Point of View, the second option is the most practical one in cost-efficient terms. It "gets the work done", which is something that Eliminativism cannot even do, while it avoids incurring in enormous metaphysical (and by extension, mereological) costs. It is simply the greatest solution in terms of metaphysical cost-effectiveness.
Is this too "rambly", for the OP of this Thread?
P.S.: Can someone just explain the dumb joke about "Edited for the sake of clarity" versus "Who is Clarity?" If you explain it correctly, I'll award you with the fictional "Immaterial Medal of Greatness".
Numbers have significance apart from counting, for instance there are four gospels in the Bible because there were four elements. Four is a symbol of the earth because there are four directions. Most people in my world know what 666 means, and so in.
This doesn't diminish your point, that numbers are used, just that counting isn't all they're used for.
What counts as one unit? We get to choose.
"We" as in "who"? The individual members of the species Homo sapiens?
The world of Iron Maiden, you mean?
If there is a "Them", then there is an "Us". That, presents itself as different options. Hypothetically:
Option 1) Us vs Them
Option 2) Them vs Us
Option 3) There is no match. There is neither Option One nor Option 2, because this is not to be decided in this context. It does not follow from that, however, that it is not to be decided in any context.
This is something h.sapiens can do that no other creature can do. If theres anything problematic it is the inability to see the significance of that.
Then I'll just share my own Philosophy of Mathematics with you all, since I have not done that so far (oddly enough, not one of you even stopped to realize that fact). In matters of metaphysics / ontology, I have already told you the following: I am a realist, a materialist, an atheist, and a supporter of scientism. From those four premises, you cannot "get" (deduce) my Philosophy of Mathematics, because it is a "hidden" axiom of the system itself (BTW, this is "the language" {it's more of a dialect, really} that I call: "Axiomatese", as in, "Ontologese", which intended to mimic "Portuguese". Pay no great attention to those facts, as they have a sort of Mind-Flayer-ish tone to them. And I am not a Mind Flayer, of that I am certain. Cogito, ergo sum et res cogitans / extensa) <- Yeah, I just "made that up", so to speak.
And that is my humble point. Some absolute restrictions are necessary in language itself, otherwise communication is not cost-effective. In the terms of Thermodynamics, it would be "too costly for not enough benefit". It would be what is now called "a viable option among many others".
Edited for Clarity.
There's a very good book that can be found online Thinking Being: An Introduction to Metaphysics in the Classical Tradition, Eric S Perl. The explanation of the origin of the Forms is highly illuminating. They're not what nearly everyone says they are.
IDK, something about a cat or a dog seems to strongly suggest that it is a single cat or dog; I am not sure how much "choice" we have in the matter. It's just like how I could refuse to use the word "blue" for my car, but it would in no way cease to "look blue to me" simply because of how I've chosen to speak. The same holds for livestock. There are pastoralists all over the world whose languages, and their domestication of the local fauna, occurred in relative isolation, and I don't know of a single one that divides up the units of what constitutes and individual mammal differently.
This seems to be a choice that is very much constrained by what things are, including how they break down into unified wholes. Good luck cutting a sheep in half, declaring that each half is a unit, and then trying to mate them to get more sheep, for instance.
Plus, the idea that a single male eagle and a single female eagle would cease to be single eagles capable of producing single offspring if the "language community" disappeared seems pretty far fetched. This is what happens if you make philosophy of language your first philosophy.
No doubt, the claim that "you need language to do any philosophy," is true. However, the person who champions a reduction of philosophy to neuroscience will be on similarly strong ground: "no one ever does philosophy without their head." The advocate of phenomenology will likewise argue that no one ever did philosophy without first having experiences and perceptions. Hence, this is not a good way to determine first philosophy.
As noted above, the language community doesn't seem to choose arbitrarily. In some cases, its choices seem more or less made for it. But the way in which these choices are constrained is exactly what realists are talking about.
Don't be too sure. Our ignorance about what other species can do is astonishing. It wasn't so long ago that scientists questioned whether other animals could even think or be conscious. Anyway, would it really affect your point very much if it turned out that some other animals could do it a little bit?
I can definitely do without "mental items in one's head," though in fairness that's a somewhat tendentious way of putting it. But I'm wondering whether, by choosing "seven" as our example concept, we haven't picked an outlier. Thinking about "seven", it does seem as if there's nothing left once we enumerate all the things we do with it. Are all concepts like this, though? Don't most concepts include structural parts, often definitionally so? Consider a major chord. I can list all the things we do with such chords, but beyond that I can describe what it is that makes this group of three notes a major chord. Why wouldn't we want to call that description the "concept" of a major chord? You see the difference with "seven" -- there isn't a similar description of what comprises "seven" or makes it what it is.
All these things are equally valid; but replace philosophy with knowledge. It applies to all knowledge whether science, philosophy, folk psychology, sports. Difference between different areas of knowledge are what you are talking about and your means of engaging with it. In that sense there are no essential features to any given parts of our knowledge and methods can vary. You don't need some specific foundation to philosophy; you just engage with things your're interested in, usually appealing to methods and insights that have accumulated over the years in those particular areas. The things stated in the quote are a field of interest in and of themselves, one I find interesting, and - from my perspective - in the kind of vein of naturalized epistemology or even Dennett's Heterophenomenology - which are kind of just particular uses of cognitive and brain science. But obviously there are many other fields not related to this. I don't have to view the things in the quote as some kind of foundation for a philosophy. They are just a particular area of philosophy I am interested in as opposed to certain other areas. I am not sure one needs some foundation - but then again, everyone settles into particular ways or habits or inclinations of belief in how they do philosophy. But this is no different to how different scientists or historians have certain inclinations or attractions to certain methods, opinions, ideas - and they don't need to be particularly philosophical about it. I have always been interested in things in the most general sense, in any field - history, nature, music, whatever. Philosophy is naturally interesting so it Was always hanging around. What became my first or top intellectual love though would be in the sciences. I would be dipping into areas of philosophy from random books I came across, random classes I chose to take. Things pop out like say philosophy of science. But then I think the real snowballing came when I start to notice parallels between narratives about how brains work (from neuroscience and cognitive science) and discussions in philosophy - people like Berkeley, Popper, Wittgenstein, others. (Philosophy of mind also obviously takes an interest for similar reasons, or because cogmitive/neural science fails to answer all questions). And I cultivate an interest in how those problems are related or diffused, deflated in a certain way. And thats just an interest, not a concerted attempt at making some foundation - albeit, obviously everything we do (and all knowledge) is actually "founded" in the brain, language and experience inextricably connected. But at the end of the day I am just doing the knowledge I find interesting along my inclinations. And in talking about this in a long paragraph all I am doing is questioning this idea of philosophical foundations as some need.
Of course, there is ample choice. You can count dogs, mammals, retrievers, brown animals, sick animals, etc. The choice of what counts as a numeric unit is fairly arbitrary.
You probably mean declarative speech acts. Commissive acts commit the speaker, declarative acts declare things to be so. But this seems to overemphasize speech. Everyone alive was born into a world where the rules of chess and counting were already well established. They are social practices that don't require speech acts to bring them into being.
But suppose they did. Suppose you were defining chess for the first time. The speech acts would specify how the game works. But it seems odd to say that the logic of the game, and all its implications (i.e. the value of the pieces) was somehow contained in the speech. The speech specifies the rules. But the rules are not themselves speech, or language in general.
I went back and read this section in its entirety. It is an excellent summary of the difference between intellection and ratiocination, as well as the decline of intellection since the modern period. :up:
Yeah, my error. i used "Commisive" for acts of commission, much as "declarative", now the term is used for acts of commitment. I'll fix it. Thanks.
Or consider two drops running down a window pane and coalescing. One plus one makes one.
One might mention gavagai here, but Quine's rabbit takes an approach to language that may be quite foreign for you.
So sure, there is a cat and a dog, and there are two animals. The salient bit is that number is a way of thinking about (talking about, treating, approaching) the animals. Being two things is not strictly a state of the world. nor strictly a thought, but a combination of the two. The dichotomy between realism and idealism is misleading.
The notion of "first philosophy" is somewhat antiquated. Aristotle appears to have been obsessed with hierarchy - perhaps it was the only tool he had at hand. More recent thinking might be a bit more holistic - we can do ethics without a complete epistemology or metaphysics; indeed, we probably have no choice about this. Arguing about what comes first is superficial.
But language is a common ground for all philosophy - amongst other things - so having a good grounding in how it works might be helpful.
Quoting hypericin
Yep.
It is interesting to consider the relevance of Kahneman's distinction between fast and slow thinking to Lewis' discussion of intellectus and ratiocination.
Kahneman's work suggests that Lewis' claim that intellection (fast thinking) is higher, is rather questionable.
Sure. What remains is that being a bishop is a way of treating that piece of wood, being a dollar coin is a way of treating that piece of metal and being two animals is a way of treating that cat and dog. Quoting hypericin
Yep. it's the doing that has import here. There needn't even have been an explicit speech act that commissioned the practice. What's salient is the idea that we can count something as something new or different, and build on that.
Seven only exists as part of an extended language game that includes one and two and a few other things. And a chord is dependent on the scale in which it sits. The first, third, fifth and seventh sound distinctly different, as does a minor chord.
But I'm not clear as to what you are getting at. If you understand that the major is the root, third and fifth, while the seventh chord is the root, third, fifth and seventh note of the scale, is there again something more that is needed in order to have the concept of major and seventh?
In a sense perhaps putting your fingers on the right strings to produce each? The doing?
If that's the import, then what's the export? What does it "get out of it", in economic and/or thermodynamic terms, and/or systemic terms?
