Is maths embedded in the universe ?
And if so does it point to a creator ?
I wish to explore this because we have come up with many mathematical formula that describe how the universe operates from the famous formula such as e=mc2 which has practical applications to many others.
But even simpler than that take for example 1+1 = 2 this can correspond to reality. Though in itself a simple mathematical calculation one apple and another apple means you have effectively applied the math to the real world.
The question is what came before? maths or apples (or the universe) and if maths can theoretically describe anything does that mean that reality is a subset of mathematics made manifest ?
Or is maths completely independent of the physical universe and it just so happens that some mathematics is good at describing some aspects of the physical universe and in fact supersedes it?
I wish to explore this because we have come up with many mathematical formula that describe how the universe operates from the famous formula such as e=mc2 which has practical applications to many others.
But even simpler than that take for example 1+1 = 2 this can correspond to reality. Though in itself a simple mathematical calculation one apple and another apple means you have effectively applied the math to the real world.
The question is what came before? maths or apples (or the universe) and if maths can theoretically describe anything does that mean that reality is a subset of mathematics made manifest ?
Or is maths completely independent of the physical universe and it just so happens that some mathematics is good at describing some aspects of the physical universe and in fact supersedes it?
Comments (213)
Quoting simplyG
Math was created within a closed system. Think of a language written in symbols. We came up with math because we need to describe the physical world predictably and reliably. We could have come up with a whole different numbering system than the one we have now.
I feel that your question is similar to saying that the periodic table of elements has always been embedded in the universe waiting to be discovered.
No and no. As @L'éléphant notes, it is a language made up by humans, although there is evidence that the capacity for numerical thinking is hereditary in humans and perhaps other animals.
Mathematics is only useful insofar as it applies to reality.
You could create a plethora of equations and none would have any bearing on our existence. The laws of math precede existence because they do not abide by time.
Math just as any tool is an idea first.
It seems to me like this is partially right, and partially missing something. Sans some interpretation of consciousness where mind does not emerge from or interact closely with nature, it would seem to me that our descriptive languages have a close causal relationship with nature.
Moreover, as points out, basic mathematical and logical reasoning appears to be a trait of many animals. I would add to this that it shows up in human babies before language, and as an emergent property of insect "hive minds," instantiated across what we take to be "individuals." Thus, it seems like there should be some causal tie in between our evolution and our ability to develop the descriptive languages we do. In the more immediate sense our descriptive languages are based on our experiences of the world.
A child locked in a room alone learns no human language and such abuse results in profound mental retardation, although there is a lot of plasticity if people are removed from these settings. In the event that you cut off essentially all sensory inputs, as well as you can without immediately killing an animal, mammals tend to die, and thus don't develop any reasoning abilities.
Hence, it seems like there is an essential way in which the world shaped how we even view our closed systems. Pace Wittgenstein, I would say that it's not a mistake to take "necessity as cause" as fundemental, vis-á-vis the "pure necessity," of logic. If anything, it seems like such "pure necessity," is simply an abstraction of the causal necessity we live with, something we create based on experiences of necessity as cause.
The periodic table is an interesting example because it is in ways arbitrary and in others not. It seems likely that any sufficiently advanced aliens should recognize the table, even if they have moved beyond seeing it the way we do.
In this sense, there are ways logic and mathematics are "out in the world" to the extent that it seems we learn about the systems from the world as much as we describe the world in terms of the systems. I mean, there is a reasons we "teach" mathematics, draw diagrams, make sensory analogies, etc. Bidirectional causality in essence.
Incompleteness and undefinablity made philosophers retreat into deflationary theories of truth and abstractly "closed systems," in the 20th century, separating logic from psychology and ontology, and I think this might be a mistake. It's a sort of fear of error that becomes a fear of truth. Seeing that there might not be an easy answer, any one system that was isomorphic to the world in all cases and yet hewed to our familiar tools of "the laws of thought," we decided that logics and mathematics must simply be "closed off" sui generis abstractions. I'd argue that simply can't be the case. The very limits of our thoughts about such systems themselves are enshrined in nature. Take a hard blow to the occipital lobe, the area used to process vision, and you can lose a lot of the ways you're able to described the geometries of mathematics. Our understanding rests on perceptual systems.
I also think it's interesting that a lot of non-neurotypical people make big breakthroughs in mathematics, Mandelbrot, etc.
Mathematician Eddie Woo showed photos of a river delta, tree, lightning, and human capillaries, which all have remarkably similar patterns, and said:
I agree with you, but it has always amazed me how often some obscure phantasmagoric math ends up being useful in the real world.
Good, thorough post. Extra point for using "sui generis."