If you want to talk about Math & Music, then we need more musical concepts here. I would suggest incorporating rhythm, harmony and melody as mathematical and musical concepts into this specific aspect of the discussion.
No, exactly that. I think that is (with a couple of technical tweaks) the concept of a major chord. But I thought you were saying that we didn't have such a concept, only the various things we can do with said chord.
Quoting Banno
OK, but the annoying question is, "Wouldn't it have to follow that 'being a piece of wood' is a way of treating Object A [specify space-time coordinates here]?"
So the Major is the root, third and fifth. It's that string, that string, and that string - and usually the root, again. That's a doing. Then you slide it up and down the fretboard, and set it out in tab or notation. More doing.
if someone blithely says that the major is the root, third and fifth, but doesn't play or listen, do they understand the concept of a major chord? Does an AI have the concept, becasue it can form the words?
On the other hand, if someone can form the shape and slide it up and down the fretboard, but can not tell us about thirds and fifths, do they "have" the concept?
The concept is what we do, and that includes the conversation.
Quoting J
Yep. This counts as a piece of wood.
But here I am relying on the grammar of the demonstrative, with all that this implies. This is shown.
Sure humans evolved, and so too the ability to count, speak, tell stories and much else besides. But that doesn't mean that Frege's 'metaphysical primitives' such as integers and logical principles, can be legitimately depicted as a result of evolution. The aim of evolutionary theory is to explain the origin of species, not an epistemology.
(Interestingly, in a parallel domain, the linguist Noam Chomsky co-authored a book, Why Only Us?, which looks at why h.sapiens alone possess language ability. 'They focus on the cognitive and computational mechanisms underlying language, particularly Chomskys concept of the "Merge" operation, which allows humans to generate infinite expressions from a finite set of elements. They critique simplistic Darwinian explanations for language evolution and emphasize the role of internal cognitive structures over external social or cultural factors. The book combines insights from linguistics, biology, and cognitive science to propose that language is a byproduct of a small genetic mutation rather than a gradual adaptation, challenging traditional narratives about its development' (from jacket description). In other words, an evolutionary leap that enabled a faculty that resulted in exponential differences from non-language-using primates.)
Quoting Banno
It would indeed be a complication, if that is what had been suggested. But Plato dismisses any such idea:
Nor are concepts 'in the head' but more like rational principles. But the ability to count and infer is nevertheless indispensable to rational ability, and that is indubitably facilitated by the highly-developed hominid forebrain that we possess. That is what is at issue: the ontological status of such objects of reason (where 'object' is used metaphorically, e.g. 'the object of thought' ) and the ability of reason to grasp them. I don't see how it can be plausibly denied, as either denying it or advocating it relies on the very faculty which is subject of the discussion.
This is tricky. I want to say that a major chord is not "that string, that string, and that string." If I'd given such an answer back in school, I would have flunked, at any rate. We both know that the term describes three notes, sounded simultaneously, that stand in a certain relation to each other. That's what I'm calling "the concept."
It sounds like you've moved to talking about what it would take to have that concept, and here we're in agreement. Someone who doesn't listen, someone who only goes up and down the fretboard, and "someone" who is an AI do not have the concept, quite right. But I thought you were saying that "concept" itself is doing no useful work here, and I'm still not seeing that.
Quoting Banno
So the "counts as" locution stops with the demonstrative? If I could give a sufficiently accurate set of coordinates for the location of the object we "count as" a piece of wood, along with a chemical description, wouldn't we have to pursue the matter further? "'Being at [coordinates] and consisting of [chemical analysis]' is a way of treating Object A-prime"? And you can see where this is going . . . right into the realm where you can't use demonstratives at all, or at least not in any ordinary-language way.
I'm not trying to refute this way of talking, I just want to understand what it commits me to.
Is that an objection to my proposal?
I'll go over the first part of the argument, again, since it's a while it was addressed and it answers what you have said. But let's move away from numbers for awhile.
We can set up a domain of discourse that contains Alice, Bob and Charlie. Alice and Bob are brave. Charlie isn't.
Simple logic tells us that since Alison Bob are brave, something is brave. That's a first order application of existential generalisation. We can fiddle with the grammar and say things like since something is brave, there are brave things, or braveness exists. Doing this does not commit us to there being anything "in the world" except Alice and Bob and Charlie. Our domain of discourse, and our ontological commitment, remains unchanged.
Well, yes, in that to have the concept and the concept amount to the same thing... the actions performed.
Again, it's not that someone can play various major chord, record and read them, and recognise them when they hear them, and yet not have, or not understand, what a major chord is, because they are missing something more... the concept.
Quoting J
All language stops with showing and doing.
But again, I don't think I've quite understood your point.
Quoting Count Timothy von Icarus
The concept of object serves a purpose for us. It allows us to unite features and attributes into a single this. The concept of feature or attribute also serves a purpose for us. It allows us to anticipate how an aspect of the world will respond to our investigation of it. When we turn our head one way, we anticipate it will move in the other direction. When we walk around it, we expect to see another side of it. So in a sense, objects are instructions for how to anticipate responses to our actions on a part of the world. Knowing about water is know how it will respond to our touching it , moving in it, exposing other objects to it. Knowing about water is also knowing where it came from, how it was created and how it can be transformed. These are important to us when we want to interact with it in special ways.
We could say that the object is an anticipatory dance between us and a part of our surroundings. But notice how the same object changes depending on the pattern of this dance. Take an object as simple as a point. Does it makes sense to talk about a point i swore t of the nature of the way we dance with it?
Note that these conventions are not just ways of describing a thing. They are instructions for how iinteract with it in particular ways in order to achieve a predictable series of responses from it. How that object appears to us is a function of what we are doing with it, how we are dancing with it. To ask if the planet Jupiter exists is to ask about a particular sort of interactive dance. It makes no more sense to imagine Jupiter the planet independently of some convention of practical engagement with it than it does to imagine a tango with only one performer, or a duet with only one singer. Is a photon a particle or a wave? It depends on which apparatus is dancing with it.
OK, that's clearer to me.
Quoting Banno
My point -- somewhat off the point, perhaps -- is that we never arrive at something we can simply take as what it is, as opposed to "counts as." Or do we? This is reminiscent of that Wang essay about Davidson, a while back.
Quoting J
Should we say that, at some given level of demonstration, we have "raw, unmediated perception"? Something we can point to and say, "This," sans interpretation?
But there is currently an evolutionary explanation of epistemology underway, and of science more generally. For now it's just a research program in the perhaps Lakatosian sense, but they have not produced any opinion-swaying papers just yet.
Quoting J
And again, PI§201. There's a way of understanding that is not seen in giving an interpretation, but playing the chord - or maybe changing the key of the tune.
Michael chose infinitesimals with due consideration. There's an issue as to whether they exist or not... odd little things as they are.
? is an infinitesimal iff 0 < ? < 1/n for all n ? ?
But this sort of account doesn't tell us what they are, only what they are not they are not the reciprocal of any natural number. This pisses constructivists off, becasue they like to have an account of what something is before they commit to it's existing. IF there are only natural numbers then there are no infinitesimals.
The account I offered is more permissive than constructivism, since it says that since we can pretend that there are infinitesimals, we might as well say there are infinitesimals. After all, all numbers are just such pretence - "counts as".
This permissiveness might be my downfall.
Quoting J
This isssue is formulated in an interesting way by Joseph Rouse, who contrasts his view of discursive normativity as functioning all the way down from the accounts of figures such as Quine, Sellars, McDowell, Davidson and Brandon, who each in different ways relies on a sovereign. account of nature to ground statements of fact.
Quoting Banno
And , if I understand Davidson correctly, there cannot be conceptual schemes thanks to what Rouse calls Davidsons assumption that semantic meaning is grounded in the token identity of mental and physical events,
One can delimit a measure arbitrarily. This doesn't mean all measures are arbitrary. To count "brown animals" requires knowing an animal, an organic whole, as a unit. I don't think this is arbitrary. For instance, show me a single culture that sees what we consider to be a cow, bear, etc. to be more or less than one of that sort of animal.
Well, the separation, (or inseparability) of thinking and being is a whole rabbit hole. My point would merely be that, when paleontologists unearth two fossilized birds who fell into a tar pit together when the branch they were sitting on snapped 2 million years ago, they (and we) are justified in thinking that there were indeed two birds that fell into the tar pit. This, despite this event being prior to man or any human languages.
Not all wholes are so obviously wholes. There is no doubt a gradient here. But individual animals, planets, etc. make good examples of multitudes.
On a side note, it is strange to me that claims running counter to my own (e.g. "Mars and Saturn being two distinct planets is a fact that is, in an important sense, not dependent on we speak of them.") sometimes feature charges of "anthropocentrism." It seems to me that claims like "there are never two tigers in a clearing, two stars in a binary star system, etc. but that man speak or think of them so," are themselves the height of anthropocentrism, a sort of desiccation of being outside the gaze of man.
Did you think that somehow this is incompatible with the account I gave? How?
Quoting Count Timothy von Icarus
Again, how would such an oddity follow from the account given? If someone counts no tigers when there are two, they are in error.
I probably misunderstood you then. I took: "number is a way of thinking about (talking about, treating, approaching) the animals" to mean that number only/primarily shows up in our (i.e. human) speech and behavior.
Quoting Banno
Quoting Banno
A way of treating something as something is a convention. How can a convention pre-exist the existence of human beings on the planet? Its one thing to say that there was a world prior to the arrival of humans and our conventions of language, but its another to specify the nature of that world (two birds, or a cat and a dog) on the basis of our contingent discursive accounts of it. It is neither true nor false to say that there were a countable number of animals prior to the arrival of humans.