I've been reading a lot of science lately - switching from my usual fiction. I'll add this to my list. It was written in 1996, do you think it's out of date? Do you know any good, more recent books.
When non-Euclidean geometries were invented (discovered?) they were considered parlor games. It was only later, when it became known that astronomical spacetime is not Euclidean that their use became evident. The description of this reality depended on what seemed to be a useless game.
I view Mathematics as the meta-physical structure (inter-relationships, ratios, proportions) of the physical universe (objects, things). In other words, Mathematics is the Logic of Reality. In that case, the math (logic, design) is prior to the material implementation (stars, planets, plants, animals). Math doesn't "supersede" the matter, but it necessarily preceded the Big Bang execution of the program of Evolution that produces the Reality we see around us. Hence Math/Logic may be the abstract invisible essential ding an sich that makes concrete substantial things what they appear to be to our senses. :smile:
Right, there is a strong tendency for the mathematical patterns "at work in," or "describing" natural phenomena to be similar at very different levels of scale. For instance, large overlaps between how earthquakes, the timing of fire flies blinking, and heart cells work.
To be honest, it surprises me how stubborn different fields are about acknowledging this. "Neurodarwinism" was viciously attacked because "natural selection can't involve intentionality, it is random." First, it's unclear if this is even the case (the whole EES debate), and it seems motivated more by philosophical concerns about teleology or pseudotelology creeping into explanations. But moreover, it seems silly because there simply IS a huge mathematical and conceptual overlap between how neurons are pruned, how genes undergo selection, how lymphocytes are selected, etc.
This doesn't mean "x and y are the same thing." It means they are isomorphic in key ways. It seems to me that it's important to recall how things are different, but also to look at how they are the same across scales. The general tension with the rise of information theory and chaos theory as the two biggest paradigm shifts in the sciences I can think of in at least a century, is that the new advocates of complexity like to look across silos, while academia as a whole is still quite siloed. And unfortunately, the silos are sometimes defended, not as useful synthetic organizing principles, but like fortresses.
That's the only book on Complexity I've looked at.
Not sure why anyone worries about teleology. The universe has certain characteristics. It has structure. That structure seems more conducive to certain relationships and ratios.
No.
This question doesn't make sense.
I think a subset of mathematics usefully describes subsets, or aspects, of reality and the rest (most) of mathematics does not. As suggested by Max Tegmark (David Deutsch, Seth Lloyd, Stephen Wolfram et al), the universe might be nothing more than a lower dimensional mathematical structure (i.e. a reality, n. naturata) imbedded in higher dimensional mathematical structures (i.e. the real,, n. naturans).
Not insofar as physical systems are (Quantun Turing) computable.
I agree as I wrore above.
I don't understand what you mean here by "supercedes".
:up:
If we take pure math to be a product of pure consciousness (whatever that is). Then these eternal concepts/abstractions/calculations/numbers which precede the physical universe are only evokable so via consciousness otherwise what would exist then? Just dumb matter.
[quote=Galileo]
Mathematics is the language in which God has written the Universe
[/quote]
Just leaving that quote by Galileo there as seems apt to my first question .
:ok:
This is a good starting point for a new thread because I was trying to discuss with @schopenhauer1 in the Kit Fine thread about what is existence without an observer.
So, I will respond to my comment that " without an observer, the world is a two-dimensional existence". And I know this will take a lot of argument but just as a start, I say that because without an observer (without us), there's no more vantage point at which we view the reality or the world. Think about "no point of view", but only the universe. All points of location can just be two-dimension.
So maybe a thought experiment about what would go away if sentient observers disappear.
https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
Numbers are eternal objects and the universe is designed around them.
Numbers exist by purely abstract means. Namely iteration and partition (Set Theory)
Start with /
iterate //
again ///
etc //////////////////////////////////////////...
Partition each step: {/} {//} {///}...
= 1, 2, 3,...
Now set them in proportions as in Leibniz's formula-
1/1, 1/3, 1/5, 1/7,...
And, very simply, we go from set theory to pi to space. Now add time and you've got the basis for a universe. Numbers are the 'atoms' of spacetime.
Quoting EnPassant
This is true. The universe is designed around numbers. But who designed the scientific concept of universe such that mathematics meshes with it so conveniently? Perhaps mathematics and the logic on which its based rest on presuppositions about the world rather than the world itself. This would mean that logic and math are derived forms of thinking or grammars.
Mathematical truth is not a supposition. It is logical independently of what we think.
Quoting EnPassant
I think Im going to put that on a T-shirt
I'm not sure if I see the direct relation. Here we're talking about a universe that has observers in it. The question seems to be: "can we say math exists in nature objectively?" Put another way, we could ask: does mathematics exist "out in the world," as opposed to being an "artefact of the sensory system and cognitive processes."