Just to keep the argument clear here, what should we say the description "a cat" is contingent upon? Obviously I'm not looking for a reply along the lines of "It's contingent upon language" -- that goes without saying. But what else? What are the factors that suggest that particular bit of language?
Quoting J
The way I think he would put it is all propositions, including 1st person plural, are derivative of 1st person singular stances, but the 1st person singular includes within its own autonomy its discursive, partially shared circumstances with others.
Quoting J
Language itself is contingent on our material interactions with the world, interactions which constitute a field of possibilities of action out of which objects emerge as what they are. It is our doings that produce such fields. If we are deprived at an early age of the ability to touch, pick up and interact with things, we dont develop the ability to see them as meaningful objects. We see a visual field, but the meaning of object only makes sense in terms of what we can do with it.
Well, this is a pretty general formula. I was hoping you could use "a cat" as an example and describe what the "contingent discursive account" looks like, which allows us to use it to "specify the nature of the world."
Since it seems that no one other than myself is voting for the answer that @Banno offered as a response to the question of the OP, please allow me to attempt to answer it in my own way. I have already suggested my answer in the preceding pages, but now I will express it in a clearer way.
Quoting Michael
No, they do not. Nothing exists in the platonistic sense, if by "platonistic sense" you mean ideal existence. It can be argued (as Mario Bunge has argued in print) that all numbers, including infinitesimals, are really just brain processes occurring in the brains of living humans. That goes for infinitesimal as well as for the set of the natural numbers. It goes for every mathematical object in general, including the objects of geometry, algebra, arithmetic, number theory, mathematical analysis, logic, and the very foundations of mathematics as such. It's not just a "Do numbers exist?" sort of question.
Quoting Michael
False. For one can declare that mathematical objects in general, and infinitesimals in particular, have "conceptual existence", as opposed to "real existence", which is precisely what Mario Bunge argues in his book from 1977 called "Ontology I: The Furniture of the World".
Quoting Michael
False. They exist only in a conceptual sense, not in a real sense, as I have just said. They have "conceptual existence", and what that means is that they are just useful fictions in a quasi-Nietzschean sense. This is precisely what Bunge argues. What infinitesimals really are, is a series of processes occurring in the brain of a living human. If you ask Bunge if "there is a number right there" and you point to a visual sign like "3", which you can physically see with your eyes, Bunge would say no, that's not "a number", that's simply a numeral. It's a meaningless visual shape, and we, humans, have agreed to give it a meaning. It means "three". Three what? Three x, whatever x may be. But all of this is conceptual existence. Numbers, understood "like that", as in realistically, are just a series of brain processes, as I've pointed out earlier.
Quoting Michael
False. This is because the entire explanation that I gave before, which is Bunge's explanation, can be accurately characterized as adhering to mathematical fictionalism. Bunge himself sees it that way, and he has manifested that belief in print, in an unequivocal way.
Is that a criticism or an explanation?
It's not a poor description of Davidson's approach. But Davidson's explanation is not an assumption so much as a description of how nouns work. "Joshs" refers to Joshs, but Joshs is the fellow who wrote that post. Asking which of these Joshs is mental and which physical makes as much sense as asking which of them are made of cheese.
But then it is the presumption that things must be either mental, and hence not physical, or physical, and hence not mental, that underpins much of the confusion expressed hereabouts. Descartes legacy.
Added:
Quoting Joshs
That last sentence is wrong. There were indeed a countable, but unknown, number of animals in the world at any point in the past. That this is so follows from the number of animals being a natural number that is not zero nor infinite.
So we might well perform a reductio, and see which assumption of the argument is in error. Of course a convention can be used to talk about the past. One Million BC is a year. We can talk about how many animals there were back then. Supposing that doing so makes no sense is a philosopher's conceit.
But even these examples are not clean.
When counting cats in the room, are you counting that wildcat? This cat is pregnant, are you counting its unborn fetuses?
When you are counting animals in the room, are you counting the insects? The gut bacteria? The mitochondria? Yourself?
When you are counting planets, are you counting moons? Planetoids? Asteroids?
The reason these are not clean is that categories like "cat", "animal", "planet" are not found in nature. They are invented, not discovered. Which is not to say they are not meaningful. Because categories are subjective creations does not mean they are whimsically chosen. They sometimes have deep ontological bases (i.e. life vs. non-life), and they sometimes do not (i.e. racial categories).
The whole crux of the problem as I see it is that while numbering entails categorization which is a subjective act, numbers nonetheless have very objective properties.
Quoting Arcane Sandwich
I'll repeat a simple argument against this.
If ? is a brain process in your brain, and also a brain process in my brain, then it is two different things.
But if that were so, when I talk about ? I am talking about a quite different thing to you, when you talk about ?.
When we each talk about ?, we are talking about the same thing.
Therefore ? is not a brain process in your brain
And here is the Bungean retort to your argument:
We don't pretend that there are infinitely many integers, because there are infinitely many integers. That's how integers work. And they work that way not just in this or that mind, but as an activity performed by our community.
Where are they, then? Are they under my table? Maybe some of them are there, I should check. Are they inside a box in my living room? Are they growing in the tree in my back yard, as if they were fruits? You say there are, emphatically. So, I ask you: where are they?
We can quantify over things that are not physical. You appeared to understand this, a few days ago. But it's late in your party of the world.
[quote=Bertrand Russell, Problems of Philosophy - The World of Universals]It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word 'idea' also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.[/quote]
The above also applies to number.
Alright, let me phrase it in communitarian terms, then, to speak your dialect for a moment. The only person (to my eyes, at least) that has attempted, in the last few days, to solve the question presented in the OP, is you. And the only person that you managed to convince, was me. These other fine people here with us in this Thread, are working on their own solution to the problem presented in the OP. As in, you have not convinced them of your solution in that sense, you've only convinced me. So, simply as an act of courtesy towards you, I'm now disagreeing with you. But I do it for two reasons:
1) Firstly, because no one is even challenging your solution to the question of the OP in the manner that I am, and;
2) Secondly, because in that specific sense, my solution is better than yours, because my solution is technically Bunge's solution to the problem. If this is reduced to community terms, I prefer to agree with Bunge than with you on that point. So, you see why there's a problem with the very notion of "community Math" to begin with as a concept. Math has to be absolute, in the formal sense that "it's not up for debate", it's not for the community of mathematicians to decide. Whatever is said in formal languages, such as Logic and Math, has to be said in such a way as to be objective and unambiguous as possible. That cannot be done in ordinary talk, no matter how sophisticated. It must be done formally, in a purely formal language, such as the language of first order predicate logic, or set theory, or some other sort of formal language.
Now, what is the explanation for that? What is the "underpinning" of it, so to speak? It is biology, apparently. As in, it is the biology of the brain of a member of the human species.
So, do numbers exist out there in the world? What exists, at most, is a visual sign, such as this two-stick looking thing that we call "seven": 7
Is that meaningless sign a number? I would say no. That's not a number, that's a numeral. And there are no numbers when you count ordinary objects: there are ordinary objects, and each of them has a "oneness" that makes it an individual object. But that is not Math, and it is not Logic, it is Ontology.
If a species evolves to the point where it can recognise 'the law of the excluded middle', does that entail that 'the law of the included middle' can be understood as a product of biology?
Hmmm... what a clever question. Are you sure that this isn't your first rodeo, partner? Let's see.
(spit to the side) The question that you're asking, Sir, is the question that John Dewey asked of the philosophies of both Charles Sanders Peirce and William James. The three of them were Pragmatists, you see, and today they are something like "The Holy Trinity of Classical Pragmatism". Make of that what you will, I just made it up because it sounded pleasing to my ear before I even said such a thing. Not that I take it back, though. Because I do not.
Right, so what did Dewey himself answer? Well, Dewey was of the opinion that, yes, effectively so. If a species evolves to the point where it can "recognize" what we, humans, call "the law of excluded middle", that does indeed effectively entail that "the law of the included middle", as you so cleverly call it in opposition to "excluded", can be understood as a product of biology. And if you simply made a mistake there, intending to say "excluded" instead of "included", that too, dear Sir, can also be understood as the product of biology.
And Dewey held that opinion. What was Bunge's opinion on that matter? I would not know. I'm afraid that no one would, apparently. It seems to be an issue that Bunge himself struggled with as a philosopher and as a scientist, so he was somewhat "silent" or "agnostic" about it.
Hang on, you will say. What about those amazing devices which allow science to reconstruct images from neural data? Subject thinks 'yacht', and lo, a yacht appears on the monitor. But let's not forget that experts in neuroscience and information technology painstakinly construct and train these systems to recognise such correlations, which allows them to reconstruct the imagery that is display on the monitor. The expertise and rational abilities of the scientists is interpolated into the picture in order to produce those results. (Also see Do You Believe in God, or is That a Software Glitch.)
What has actually happened is the cognitive science, not neuroscience as such, although incorporating aspects of neuroscience, has discovered that the brain/mind actually manufactures or constructs what we take to be the 'objective world', the world within which the firm and unyeilding statements of the natural sciences are meaningful. Of course, one of Bunge's nemeses, Arthur Schopenhauer, anticipated this long before either neuro- or cognitive science existed:
[quote=WWI]materialism is the attempt to explain what is immediately given us by what is given us indirectly. All that is objective, extended, activethat is to say, all that is materialis regarded by materialism as affording so solid a basis for its explanation, that a reduction of everything to this can leave nothing to be desired (especially if in ultimate analysis this reduction should resolve itself into action and reaction). But ...all this is given indirectly and in the highest degree determined, and is therefore merely a relatively present object, for it has passed through the machinery and manufactory of the brain, and has thus come under the forms of space, time and causality, by means of which it is first presented to us as extended in space and active in time. From such an indirectly given object, materialism seeks to explain what is immediately given, the Idea (in which alone the object that materialism starts with exists), and finally even the will from which all those fundamental forces, that manifest themselves, under the guidance of causes, and therefore according to law, are in truth to be explained.[/quote]
Bolds added.
Fine, then, you might say. Let's detect the system in the brain which supplies this 'machinery and manufactory' so to show once and for all that it is a physical system. But neuroscience has been able to do no such thing! It has found that 'enough is known about the structure and function of the visual system to rule out any detailed neural representation that embodies the subjective experience.' This provides direct scientific validation of Chalmer's 'hard problem of consciousness', something which the same paper actually says.
So - what of numbers, universals, and the like? I say, along with the phenomenologists, that these are regular structures in consciousness, something like laws of thought. But you'll never trace them back to neural transactions, as such, as they possess a unitary and simple nature that is of a different order to the phenomena of neuroscience. This is why I will insist that numbers (etc) are real but not existent. They obtain and hold within a universe of discourse (wittgenstein's 'language game') - whereas Bunge's crude materialism wants to imagine them encoded in biochemical format, as kind of physical symbols, as oxymoronic conception as there has ever been.
Alright, let me phrase it like this then: consider a fraction, any fraction, I don't know, two fourths, for example: 2/4.
You with me? Good, don't get lost. One must be very concentrated for this. Now, picture another fraction, like 1/2.
OK? Now, Imagine that I said that 2/4 is reducible to 1/2.
Why? Well, take a look:
2/4 = 1/2
And here is where I say "right"?
And you say "I don't agree with you, that looks like nonsense to me. You shouldn't be a reductionist. Why would you reduce two fourths into one half. What happened to the other half? Did you lose it? Is it lost in the world, somewhere? Poor thing, it must be very hungry, especially without the other half."
That's what you sound like to me. Now, you're free to believe whatever you want, but that's just my honest impression of your beliefs in the Philosophy of Mathematics.
The 'solution' on offer not only agrees with this but explains how it comes about. "Counts as..." illocutions set up new games to play. If you decide to move your Bishop along a row, you have ceased to play Chess, and your piece no longer "counts as ..." a Bishop. If you decide that 3+4=8, then you have ceased to do maths, and your "3" and "4" no longer count as 3's or 4's.
That's an equivalence, not a reduction.
The sort of reduction in question occurs when one language game is thought of as a part of anther. In this case you are in effect claiming that mathematics is a game within biology, and not a distinct, seperate activity.
Seems pretty plain to me that this is a mistake. Maths is no a variation of biology any more than Chess is a variation of Poker. They are very different activities.
And the usual scientistic, materialistic retort to that is that if you perform an autopsy, and you open a stomach, you won't find the feeling of "I'm hungry" anywhere, on your anatomy table. It does not follow from an assumption of that nature, that the mind should not be studied as biologically and as mathematically as possible. To say nothing of how it should be studied in a philosophical sense, including our beloved Phenomenology and, more generally, our beloved Continental Philosophy. Among other philosophical traditions, of course.
Quoting Wayfarer
I've never heard of such a thing. I don't think that's possible, I would have heard of it, since I follow the latest developments in the field of cognitive neuroscience, as Bunge did himself.
Quoting Wayfarer
Why are you against the very concept of cognitive neuroscience to begin with? That's the part that I can't seem to wrap my head around. Like, it's not that crazy as you make it sound, man. Bunge himself said that one of the cutting edge sciences of today is cognitive neuroscience. Gosh man, it's not that hard to explain it to people: you take Cognitive science, you take Neuroscience, and you combine them into a single, new academic discipline called cognitive neuroscience. Why are you even opposing those two concepts to begin with, @Wayfarer. Why don't you believe in their "Dialectical Synthesis", so to speak? You can be a Dialectical Idealist, like Hegel, if you want. No one's stoppin' ya. I'm not the "Philosophy Police".
Quoting Wayfarer
He's not one of my nemesis, Wayfarer. Why are you throwing around crazy implications like that? I'm not Bunge. I'm not sure if you're aware of this, but Bunge has been dead for several years. And I don't know about you, but I can't speak with ghosts. I love Schopenhauer by the way, extremely funny and witty.
Quoting Banno
The solution to this is to say that there are potentially infinitely many integers. Once the logic of iteration is in place, there are potentially infinitely many integers just because there is no inherent logical limit to iteration.
Salient bit is that it's not a pretence that there is no largest integer, it's just what we do with integers.
Exactly, that's what I'm saying. Math has to be objective and absolute. As in, it has to have rules, and if you break those rules, then you're not doing math. But that's trivial, because the only rules in math are syntactical, at the end of the day, anyways. For example, if I say:
= 7 2 + 9
That's not math. It uses mathematical signs, but that's not math. It's not a mathematical formula to begin with, from a purely syntactic point of view. Why not? Because the rule itself as a concept say so, just like the rules of Chess say that you can't move the bishop horizontally. It's a rule, in the sense of "regulation" (Reglamento). A correct formula in this case would be the following one:
7 + 2 = 9
Or the following one:
2 + 7 = 9
Or the following one:
9 = 2 + 7
Or the following one:
9 = 7 + 2
We then say that all of these expressions are, in turn, equivalent to each other. And so, and so forth, and welcome to the lovely world of the Foundations of Math. It is a barren landscape, much like a desert. So, are we just going to pretend that this is a "community thing?" No, because "community things" as you understand them, are not isolated from biology, as you seem to suggest. Like, if someone has severe brain damage, from blunt force trauma, in such a way that it causes a specific type of dementia, that person might not believe you when you tell that person that the formula 2 + 2 = 4 is mathematically correct. They "take your word for it", they "trust you" that this is indeed a mathematical formula, but they just don't believe you. Or perhaps in other cases, they try to convince you that 2 7 = + is a legitimate mathematical formula, it just so happens that it's not "Conventional Math", and that the "Community of Professional Mathematicians" have a bias, and that such a bias justifies their discriminatory practices towards people who think that 2 7 = + is a legitimate mathematical formula, and so forth.
(spit to the side, now with a Yankee tone): That's an opinion, not a fact.
Quoting Banno
So are you an Australian Realist, yes or no? You speak Australian English, you don't exactly strike me as the sort of person that would be allowed to speak to King Charles himself. Sup' dawg.
Quoting Banno
False. You're comparing biology to Poker, and that's a fallacy.
I don't know, maybe. But if so, then you're no longer doing mathematics, you're doing something else.
Who cares? There's no set that contains all of the other sets, and no one in their right mind would say that "sets exists" in the same sense that you folks are discussing "do infinitesimals exist?"
No kidding. Anyone will know that corpses do not have appetites.
Quoting Arcane Sandwich
I'm not opposing them. I'm saying they don't support the view that neural states are identical to the contents of thought or that the elements of consciousness can be reduced to the neurophysiology.
The point I've made, which indeed you haven't wrapped your head around, is that the world within which materialism is true, is one created by the brain/mind. I'm saying materialism gets it backwards or upside down, in pursuit of so-called scientific certainty.
Quoting Arcane Sandwich
But you did say:
Quoting Arcane Sandwich
That is the view that I was critiquing, whether or not you later chose to defend it.
Quoting Arcane Sandwich
So what? Materialism and scientism are not the only premises of my personal philosophy. One of my other premises is realism. So, I don't need to take your word for it, or anyone's word for it, for that matter. I am free to believe whatever I want to believe, even if my beliefs are mistaken. What I am not allowed to do, is to utilize my mistaken beliefs as mere tools to be strategically and tactically deployed in any given context. Conversation simple does not follow those rules, it does not abide by them.
Quoting Wayfarer
And I'm saying that you get it backwards or upside down, in pursuit of so-called anti-scientific certainty.
Philosophy in Australia is not that simple.
But without any supporting argument.
Then don't debate with me. No one's forcing you.
Quoting Wayfarer
I disagree. Give me a specific example of such behavior on my part. With quotes.
Quoting Wayfarer
Sure. I'm allowed to agree on some points, and to disagree on some other points, about anything, with anyone. You have the same basic right. Everyone does.
That doesn't answer my question though.
I did just that, but you're in such a hurry to reply that you didn't notice.
Quoting Arcane Sandwich
Sure thing. Hope you enjoy your time here, but might serve not to spread yourself too thin.
I disagree, I considered it, and I arrived at the logical conclusion that this specific example that you quote is not indicative of the behavior you claim to observe in the visual recognition of my writing habits and patterns. Therefore, I claim that what you have presented does not qualify as evidence in the way that you intend it.
Quoting Wayfarer
I'm having a great time here, it's the best Forum I've ever seen. A bit "rambly" at times, but it's a nice atmosphere. I like the colors, green is actually my favorite color.
Quoting Arcane Sandwich
Fifty posts a day is a lot. Make sure you take time to step away from the screen.
I agree it's not a pretence, it's a logical entailment.
Quoting Arcane Sandwich
What we are doing here is not mathematics but philosophy of mathematics. So, all I'm saying is that I think what I outlined is the best way to understand the situation regarding what is a given in mathematicsthat there are infinitely many integers.
But the question of the OP literally asks if they exist in a "Platonistic" (sic) Platonic way.
If the infinitely many integers are understood to be merely potential as a logical consequence of a conceptual operationin this case iterationand are not considered to be actually existent, then the need for a Platonic 'realm' disappears.
Thanks for the link, will read with interest. As Ive often mentioned, Armstrong was HoD when I was an undergrad, and as an aspiring counter-cultural philosopher, I was duty bound to reject Materialist Theory of Mind on the basis of the title alone. Of course he was an erudite and persuasive fellow, but Ive formed the view that the variety of materialism he advocated was basically a form of Christian heresy, based on re-interpreting the Aristotelian universals as scientific laws.