This question doesn't seem that hard to me. Objectivity as a concept only makes sense in terms of observers. Without observers the entire concept of "objectivity," becomes contentless. In an observerless context it becomes a term that applies to everything equally, thus conveying nothing. Something's being "more or less objective," is only meaningful in the context of the possibility of thing's being "more or less subjective."
And it doesn't make much sense to say "what does the world look like without eyes," or "how would we think about the world without minds."
Objectivity then is about descriptions that smooth out the differences that arise from variances in subjects' phenomenal experience. You view the same phenomena in many different ways, using tools, experiments, etc., and identify the morphisms between all perspectives.
Of course, objectivity ? truth, but in terms of objectivity I would say "math existing out in the universe," as an objective fact is about as secure as anything. We can see the same ratios at work across a huge range of phenomena, while looking at them in all different ways. The instantiation of mathematical patterns in the world seems to me to be on more sure footing than even bedrock concepts like mass or energy, both of which have shifted over time.
I think the reason this question even gets any traction is because of some common conflations that are easy to fall into.
First, conflating objectivity with truth, such that the truth of the universe is "as seen without eyes and thought of without a mind," which leads to all sorts of conceptual difficulties.
Second, the idea of the world of phenomena as somehow illusory, as opposed to a noumenal world where true causal powers lie. In a lot of ways, this division seems akin to that made by Plotinus, Proclus, and Porphery about the relations between Nous, Psyche, and the material world.
In this view, only the higher, noumenal realm can be causally efficacious, or at least there is only downwards causality from the noumenal onto the phenomenal, not the other way around. To my mind, this creates an arbitrary division in nature that many don't really want to defend, but which it is nonetheless easy to accidentally fall into.
The second point might take us too far afield, but it does shine some light on a third conflation, that the distinction between subjective / objective is essentially the same thing as the distinction between phenomenal / noumenal, treating them as synonyms. They aren't synonyms though, the second distinction comes with far more baggage.
If we avoid these conflations then it's easy to see that the observation of mathematical patterns that describe and predict the world are among the very best established empirical facts.
To this point, I would argue that thinking of math as a "closed," system can be misleading in this context. Obviously our development of mathematics doesn't appear to be causally closed off from the world.
The idea that mathematics is a closed system is a fairly modern invention. To be sure, prior to the use of this language there was a strong tradition of "mathematical Platonism," but people also generally thought of math as simply the discovery of relations that obtained due to necessity. For example, Euclidean geometry was thought to be the only valid geometry and it was thought to be a prime example of how the world (necessarily) instantiated mathematical principles.
[Quote]
I feel that your question is similar to saying that the periodic table of elements has always been embedded in the universe waiting to be discovered.[/quote]
There obviously is a sense in which the periodic table always was waiting to be discovered. Barring conciousness being non-natural, it seems obvious that living things must incorporate within themselves descriptions of nature that are isomorphic to nature. Such descriptions might be highly compressed, based on heuristics that make them prone to error, etc., but this doesn't preclude the fact that they are to some extent accurate descriptions of nature. And, to the degree they are accurate, I don't see any problem with saying something like "what the periodic table describes exists in the world." It's a claim that can be supported better than many empirical claims.
Math is imbedded in the universe non-computationally through its many proportions, if you mean the universe which we refer to inside experience, but the concepts we invent in our minds does not exist in that universe apart from us, just like how the laws which describes its behaviour does not exist inside it, the concepts of our minds can never be abstracted from these proportions alone, instead we must apply dualities onto these proportions to describe them in terms of a language thinkable to us, there is no reason to believe that this language applies to those proportions independently of the process we go through to think in terms of that language.
"Discover" - Middle English (in the sense make known): from Old French descovrir, from late Latin discooperire, from Latin dis- (expressing reversal) + cooperire cover completely. So, to uncover or make clear something previously unknown. A great deal of scientific discovery concerns things that are 'embedded in the Universe waiting to be discovered', the Periodic Table of Elements being one.
Quoting simplyG
Of course. Numbers are fundamental artifacts of reason, they are basic to the means by which rational thought is able to analyse and predict events and establish causal relationships. Further, mathematical statements are true in all possible worlds, not just in the world we've happened to experience.This universality and necessity cannot be accounted for if mathematics is merely a generalization from experience. Indeed there is a sense that they possess a kind of logical order which is assumed by empiricism.