Keith Campbell, on the other hand, I liked a lot. His Philosophy of Matter unit was the best individual course I did in philosophy. Got an HD for an essay on Lucretius. :cool:
The relevant point is that philosophy in Australia has never been monolithic.
Is that University of New England?
I agree with the conclusion of that argument, really. We cannot eat oysters as they are in themselves. That is true. I only wish the premises were true as well.
That's actually really good advice. I'll try to do that. Thanks.
Because once eaten they are no longer "in themselves" but in us?
Hey, could be. Why not?
Mathematics is a very social endeavor. We explore, discover or create the subject, then place our results on paper, then digitalize and submit for others in the profession to read. Initially, it is a product of our minds, then when others read or hear about it, it becomes part of their minds, as well. If they find it interesting they may pursue the topic further and the process repeats itself.
Frequently, I can draw lots of images with pen and paper that help me understand a math idea. That helps make the topic "real". But there are limits. I can draw a line, an interval, and a point (you know what I mean), but I cannot draw an infinitesimal, no matter how tiny a point I can scratch on the paper. For me, infinitesimals are the metaphysics of math. Something I can work with but not develop an intimacy. I leave that to math people who indulge in non-standard analysis (NSA) or hyperreals.
Incidentally, there are very few universities that offer more than a course or two or independent study in NSA. The only two in the USA seem to be U of N Colorado, and U of Wisconsin - even there the pickings are slim.
Best not to be captivated by infinitesimals. The limit concept came along and did the little buggers in.
Could it be because they are the Kantian oysters? Oysters in themselves are in noumenon. They are not available in the physical world. You can only eat the oysters in phenomenon, which are are brought under the physiological and chemical conditions
Something that applies to Mathematical Platonism is the unrestricted comprehension principle.
For me, Mathematical Platonism just leads to paradoxes. It leaves the door open for all sorts of problems.
I think mathematical objects can contradict.
Brains; (mathematical object 1)
Brains; (mathematical object 2)
No problems....they both exist as mental content.
They exist in the standard form of brains instantiating non-physical objects
Exactly. That is the correct answer. You can then add more recent metaphysical theory to that, for example Object-Oriented Ontology, also known as OOO, or simply Triple O.
But folks here don't seem to like Speculative Realism too much for some reason. I blame Alain Badiou for that.
I'll comment on this: I'm not sure why you would say this, viz., "Hinge propositions are said, but never quite rightly." They are often mischaracterized and taken as normal propositions, so in this sense they are often "never said quite rightly." However, they can be talked about if one understands what they are and how they function. Indeed, they aren't justified but neither are they true, i.e., they are outside of epistemological talk. This means that not only are they outside talk of justification, but they are outside talk of truth, at least in the epistemological sense. They are true in the sense that the rules of chess are true. This use of true is not epistemological.
The point of OC 1 is not about showing. It's about saying to Moore that if he does know as he claims, then Wittgenstein will grant the rest of his argument. But of course, Wittgenstein demonstrates that Moore doesn't know in the JTB sense. He's using the concept know, not epistemologically, but as an expression of a conviction. It's purely subjective. This is where people seem to get confused, i.e., they don't understand this point.
Where we do see the idea of showing in OC is that many hinges are shown in our actions even prior to the expression of the belief. Showing is prior to the expression in many ways, but not always. In the most basic of hinges, showing is bedrock.
I given a more detailed explanation in my most recent posts in my analysis of OC.
But you say that in a very perplexed way, and I'll I'm saying is that it's not that perplexing. What would be the perplexing "thing" about it? The possibility that essences can be destroyed? Why? Who says that essences have to be eternal, or even non-physical? Aristotle already dealt with this problem, way back in the day, so to speak. A small seed turns into a sapling, then into a mighty oak, then a lumberer cuts it down, hands it over to the carpenter, who then makes a table. The tree has lost its essence by that point, it has been destroyed. What exists now, in the form of a wooden table, is not a tree. So why is it so perplexing that the oyster's identity is destroyed once you digest the oyster?
The difference is sometimes in the illocutionary force. So "Here is a hand" can be treated as a declarative rather than an assertion - as "This counts as a hand". And as such it can be true, and we can conclude that there are hands.
And treating "Here is a hand" as a declarative would indeed be a showing rather than a saying.
Right but then if it's plain old oddness that you want to talk about, I'd say that Mathematical Platonism in general is far more odd than Mathematical Fictionalism. It is less odd to say "infinitesimals are just fictions, which means that they are a series of brain processes" than to say "infinitesimals exist in some sense in the external world, structuring reality itself from outside of spacetime itself in some mysterious way that is incomprehensible to modern science."
As I said earlier: "If the infinitely many integers are understood to be merely potential as a logical consequence of a conceptual operationin this case iterationand are not considered to be actually existent, then the need for a Platonic 'realm' disappears."
How much lerss would we need to think of infinitesimals as actual existents, and how incoherent is the idea of an actual existent being "outside of spacetime itself in some mysterious way that is incomprehensible to modern science" ?
The problem I have with some platonists is that they want to say that the forms are real, but not existent, and the idea of a "realm" is an incoherent reification, but they cannot say how the forms (or numbers) could be real in any sense other than the merely logical or the empirical.
So what are you asking me, @Janus? If your solution is the right answer to the question in the OP? Because there's also @Banno's proposed solution, as well as the one that I proposed myself (mathematical fictionalism). How do you propose to solve this, in practical terms?
Not a good wording. If they are true, they have epistemic standing. "Here is a hand" justifies "There are hands". Hinges have truth values.
Can you explain what about Wigners famous paper you think is confused?
Wigner believed that mathematics is unreasonably effective at producing forms of description that just so happen to fit the patterns of the physical world remarkably well. In so doing, he confused a passive representation of how things really are with an organizing scheme that forces us to see the world in a particular way (mathematical idealization) and to ignore other equally valid ways of conceiving it.
A big part of that paper is not that maths just happens to work, but that powerful predictions can arise from mathematical models that were not at all expected when the model was initially created, sometimes in subjects that seem remote from the one to which it was initially applied. So why is it that mathematical predictions so often anticipate unexpected empirical discoveries? He doesnt attempt to explain why that is so, as much as just point it out.
I myself am a critic of scientism, the attempt to subordinate all knowledge to mathematical quantfication, but I dont think that invalidates Wigners point.
Indeed. My late ex-father-in-law, a Hungarian aristocrat - exchanged letters with Wigner, and he translated a few of these for me. I don't find it surprising that occasionally a development in math portends a scientific discovery. Mathematics arose from observing phenomena in the physical world, and those initial discoveries generated logical consequences, some of which provide insight into that same physical realm.
And, more than observing. Cats and dog are quite capable of observing the things humans observe. But only h.sapiens can measure and quantify.
(I read somewhere in my incessant stream of internet content that the basics of physical geometry were invented - or discovered - by the Egyptians, as a consequence of having to re-create fence lines on the Nile delta after the annual flood season. This involved apportioning highly irregularly-shaped parcels of land so that each landowner ended up with the right quantity, even though the shapes of their allotments were completely different to the year before. But then, they did build the Pyramids ..)
I am pretty sure that oysters don't know they are oysters.
They don't. But just because an entity cannot know much (i.e., oysters), that doesn't mean that it doesn't have certain features, which it cannot know. I don't know how many individual hairs I have on my head. That doesn't mean that I don't have hair.
If you managed to count them, you would know how many. It is not infinity for sure.
In that case, I will offer a different example: I have never seen my own heart, but that doesn't mean that I don't have one. An oyster cannot know what it is, but that doesn't mean that it is not an oyster.
It is an inductive statement with very high probability. You have never seen your heart, but from the empirical fact that all living humans have heart, therefore you must have one. No problem with that.
Quoting Arcane Sandwich
OK, it sounds valid. (Had to edit my initial comment)
If oysters don't know they are oysters, then is it right to call them oysters?
Quoting Banno
I thought the whole point of hinge positions , language games and forms of life was that the concept of truth was precisely irrelevant to them? Hinge propositions, as the grounds of truth-apt assertions, are themselves neither true nor false.
94. But I did not get my picture of the world by satisfying myself of its correctness; nor do I have it because I am satisfied of its correctness. No: it is the inherited background against which I distinguish between true and false.
199. The reason why the use of the expression "true or false" has something misleading about it is that it is like saying "it tallies with the facts or it doesn't", and the very thing that is in question is what "tallying" is here.
200. Really "The proposition is either true or false" only means that it must be possible to decide for or against it. But this does not say what the ground for such a decision is like.
205. If the true is what is grounded, then the ground is not true, not yet false
(On Certainty)
Quoting Wayfarer
Apparently he has some ideas concerning why that is so.
Wigner wrote:
Quoting Wayfarer
If Wigners point is that the laws of nature are written in the language of mathematics, then thats precisely what Im trying to invalidate. Its the human-constructed norms of nature that are written in the language of mathematics, not anything to do with nature in itself.
I think so, yes. Because we're the ones calling them "oysters", they don't call themselves that. They can't. But a stone can't call itself a stone either, and it's still a stone nonetheless.
I thought you were discussing about the identity of oysters, hence asked the question. I know what your saying, but questions still remains.
Identity means the owner of the identity claims who it is. They don't get given identity by some authorities like hey arcane sandwich this is your identity. But arcane sandwich applies for the identity to his local council or passport office, saying name is arcane sandwich, date of birth is 25 12 1985, place of birth Argentina. Marital Status: maybe, Job tittle: Professional Metaphysician ... etc etc.
But in oysters case, I am pretty sure they don't claim their identity details to anyone. They might have all the details for their identity, but maybe they don't see the point of applying for identity, or simply aren't able to due to lack of resources whatever.
They still get called as oysters, even if they don't know they are oysters, and that is fine, no problem with that. But when you said identity of oysters blah blah, I thought wait a minute here, something is not right, and did ask you the question.
But doesnt that assume the very separation between mind and world that elsewhere youre very keen to criticize? Humans are, after all, part of the very world which mathematics describes so effectively. While its true that not everything that counts can be counted, the human ability to intuit the quantifiable forms of nature seems, as Wigner says, tantamount to a miracle. (Plato has Socrates say it is something the soul learns before the descent into the material world.)
Applied mathematics has been extraordinarily effective because it enables us to connect mathematical with physical principles. Schopenhauer noted in passing that science really teaches nothing more than the relation of one idea to another because, for him, the entire domain of phenomenal experience comprises ideas. He also says that science cannot get at the inmost truth of things, with which I also agree. But it nevertheless enables an enormous range of powers. Thats the sense in which Plato deems Dianoia (mathematical and geometrical knowledge) higher than sense perception, although not the highest form, which is noesis.
Ask @Sam26.
Quoting Wayfarer
On the contrary, it is because mind-body and world are inseparable that the world we perceive is a world that matters to us in particular ways We are not just part of the world, we interact with our portion of the world in normative ways. as does one aspect of the world with another. There is no one way the world is in itself , it world can show up for us in many different ways, depending on how we choose to cut it up. If we carve it up by way of idealisms like mathematical logic , bodies ina geometric space and physical causality, it will appear to miraculously conform to our calculative specifications. If we burrow beneath these idealisms, the world will show up for us not as conforming to mathematical rules and laws, but as amenable to an infinite variety of patterns of normative relationality with respect to our practices or knowing.
Quoting Sam26
Chess rules are not true or false in themselves, the moves in the game which these rules specify are true or false.
Since the laws of chess are the ground in the basis of which moves in the game can be correct or incorrect, the laws of chess are not true, not yet false. Is this what you meant?
Quoting Arcane Sandwich
The only question in the post you are respionding to is this:
Quoting Janus
and it is a rhertorical question. So I wasn't asking you anything.
You ask me how I proposed to solve this in practical termsthe only solution (more a dissolution) I am offering was the one at the top of the post you were responding to:
Quoting Janus
Does that count for you as a practical solution? If you are seeking an empirical solution to such questions, I'd say you are wasting your time. Seems it would be impossible to establish a fact of the matter.
I find this some of the most interesting ideas on the forum. The notion that scientific laws and maths are contingent human artifacts rather than the product of some Platonic realm seems more intuitively correct to me. But as an untheorized amateur, I would say that.
I'm just asking how you propose to solve the problem of multiple answers to the OP, that's all. Don't jump to conclusions or assume things about me, sweet chicken. If your solution is the correct one, then what do you propose that we do? Should we vote? Should a mod step in and mark you solution as the correct one? What?
I agree.
Quoting Tom Storm
We are all amateurs in this regard. Mathematicians rarely spend their time discussing or arguing the issue. It has so little to do with traditional math research. But times change for any human endeavor, and "modern" mathematics, category theory e.g., is an elevated and abstract perception of the way the subject has been for millennia and is possibly closer to the Platonic conundrum, although I can't see how.
And can you see how this notion doesnt take away from science the usefulness that we know it has in our lives? People tend to go into a panic when you suggest his to them, as if the ground has been pulled out from under them and suddenly cats will be mating with dogs and murderers will run rampant in the streets. But accepting this idea of science as contingent artifact leaves everything exactly as it has been. It just gives us further options we didnt see before.
Artefacts are made from the stuff around us. It's not an either-or.
What I present is nothing more than how I look at itfor me the purported problem regarding whether mathematical entities exist in any platonic sense is a non-issue, a collateral result of reificational thinking.
It was a joke. You know that, right?
Quoting Janus
Have you solved the problem of the OP? If yes, cool. If not, what are we arguing about, you and me? Clue me in, as I've no idea.
How would I know?
Quoting Arcane Sandwich
I've solved the OP to my own satisfaction, which no doubt will count for little for others. It's not clear to me that we are arguing about anything.
Because I said "sweet chicken" at the end? Who says that seriously?
Quoting Janus
Then why are you hassling me, matey-mate?
I don't know you and thus I have no idea what you might be serious about.
Quoting Arcane Sandwich
I have and have had no intention of hassling you. You have been responding to my posts and I to yours. It's called a conversation, or at least an attempt at one.
Ok. Lets converse then. I believe that you have offered a good solution to the question of the Platonistic (sic) existence of infinitesimals.
Quoting Tom Storm
I don't think it's so black and whiteeither this or that. We formulate the laws of nature, but we are constrained in those formulations by what we actually observe to be so. We see regularities and invariances everywhere we look. We encounter number in our environments simply on account of the fact that there are many things.
So mathematics has its roots in experiencethe world really is mathematical, but not (obviously) explicitly soit is we who make it explicit, and it is not a contingent enterprise, but must be in accordance with what we actually experience. What we actually experience is not up to us. It's like we speak the language that the world teaches us, a language it does not know or articulate by itself.
I think there is confusion around the term 'platonic realm'. There is a domain of natural numbers, right? Where is it? Obviously a silly question; 'domain' is in this context a kind of metaphor, like a 'place' or 'realm', when there really is no such place or realm. Nevertheless the domain is a real one, in that it includes integers but not imaginary numbers. Go back to that essay What is Math I quoted right at the start of this thread. We read 'Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing outside of space and time makes empiricists nervous.' And that, I reckon, is what is behind the myth of the 'platonic realm'. We try to imagine it as a literal domain or place, which doesn't make sense, but then, only things that exist in space and time are considered real. So the 'platonic realm' then becomes imagined as a kind of ghostly palace with ethereal models of ideal objects, when it is not that at all. It is a domain of 'objects' that can only be grasped by reason.
You never answer the question so often posed to you. How could something that does not exist in space and time be real? Real in what sense?
Is the "domain of natural numbers" more than merely an idea? The set of all sets, is it real?
Quoting Wayfarer
That may be how you try to imagine it. I have no doubt your imagination is not representative, given human diversity, so I think there is an element of narcissism in your thinking we all imagine in this kind of way.
Quoting Janus
What do you mean, 'I never answer it'? I have >23k posts on this forum, and a significant proportion are devoted to just this question. I've said already in this thread:
Quoting Wayfarer
So there's my answer to it, it was the substance of my first forum post. Criticize it all you like, but don't say I haven't tried to answer the question! Which is, a distinction between what is real, and what exists, where the latter is a small sub-section of the former.
This was my first ever forum post, around 2008:
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Well, sometimes it should be a conversation terminator, I suppose. If you've already solved the problem of the OP, what more is there to talk about, in this Thread? I'd continue the conversation in some other Thread.
Quoting Banno
Not from, with. Its an important distinction. Artifacts are produced by the way we incorporate elements of our world. What that stuff is is their role in the normative gestalts we construct.
If you must.
Yes, I'm aware of these arguments and well summarised. But what we don't often hear are the ideas @Joshs has proposed in more detail. I find them particularly interesting. I guess I used the term platonic realm as a short cut for transcendental.
Sure. I guess this is a common sense account. By the way, I have no commitments either way, I am just interested to hear more.
Absolutely. I accept that something doesn't have to be 'true' (or correspond to reality in some mysterious way) to be incredibly useful.
I've found a book on Husserl, phenomenology and mathematics. Tough going but I think my very simple grasp of philosophy of maths can co-exist peacefully with Husserl's.
Is it physical or non-physical?
Let's say,
Physical is notated by square brackets...[ x ]
Non-physical by parenthesis....( o )
A grouping required for existence by braces..{ a;b }
(Mathematical Platonism),
Is notation for non-physical Platonism.
{ ( Mathematical Platonism) },
Is the notation for existence with no requirement for physical form.
Probably not viable.
A brain being physical is [ Brain ]
A Brain with non-physical content is,
[ Brain ]; ( Mathematical Platonism )
And giving it the designation of existing...
{ [ Brain ]; ( Mathematical Platonism ) }
Another variation?
{ [ Unknown physical phenomenon ];
( Mathematical Platonism) }.
I like the Brain; ( non-physical ) form.
I could try some others
(Mind)...creates...[ Matter ]. ???
{ [ Matter ] }...{ [Brain]; (non-physical content) } is emergent and exists.
Any more?
The problem I find here is that number does appear in the phenomenal worldwe encounter great numbers of phenomena, and you seem to be ignoring that fact. Also what does it mean to say that number, laws etc are objects of nous? Does it simply mean that they are ideas?
If numbers, laws etc., and all other objects are ideas in the "One Mind" then surely, they exist as such. Do you believe they stand out for the "One Mind" ? If so then they must exist for that mind, no?
I have often said to you that your position needs a universal mind or God in order to explain how we all experience the same world. But you always seem to pass this over and to be reluctant to posit such a mind. That is why your position seems confused and inadequate to meyou seem to want to make a claim, but then when asked just what your substantive claim is, you seem to have no answer.
Quoting Tom Storm
Do you think it is more plausible that our formulations are completely arbitrary or that they are constrained by what we actually experiencethat the whole logic (grammar) of our language evolves in keeping with the primordial, given nature of that experience.
Note I am referring to the logical structure of language, not to the particular sounds and marks that conventionally represent this and thatthey are, onomatopoeia aside, seemingly mostly arbitrary.
Quoting Arcane Sandwich
:up:
Because as a rational sentient being, you can number them.