Quoting Julian August
One of the most interested popular articles on philosophy of maths is Eugene Wigner's essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Wigner emphasizes how mathematical concepts and equations often prove extraordinarly apt in describing and predicting physical phenomena. He marvels at how mathematical structure can correspond so closely to the behavior of the real world and points out that mathematical concepts have often been developed before they find any application in the physical sciences, where they turn out to be very powerful. There is the famous case of the discovery of anti-matter. In 1928, Paul Dirac formulated a relativistic quantum mechanical equation (now known as the Dirac equation) to describe the behavior of electrons. This equation incorporated both the principles of quantum mechanics and the theory of special relativity, describing electron behavior at relativistic speeds.
However, the equation had solutions that implied the existence of an electron with positive energy (which was expected) and another set of solutions that implied an electron with negative energy (which had never even been considered). Initially, this negative energy solution was a conundrum. Instead of discarding it or considering it a mere mathematical artifact, Dirac proposed that it could correspond to a particle that had the same mass as an electron but with a positive charge - purely on the basis of the mathematics. In 1932, just a few years later, Carl Anderson discovered the positron (or positive electron) in cosmic ray collisions, which was the exact particle Dirac's equation had predicted. The discovery of the positron, the antiparticle of the electron, marked the first evidence of antimatter and validated Dirac's groundbreaking prediction. Many analogous discoveries came out of Einstein's discovery of relativity theory, which often made mathematical predictions well in advance of the means to empirically validate them (hence the oft-repeated headline, Einstein Proved Right Again.)
Wigner concludes by suggesting that the deep connection between the mathematical and physical worlds is something of a miracle. While there might be no definitive explanation for this connection, the fact remains that mathematics serves as an invaluable tool for understanding and describing the universe. (In fact, the word 'miracle' occurs a dozen times in the essay.)
Does this 'point to God', as the OP asks? That's a moot point. But Wigner points to the relationship between mathematical insight and empirical discovery as compelling evidence of the deep ties between the mathematics and the workings of the physical universe. And I think it's safe to say that this relationship transcends naturalist accounts of mathematics - it truly is a metaphysical, not a scientific, question. (See this great CTT interview with Roger Penrose, Mathematics - Invented or Discovered?)
That's why Shannon's work is fundamental to data compression on digital devices. It lead directly to the ability to greatly reduce the number of bits required to encode data.
[quote=Source; https://www.eoht.info/page/Neumann-Shannon]Shannon, the pioneer of information theory, was only persuaded to introduce the word 'entropy' into his discussion by the mathematician John von Neumann.
The theory was in excellent shape, except that he needed a good name for missing information. Why dont you call it entropy, von Neumann suggested. In the first place, a mathematical development very much like yours already exists in Boltzmanns statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position of advantage.[/quote]
I don't know how to define "closed" in this context, but I agree. With over 26,000 Wikipedia pages, and counting, mathematics continues to expand its realms, especially into abstractions and generalizations. I suppose "closed" could mean based on axiomatic set theory, which it normally is, although frequently some distance from Cantor's creations.
Quoting Wayfarer
A nice post. But I'm curious about this statement. How do you know this? :chin:
If a statement is necessarily true, it means that there is no possible world in which the statement is false. It holds true in every conceivable scenario or possible world. An example of a necessary truth might be a tautological statement like "All bachelors are unmarried".
Conversely, if a statement is possibly true, it means that there is at least one possible world in which the statement is true. However, there might be other possible worlds where the statement is false. An example might be "There is a planet entirely covered in water." It's possible, but it's not necessarily true across all possible worlds. It's contigent as distinct from necessary.
Lastly, if a statement is necessarily false, it means that there is no possible world in which the statement is true. For instance, "A square has five sides" would be considered necessarily false.
I think there's a relationship between this and basic arithmetical logic - I can't see any other way for it to be. That's why I'm generally of the 'maths discovered not invented' school - I think it rests on a foundation of the discovery of necessary truths (although with mathematical ability, also comes the ability to create imaginary number systems and so on, which muddies the waters somewhat.)
Sadly, I know nothing about any of this, so Im already lost. But I thought it fit the topic nicely.
For a really fun book on a lot of the "big picture," ways information theory could really become a paradigm shifter across the sciences the book "The Ascent of Information," is quite good. It had a good audio version too.
And then the Great Courses "Science of Information," course is really great too. Probably the best condensed intro I've seen is the intro chapters to "Asymmetry: The Foundation of Information," but it's a hideously expensive small print academic book, so outside of working at a university or LibGen it's not really a good option.
But yeah, it sort of shocks me how this stuff hasn't become more essential to basic science education. It's not a new shift, although it is picking up steam. But it's still crammed into this weird interdisciplinary space the way chaos theory and complexity studies is. The two have a ton in common too. I wish I could have stumbled across a book like "Complexity: A Guided Tour," when I was in school, it would have probably change my life lol.