Quoting Janus
The point about objects of intellectual cognition such as numbers, geometric and scientific principles and the like is that while they are ideas, they are the same for all who think. They're not the property of individual minds. See in this post 'Augustine on Intelligible Objects'.
Quoting Janus
There are many difficult metaphysical questions involved in this enquiry. First, I don't believe, on the same grounds that I don't believe numbers exist, that the 'One Mind' exists. It is an expression, like a figure of speech, to convey the irreducibly mental side of whatever can be considered real. Put another way, whatever is real, is real for a mind. But that mind is never an object of experience, it is only ever the subject to whom experience occurs.
(From Eriugena, "things accessible to the senses and the intellect are said to exist, whereas anything that, through the excellence of its nature, transcends our faculties is said not to exist. According to this view, God, because of his transcendence, is said not to exist. He is described as nothingness through excellence. Likewise Paul Tillich 'to argue that God exists is to deny Him.')
I've started to explore the connection between the unknowable subject and Terrence Deacon's absentials. Absentials, as you will recall, are 'constitutive absences: A particular and precise missing element that is a critical defining attribute of 'ententional' phenomena, such as functions, thoughts, adaptations, purposes, and subjective experiences.'
Quoting Janus
Because it's a reification. To declare that such a mind exists is to make of it an object, one among others. The sense in which intelligible objects are reified into 'objects' parallels the sense in which God is reified into 'a being'. (Heidegger also makes a similar point in his distinction of seine and seiendes.)
As for how we experience the same world, I invariably reply that as we are members of the same species, language-group, culture and society, then there is a considerable stock of common experiences which we will draw on in interpreting what we see. But it's nevertheless true that different individuals all experience a unique instantiation of reality albeit converging around certain commonalities.
I agree oysters have properties and essence for being oyster. Likewise stones and golds do too.
But I am not sure if oysters have identity. Having identity sounds like the owner of the identity has some sort of idea of self e.g. arcane sandwich identifies himself as an Argentinian, and also a professional metaphysician. Before arcane sandwich identified himself with the property, no one in the universe knew the identify apart from arcane sandwich himself and the ones who knew him already.
Hence when you say oyster has identity seems to imply that the oysters are self conscious, and know who they are, and also let the world know they are the oysters.
But from empirical observation on oysters, that looks a highly unlikely case. Here lies a contradiction which could be clarified. :)
Right, what you're talking about there is something similar to identity politics, but that's not what I was talking about. What I was referring to is something more like the classical Law of Identity, also called the Principle of Identity. It says that every entity is identical to itself, A = A, or in first-order logic, ?x(x=x). What the Principle of Identity doesn't say, by itself, is if Reality is One or Many (i.e., a single gigantic, indivisible Universe, or a Universe in which there are many different individual things). In that sort of the debate, I'm with the "Many" camp, I think that the Universe is many things, not one gigantic thing that cannot be divided. In that sense, the Principle of Identity, together with the premise that there are Many things, not just one, entails not only that each entity is identical to itself, but also that it is different from other entities. What is it that guarantees that difference? It might be the identity that each entity has, be it a human, an oyster, or a stone. But the identity of each thing doesn't tell us much, it only tells us that this oyster = this oyster, it doesn't tell us how that oyster is different from a stone. Which is why, arguably, you need the concept of an essential property, or an essence. Perhaps there's nothing more to that than the concepts of spacetime and uniqueness: for example, this oyster has a different spatiotemporal location than that other oyster, and each of them is unique in its own way. Otherwise, they would be the same oyster, instead of being two different oysters. However, insofar as both of them belong to the same group (the group of oysters), they presumably have something in common, which differentiates that group from other groups (for example, the group of stones). So, oysters in general, as a group, probably have something that makes them unique and different, and that is what you may call the oyster's essence, essential property, or even identity.
Great explanation. I see your point. Yes, I was talking about the identity which identifies an individual or an entity as denoting or naming. You must have been talking about identity as the principle of identity A=A or ?x(x=x).
I still don't get it, because you don't say oysters are identical to oysters or oyster groups, or stones are identical to stones or stone groups. You just say, oysters are a specie of fish, or stone belongs to the non-metallic mineral type material.
You never say humans are identical to the human group. The word human already has meaning for the entity belongs to human specie.
Hence, I am not sure if it makes sense to say oyster has identity to mean oysters are identical to the other oysters or oyster group.
Technically they're mollusks, not fish, but it's an understandable mistake. People call them "shellfish" (literally meaning "fish with a shell"), but they're not fish. Some other people think that whales are fish, for example, but they're not fish either, they're mammals. If these creatures had no identity, if they had no essential property, then we humans would not be able to recognize them as different creatures. There are counter-arguments to what I'm saying, I'm aware of that, but I think that those counter-arguments can be defused.
Quoting Corvus
Sure you do. Every human is a member of the human species, Homo sapiens. I understand species as groups, not as composite objects. But what is it that allows us to group humans into a single species? It must be something that each human has, some "human essence", if you want to call it that.
The very word "essence" is a very loaded word, and scientists usually avoid it. But I see no reason to avoid it, other than the fact that it has some religious and metaphysical connotations. But if you remove those connotations, it's actually quite a practical term.
:ok: :fire:
The problem with that question, in my opinion, is that it wrongly assumes that vegans do not eat animals because they are animals, and not because they are entities capable of suffering. If it turns out that oysters cannot feel pain, then vegans can eat oysters. For the purposes of veganism, it doesn't matter that they are animals. What matters is that they cannot experience suffering.
EDIT: Another example. Imagine that someone discovers a new species of plant, in the Amazon or somewhere else. And imagine if that plant could feel pain. In that case, it would not be vegan to eat it. Why not, if it's just a plant? Well, it doesn't matter. It would not be vegan to eat it because it can experience suffering.
So, it's complicated.
Quoting Arcane Sandwich
It is, which makes Philosophical discussions and readings fun.
Animals also apprehend great numbers of things. but they don't have the language to name them and declare their quantities.
Quoting Wayfarer
They were probably first articulated by an individual mind. The fact that they make sense to most all human minds can be explained by the idea that human brains have evolved to be generally structurally the same as each other.
Quoting Wayfarer
But you believe numbers are real and you believe the One Mind is real.
Quoting Wayfarer
Of course considering something real is irreducibly mental. and whatever is judged to be real is judged to be real by a mind. Do you think experience occurs to anything other than individual subjects? Does the One Mind experience everything like God is said to? Do you think the minds of individual subjects are somehow connected, connected in some way hidden from us and that that explains why we all experience the same world?
Quoting Wayfarer
I would agree with you that it is a reification. But those who believe God is real (as opposed to imaginary) would deny that their belief is a reification and would also deny that God is an empirical or abstract object. So, it is not necessarily either/or.
Quoting Wayfarer
For me Deacon makes too much of absentials. It's not controversial at all that sentient creatures can be motivated by the absence of things, by lack. So, in that sense the absent has causal efficacy. But the feeling or apprehension of absence is not itself an absence.
Quoting Wayfarer
I've addressed this idea of yours before. It just doesn't pass muster. That we are all similarly constituted as perceivers explains that we see things like colour in the ways we commonly do. But it cannot explain the fact that we see precisely the same things in the same places at the same times. Either there are real existents there that we are seeing, or existents are ideas in a universal mind in which we all participate or our minds are connected in some way we have no idea about.
Any other explanatory ideas come to mind for you?
Hence the distinction between what exists and what is real. I said, I know it's a difficult distinction to make and that it's controversial, and that it's an heuristic rather than a theory as such, but I hope you can at least see what I'm getting at. (I think @Tom Storm does.)
Quoting Janus
That's convenient for you. It happens to be central to his entire project of Incomplete Nature.
Quoting Janus
That's because we don't. The most detailed analysis of objects is, of course, physics. And quantum physics is the most detailed form of physics. And here, it has been demonstrated that no two observations of quantum events are exactly the same for different observers. See A quantum experiment suggests theres no such thing as objective reality. Why also I refer to Christian Fuchs and QBism - he says:
And this is because there is an ineluctably subjective aspect to anything we perceive as real. Our minds construe the same things in the same ways because we are similar kinds of subjects, so we can arrive at inter-subjective agreement with respect to objects. Of course those objects exist, but the reality we impute to them originates with the mind, through identification, naming, apperception, etc.
Quoting Janus
That is very much the thrust of Bernardo Kastrup's analytical idealism, with which I'm definitely sympathetic (despite disagreement with some of his polemics). I think it's also implicit in neo-platonist philosophy. It's much nearer to what I believe to be the case, than the direct realism which holds that the world comprises individual subjects and particular objects that are all independently real.
Yes, and I've read it; although more than ten years ago now. Is he an authority? Must I agree with him?
Quoting Wayfarer Of course we do. The dog sees the ball I throw. If you and I stand in front of a complex painting and I point to a particular spot on it and ask you what colour you see there, we will almost certainly agree. I see a tree three feet to left of the post of my carportdo you imagine you might see something different therea mouse, a car, a tractor. If you were here with me now, I could point to hundreds of objects in the house and environment and ask you what you see there, and we would agree every time about just what it was I was pointing at. You are simply wrong about thisyou just don't want to admit it because it doesn't suit your narrative.
Quoting Wayfarer
So, you don't actually believe it, but it's nearer to what you do believe. Then what is it that you do believe?
Of course not. When I cite a source for support, it is to orient my arguments with respect to others, standard practice in debates.
Quoting Janus
And you're what Kant describes as a transcendental realist. That is a term he uses to describe the philosophical position that treats objects of experience (phenomena) as if they exist independently of the mind and are exactly as they appear to us. In other words, a transcendental realist assumes that the world as we perceive it corresponds directly to the way the world truly is, independent of our cognitive faculties.