Thank you very much. I dont have a clue about what I dont know about the topic. For example, I dont have any idea what symmetry has to do with it.
Never heard of The Great Courses. I think Ill pass on that $239.95 option. :D
Asymmetry: The Foundation of Information Is $42.77 on kindle. Thats no problem.
But maybe Ill start with The Ascent of Information. Only $9.99, and it sounds very interesting.
If you are speaking of "worlds" in our universe, or in some parallel universe, worlds we can reckon with, then probably yes.
If you are speaking of worlds that are "possible", but not possible for us to envision, then, how could you possibly know? You wouldn't know they were possible to begin with. Are there "things" beyond our comprehension, things we don't know we don't know? How could you know? Why can you assume in some universe beyond our imagination our brand of logic must hold?
Logic is in the mind, but not of it. Its not our invention but what we are able to discover through reason. I really dont think that the idea of a world where there are no necessary facts is even an hypothesis.
You are saying you can't imagine any sort of alternate world in which the logic we enjoy would not exist. How do you know this is a universal limitation rather than a human shortcoming? A lot hinges on the definition of "possible" and our limitations thereof.
Im saying its an idle thought. It has no meaning.
With which I agree. Welcome back from your vacation. :cool:
I think the Great Courses are pretty much all on Audible for like $15 or Amazon for like $10 a month. Or free on Wonderium with a trial and then if you cancel that it's like $9 a month. I don't know who they get to pay their original prices lol, the resellers are way cheaper. Probably an economies of scale thing.
Thanks
Quoting Wayfarer
You are allowing yourself to be fooled by your invented grammar. Mathematics, and the logic it is based on, rests on a peculiar way humans decided at a certain point in their history ( actually, as a gradual process of development) to formulate the idea of the persistingly present, self-identical object. Doing so led to subsequent assumptions such as the law of identity, the law of non-contradiction, geometrical forms such as lines and magnitudes, and propositional statements binding or separating a subject and predicate. Mathematical structures are only embedded in the world to the extent that we force the world into such odd forms. But such processes of objectivation are derived modes of thinking which hide within themselves what gives them their sense and intelligibly. Put differently, a persisting object only persists for us in its meaning by continuing to be the same differently.
2+2 is true because of the shared presupposition built into the grammar of 2+2. A=A is true because it is presupposed as a basis for our formulation of objectness. Presuppositions are true in all possible worlds only to the extent that all possible worlds share the same or similar presuppositions. Given that presuppositions are contestable, partially shared constructs emerging from and maintained in actual interpersonal contexts of use, the truth of a proposition is dependent on this preserving of a particular meaningful sense of a proposition. When underlying presuppositions change , the propositions whose intelligibility depends on them dont become false, they either change their meaning and criteria of truth, or become non-sensical. When the sense of a proposition changes slowly enough, we tend not to notice the change in meaning and instead reify the proposition as self-identically repeatable. This is how we end up fooling ourselves into believing that mathematical structures are embedded in the world. What is embedded in the world is human discursive interactions, not the abstract forms that we fabricate out of these relationships.
Quoting Count Timothy von Icarus
I hadn't thought of it in those words before. I save that to use when I'm talking about Taoism.
Quoting Count Timothy von Icarus
In Taoism, as I see it, the relationship you describe between noumenal and phenomenal is made explicit as the fundamental basis of reality, although rather than "arbitrary" I'd say "human."
Do we view the same phenomena or view similar phenomena that we call the same for the convenience of fabricating the kinds of objects that are amenable to mathematical calculation?
Quoting Count Timothy von Icarus
Karen Barad is among those who suggest that the geometric notion of scale must be supplemented with a topological notion of it. What this means is that scales interact each other to produce not just quantitative but qualitative changes in material forms.
Quoting Count Timothy von Icarus
Thats because the presuppositions concerning the irreducible basis of objectness which underlie mathematical logic guarantee that it will generate a world of excellently established facts. It fits the world that we already pre-fitted to make amenable to the grammar of mathematics. The very prioritization of established facts over the creative shift in the criteria of factuality demonstrates how the way mathematical reasoning formulates its questions already delineates the field of possible answers.
Quoting Count Timothy von Icarus
It depends on how we describe living things. From an enactivist perspective, an organism is an inseparable system of reciprocal relations among brain, body and environment. There is a certain operational closure giving organisms a normative goal-oriented orientation toward their world but, strictly speaking, no inside and no outside, no separable parts or forms. The cognitively knowing organism doesnt represent its surroundings, it interacts with it guided by expectations and purposes that can be validated or invalidated. If there is anything isomorphic between such self-organizing organisms-environment systems and nature in general it would not be particular contents but a general principle of organization that applies to all living things. Piaget identified such a formal principle as the equilbrating functions of assimilation-accommodation, which he suggested could be extended to non-living complex systems.
I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. The entities are nothing but the changing interactions themselves, which tend to form relatively stable configurations. According to this approach, the world is not representation but enaction.
What a happy coincidence how well the products of mathematical science work! We should all thank our lucky stars.
Quoting Wayfarer
Thats the point. To understand the origin of mathematical
logic in certain presuppositions about the way the world is constructed is see why it is not coincidence at all. As you say, the products of mathematical science work well. I would add that they work precisely, accurately in the sense dictated by the demands of formal logic.
I thought that's what I was arguing for :chin:
Incidentally, I haven't attempted Husserl Philosophy of Arithmetic as it seems a very challenging read. But is this thumbnail sketch of Husserl's philosophy of math any good?
"Husserl was interested in the psychological origin of number concepts. He explored how individuals move from concrete individual experiences to abstract generalizations that constitute numerical understanding. For Husserl, numbers aren't just abstract entities; they have their roots in our lived experiences and acts of grouping and collecting.
Husserl examined the act of counting as foundational to the concept of number. Counting isn't just an external action but involves internal acts of consciousness, where one recognizes and groups objects together as units. This grouping then forms the basis for the abstract notion of number.
Collective Combination (Kollektiv-Vereinigung): This is a key term in Husserl's analysis. It refers to the act of consciousness by which we perceive a group of objects as a singular totality. For instance, seeing a group of five apples not just as individual apples but as a collective "five." This act of collective combination is essential for the emergence of numerical concepts in consciousness.
Criticism of Psychologism: While Husserl was interested in the psychological origin of mathematical concepts, he argued against the idea that the validity and truth of mathematical principles were dependent on psychological processes. This distinction paved the way for his development of a rigorous phenomenological method that sought to distinguish between subjective acts of consciousness and the objective structures they intend.
Husserl was deeply interested in how consciousness constitutes mathematical objects and how these acts of constitution relate to the objective validity of mathematical truths."
This is exactly what I've many times said to you, arguing against your Platonic notion of numbers.
Perhaps. Quantum theory is still searching for a way to understand what's happening down there. Other sciences, I'm not so sure. Intra-actions . . . who knows?
My only argument is that numbers are real but not material. It's quite compatible with Husserl's attitude as far as I can tell.
Quoting Wayfarer
The only issue I have with it is that one could get the impression that the reason Husserl argued against the idea that the validity and truth of mathematical principles were dependent on psychological processes was because he thought their validity and truth was dependent on the world. What he was trying to do was avoid psychologism (which he was accused of in Philosophy of Arithmetic) by grounding mathematical principles in transcendental
phenomenology.
Quoting Janus
As an abstract concept, it's a universal. More to the point, per my earlier posts in this thread, is that mathematics can be used to make discoveries hitherto unknown about nature herself, thereby demonstrating that they are something more than simply 'mental constructs'.
What is the difference between a universal concept and a generic concept? You are talking about math as an aid to science, right...can you give me an example of pure math being used to discover anything about nature? Do you think any discoveries about nature are about nature as it is in itself or merely as it appears to us?
Good question. In the context of Aristotle's philosophy, as well as in biological classification and other systems of categorization, a "genus" is a class or group that includes different species. Note however its ultimate source in Aristotle. That's where the concept of 'genera' and 'generic' originated.
Quoting Janus
See this post about Dirac's predictions of positrons.
Quoting Janus
I'm incllined to agree with Bohr's aphorism 'It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.' Also Heisenberg's 'What we observe is not nature in itself but nature exposed to our method of questioning.'
It seems to me that maths, based on number, is grounded in immanent phenomenology. We encounter diversity, difference and similarity, everywhere.
Quoting Wayfarer
Right, so a generic concept is the concept of a class of things which share some salient similarities, a class of species. You haven't said what you think a universal concept is, and whether it is the same or different than a generic concept.
Quoting Wayfarer
This is an equation belonging to quantum physics and relativity theory, not pure math.
Quoting Wayfarer
We agree on that.
Nevertheless it could never have been discovered without mathematics.