This is not part of 'my narrative' but a philosophical argument which you've never demonstrated a grasp of, then, having failed to understand it, at which you lob various ineffective responses. But, thanks for the target practice!
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Having carefully distinguished between transcendental idealism and transcendental realism, Kant then goes on to introduce the concept of empirical realism:
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Your argument should be support enough for your position. But you don't present arguments, you just cite authorities.
Quoting Wayfarer
Typical! Instead of engaging with my point, that we all see the same things in the same places at the same times you seek to dismiss me by labelling. The question as to whether or not things exist in themselves exactly as we perceive them to be (which I think is probably an incoherent question anyway) is irrelevant to the point. What has to explained is the incontrovertible fact that we (and even animals) all do see the same things.
And you don't answer anything that would commit you to a definite position:
Quoting Janus
I've reached the point where I cannot even take you seriously. My honest opinion is that you do not argue in good faith. I guess it's time to stop trying.
I'd agree with that. I've tried to field your many repetitive complaints in good faith for a lot of years, but it does become wearisome.
This thread is a continuation of the ancient philosophical debate between Realism and Idealism*1. Today, the debate is mainly between the here & now authority of pragmatic Science and the timeless logic of theoretical Philosophy.
Modern Quantum Physics is often described as the "most thoroughly proven" (mathematically) of the sciences*2. Yet, it is not true-false proof, but statistical probability calculations to support interpretations (beliefs) about Reality : Quantum Bayesianism. Consequently, the science of fundamental material reality does not support objective Certainty, but degrees of subjective Belief that may be "closer to truth".
Our generalized beliefs are not Real (ding an sich), but Ideal (concepts, not percepts). The directly perceived tree is as real as it gets, but the whole forest is an idea about trees-in-general. :smile:
If the world is an illusion, why does it seem so real?
The reason the world "seems real" is because our brains actively construct our perception of reality based on sensory information, creating a seemingly solid and consistent experience, even though the underlying reality might be different at a fundamental level; essentially, our brains interpret and present the world to us as a cohesive, tangible experience, making it feel real, regardless of its true nature.
___Google AI overview
Empirical Science is Probabilistic
Down at the level of atoms and electrons, quantum physics describes the behavior of the very smallest objects. Solar panels, LED lights, your mobile phone and MRI scanners in hospitals: all of these rely on quantum behavior. It is one of the best-tested theories of physics, and we use it all the time.
https://www.scientificamerican.com/article/quantum-physics-isnt-as-weird-as-you-think-its-weirder/
Note --- Practicing quantum physicists have been forced to "shut-up" about the Reality of the world, and to "calculate" their best approximation of probabilistic physical Truth. They don't observe the Higgs Boson, The detect it mathematically. And they believe its ephemeral existence helps to make sense of their philosophical Standard Model of particle physics.
So, if we read that statement literally, what you're saying there is an anti-formalist comment. In that sense, your comment is a materialist one (it's the "form vs matter" debate, nothing to do with idealism in that sense).
Hinges aren't true in the epistemological sense, i.e., justified and true. However, one can use the concept of true in other ways, just as the concept know can be used in other ways. For example, someone might ask when learning the game of chess, "Is it true that bishops move diagonally?" You reply "Yes." This isn't an epistemological use of the concept.
I wouldn't use the phrase "true or false in themselves." I think that just confuses things even more. However, if you mean that the rules of chess are not something we discovered as a fact of reality (JTB), then I agree. The point is that what we accept as true can be independent of provability. So, hinges can be accepted as true, i.e., apart from provability and epistemological uses. I believe this is also how we should see some mathematical truths, e.g. 2+2=4 is true.
Quoting Joshs
This is slightly different but related. The rules of chess do not describe the truths of reality in the same way that "water freezes at 32 degrees F" does. Instead, they constitute the very framework within which true and false (correct and incorrect) can be assessed.
Quoting Sam26
But 2+2=4 is not arbitrary in the way that "bishops move diagonally" is.
Or rather, 2+2=4 follows the rules of adding in the same way that a diagonal bishop move follows the rules of chess. But the rules of adding are not mere convention, they capture some sort of truth that has not been stipulated into being, like the rules of chess were.
Yes, you are correct; it's not the same. However, any system, whether epistemological (JTB) or formal mathematical systems, will have hinges (hereafter referred to as basic beliefs) that are true, but not in the JTB sense. All I'm saying is that both are basic statements of belief, and they function in similar ways. In both systems, these basic beliefs are bedrock to the system and function in a way that's not provable within the system. Some mathematical statements are accepted as true for the system to function.
Quoting hypericin
Some basic beliefs are arbitrary and some are not, but both are basic and needed for the system to function. The difference in the use of truth is that one use is epistemological, and one is not. This is where part of the confusion lies, at least in OC. Another part of the confusion is the idea of hinge proposition, which is why I think they should be called basic beliefs.
I believe that mathematical systems are the product of minds and that anything created by that mind/s involving mathematics will have mathematical systems intrinsic to it. In other words, mathematics will be discoverable within that creation, by other minds, which is the case when we discover math as an intrinsic part of the universe. I'm an Idealist and believe that at the bottom of reality is consciousness (other minds). So, I believe, mathematical knowledge is intrinsic to this consciousness or mind. So, the answer to the age-old question, "Is mathematics discoverable or created by minds?" - it's ultimately a product of a mind/s, but it can be discovered as part of a creation too. So, again, if any mind uses mathematics to create something, then mathematics will be discoverable within that creation.
One can believe this as an idealist without believing in some religious doctrine.
Quoting Sam26
So for example, when Moore raises his hand and says I know this is a hand, and therefore it is true that it is a hand, he is confusing an epistemological with a grammatical use of the concepts of know and true, because he considers his demonstration as a form of proof. Would you agree? But then what would be an example of a grammatical use of the word true in Moores case? Something like: it is true that Moore is invoking a particular language game by raising his hand and saying he knows it is a hand?
Quoting Sam26
Wittgenstein seems to suggest that the intelligibility of water boils at 100 C. depends on such a bedrock of hinge propositions ( a whole way of seeing nature).
The way I explain Moore's confusion, which is Witt's point, Moore's use of know is more akin to an expression of a conviction. In other words, a subjective feeling of truth expressed by emphasis or gesticulation. A feeling of certainty, not to be confused with objective certainty or knowledge.
Moore does consider "I know this is a hand," to be empirical proof, a self-evident truth. In the Wittgensteinian sense "This is a hand" would be a grammatical truth by virtue of the language game and context. However, Moore is saying something different, he thinks he has good reasons to suppose that he knows "This is a hand." Wittgenstein disagrees.
I edited this in later, so you may not have seen it.
Quoting Sam26
Wittgenstein seems to suggest that the intelligibility of water boils at 100 C. depends on such a bedrock of hinge propositions ( a whole way of seeing nature).
I'm not sure it's needed though. Denial of an extra-self world seems like a philosophical (maybe psychological) problem alone, a Cartesian curse. Should we expect a purely deductive dis/proof?
Quoting Sam26
Done.
Well maybe God thought of numbers first so they exist in God's mind?
Here's a thing-
On the x-axis mark the line 0 to 1. You have one unit made of infinitely many points. These points are dimensionless; they have no width. But if you assert you are at 1 unit on the x-axis how did you get there? By lining up an infinity of dimensionless points? If this is the case you assert 0 + 0 + 0...for infinity add up to extension or width. So it would seem that an infinity of zero widths add up to a unit of width. Go figure.
Can't one just say there are potentially infinitely many prime numbers? Also one can say that-
1/p1 + 1/p2 + 1/p3 +...diverges to infinity where these p are the primes.
But what does it mean to say there are infinitely many? What does 'are' mean? Does it mean they exist or potentially exist?
Saying mathematics exists independently of our minds and saying numbers exist independently are two different things. Mathematical truth, as it really is, may be something we have never imagined.
@Michael "3. If there exist any abstract mathematical objects, then human beings could not attain knowledge of them. Therefore,"
Why would consciousness be limited to physical spacetime? Mysticism asserts that consciousness transcends the physical.
I don't believe it is, and the hard problem of consciousness suggests it is not, but naturalism assumes that it is. There was a lot of discussion earlier in this thread about that conflict.
Bertrand Russell says something like: "mathematics is the field where we believe we know things most certainly, and yet no one knows what mathematics is about." By contrast, earlier mathematicians often did think their subject had a clear subject matter. Where they simply mistaken? Naive?
Here is the argument, the difference is one of equivocation. Barry Mazur has this really nice article called: "When is one thing equal to another?" https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf&ved=2ahUKEwiPlpKX5_WKAxXmhIkEHcOREwcQFnoECBgQAQ&usg=AOvVaw0j1f7DfoQP7OKuvRZ37rIU
If you read older mathematics though it might seem like they could be talking about different subjects, because there is often a strong distinction between magnitude and multitude, and both are primarily derivative of/abstracted from things. That is, there can be a multitude of things, e.g. 6 cats, or magnitudes related to things, e.g. a wood board that is twice as long as another. Mathematics is the consideration of the properties of magnitude and multitude in the absence of any other properties. For instance, a ratio would be understood as specifically a relationship of magnitude, never as a number.
Because of this, metaphysics and the philosophy of perception/epistemology end up bearing a closer relationship to mathematics.
Anyhow, on first glance, if one accepts this and a "study of magnitude and multitude," it seems like it may make various flavors of realism more plausible (immanent realism or platonism).
Hmmm . . . never thought of it that way.
Mazur's article on category theory introduces one to modern mathematics. Not necessarily mathematics as practiced by a great many professionals. As time passes levels of abstraction increase and the subject seems more and more like philosophy and less and less like calculus, for instance.