For Aristotle, universals are real in the sense that they genuinely exist as aspects or features of particular things (hence, 'moderate realism'.) They are not mere names or linguistic conventions as some nominalists would later argue. In Aristotelian realism, when we recognize a universal like "redness" or "humanity," we are recognizing something real but this universal only exists as it is instantiated in particular objects (like a red apple or a specific human being). So, while universals don't have independent existence outside of particulars as they do in Platonic realism, they are nevertheless genuinely real aspects of the empirical world in Aristotelian realism. There's a nice essay about Aristotelian philosophy of maths on Aeon.
The view I'm developing is that numbers and universals and the like are real, but not manifest or existent. They are implicit in reality and are manifest or instantiated by particulars. It's reasonably close to Scholastic realism. As I understand it, C S Peirce held a similar view, and was opposed to nominalism. 'Peirce understood nominalism in the broad anti-realist sense usually attributed to William of Ockham, as the view that reality consists exclusively of concrete particulars and that universality and generality have to do only with names and their significations. This view relegates properties, abstract entities, kinds, relations, laws of nature, and so on, to a conceptual existence at most. Peirce believed nominalism (including what he referred to as "the daughters of nominalism": sensationalism, phenomenalism, individualism, and materialism) to be seriously flawed and a great threat to the advancement of science and civilization. His alternative was a nuanced realism that distinguished reality from existence and that could admit general and abstract entities as reals without attributing to them direct (efficient) causal powers. Peirce held that these non-existent reals could influence the course of events by means of final causation (conceived somewhat after Aristotle's conception), and that to banish them from ontology, as nominalists require, is virtually to eliminate the ground for scientific prediction as well as to underwrite a skeptical ethos unsupportive of moral agency.'
The problem though is that mathematicians do not adhere to the law of identity, they actual violate it. By affirming that whatever is referred to by the symbols on the right side of the "=" symbol is "the same" as whatever is referred to by the symbols on the left side, they use "same" in a way which violates the law of identity.
Physics itself would not be possible without mathematics. If, as you agree, it is not the task of physics to find out what nature is, but rather to produce models that present the best human understanding of what is observed and measured, then it doesn't seem to follow that mathematics is embedded in nature at all, but rather that it is embedded in the human understanding of nature. But that mathematics is embedded in the human understanding of nature is hardly controversial.
I know it's a bit of a tangent, but you haven't provided a reference for that passage about Peirce you quoted.
I'm guessing most of my colleagues in the profession would agree with this. A mathematical universe is inexplicable conjecture.
But I am tempted by the possibility of mathematics being reified at the quantum levels. :chin:
I've always been somewhat intrigued by this:
[quote=Kumar, Manjit. Quantum (pp. 98-99). Icon Books. Kindle Edition. ]Nicholson showed that the angular momentum of a rotating electron ring could only be h/2? or 2(h/2?) or 3(h/2?) or 4(h/2?) all the way to n(h/2?) where n is an integer, a whole number. For Bohr it was the missing clue that underpinned his stationary states. Only those orbits were permitted in which the angular momentum of the electron was an integer n multiplied by h and then divided by 2?. Letting n=1, 2, 3 and so on generated the stationary states of the atom in which an electron did not emit radiation and could therefore orbit the nucleus indefinitely. All other orbits, the non-stationary states, were forbidden. Inside an atom, angular momentum was quantised. It could only have the values L=nh/2? and no others.[/quote]
Only multiples of integers allowable!
Math describes the objects in the external world, and that is it. It is just a numeric and logical language operating from the mind. Our spoken and written literal language describes the objects, world and even mental states in the propositions we express. But math can only describe the objects and world in numeric forms.
Unlike the literal language, math cannot describe mental states of the human mind. For example, the literal language is able to say something like "I l feel tired." or "I am anxious." "I am excited about the new book I just ordered." Math cannot describe that at all in any shape of form or ways.
Therefore math is limited to be applied to only physical objects, movements of the objects, location of the objects, temperature, speeds, brightness pressures etc of the external world.
When one says, 1 apple + 1 apple = 2 apples. In this case, there is absolutely no necessary connection between the apples and the numbers. The number was added by the observer and the counter empirically. The apples are physical objects in the world. The numbers, and the deducted total are from the human mind observing and counting the apples.
And when you say, the car was travelling at 60 miles per hour, it is the same case. The car and 60 miles per hour has no necessity at all. It was just measured by a speedometer (speed = distance ÷ time
) or laser speedo gun at that moment of observation, the car was running at the speed.
So, math is just a measuring and calculating tool using numbers applied to describe and predict the measurable properties of the external objects and movements. Math is not embedded in the universe. Of course not !
I agree that 'embedded in nature' is a poor way of expressing it, but the predictive capacities of mathematics and the way that it enables genuine discovery can't be disputed. That Peirce ref is here.
A useful current reference to the whole topic is here, What is Math? from the Smithsonian Magazine. The Platonist view (i.e. 'numbers are real) is represented here:
The empiricist objection is that
My belief has always been that numbers are real but not physical. Of course, that contravenes physicalism, for which everything must be reducible to the physical, so it can't cope with that idea. It has to reject it. So I think those comments are revealing of the real philosophical issue at stake: that mathematical realism, the idea that numbers and mathematical relations are real but not physical can't be allowed to stand.
Both obviously. You might use many different tools to measure a single tornado, ground sensors, aircraft sensors, and satalites, each measuring different things, and then you might also measure many different tornados.
And then you can generalize from tornados to dust devils to water spouts, to vortexes of all sorts and see that there are some general principles that hold for all of them and some differences between each occurrence (or even in the same occurrence over time).
But of course no one mistakes a hurricane or a vortex in a river or even a dust devil for a tornado. If you've seen a tornado, and it's aftermath, it's fairly easy to ascribe to it its own sort of natural kind. Nothing else rips six story concrete buildings off their foundation like a child kicking over a toy. It's causal powers have a particular sort of salience. You can see why God picked one as a vehicle of the divine presence to overawe Job.
However, if you're studying vortices on Jupiter you might safely throw 10 meter wide vortexes in with 10,000 meter wide ones. The salience of size differentials there is less relevant to us. So, of course the types are "constructed," but they are also constructed in ways that are posterior to the advent of human beings, e.g. relevance to an ecosystem or the scale of the relevant system.
[Quote]
Karen Barad is among those who suggest that the geometric notion of scale must be supplemented with a topological notion of it. What this means is that scales interact each other to produce not just quantitative but qualitative changes in material forms.[/quote]
I'm not sure what this means. I'm guessing something to do with local versus global changes? What would be an example of a qualitative change? Is this sort of like strong emergence?
IDK, lots of phenomena seem to elude our attempts to understand them. If the world is so easily shaped by how we view it, why did so many discoveries have to wait for millennia before yielding to inquiry? That people in the West bought into Aristotlean physics for millennia did not turn our world into one in which Aristotlean physics held. Instead people had to invent epicycles, etc. to explain why the world crafted by thought did not correspond to the world of sensory experience. For a modern example, we could consider the causes of conciousness.
I'm not sure about mathematics necessarily entailing some sort of necessary objectness; it seems to me that process metaphysics works just as well with mathematics as more popular substance interpretations. Plus, mathematics allows for plenty of creativity, far more than the natural sciences I'd say. Hence why it is still often considered under the liberal arts.
Agreed. Process explanations are replacing substance ones everywhere. The periodic table is more a classification of long term stabilities in process that are common in the world. This means it isn't, as originally thought, a map of primary substances. But such stabilities are still out in the world waiting to be discovered.
Obviously, if no one "enacts" the discovery it isn't discovered, but if you interact with helium it is still different from interacting with nitrogen.
Is the observer not in the universe? If they are, then it seems like the observer should have a body. But then isn't mathematics embedded in the body of the observer, part of the universe?
In this sense, it seems like mathematics must be "embedded in the universe." So the question seems to be more "how did our mathematical intuitions and those of other animals emerge and did mathematics not exist in any sense prior to the first animal that possessed mathematical intuitions?"
Moreover, animal bodies have a causal history, and that causal history must be such that it resulted in animals that understand aspects of mathematics. Additionally, mathematical understanding appears to be something individuals can gain from interacting with the world. Someone locked in a room doesn't learn calculus. Someone with severe brain damage likely cannot learn calculus or remember the calculus they once knew. So what is the connection there?
If mathematics wasn't "out there," how and why did mathematical intuition become common to several organisms? If mathematics isn't anywhere in the world prior to this, what did this sui generis intuition emerge from?
Neoplatonism had a good answer for this with the three hypostases, and the immateriality/immortality of the soul, but unfortunately their ontology seems less and less plausible today because of the tight interaction of mind and body.
Good point. I believe that humans are alienated from the universe. They live in the world, but they are not part of the world. The world presents itself to humans as an unknown object (M. Heidegger). Humans cannot fathom the world in full, and definitely is not part of the world, i.e. the universe. (Kant, Schopenhauer)
Even if all humans reside in their own bodies, they don't know what is happening in their own body, or how long the bodies will keep functioning for them. After deaths, bodies disintegrate into the space separating the mind evaporated into the thin air. Where is the connection between the humans and the universe?
All humans are alienated, and separated not just from the world, but from other human beings too. No one can access another's mind, for example. We only communicate via language use, and of course, with the gift of reason, we can come up with knowledge, logic and mathematical intuitions which are part of the reasoning. Without these tools, we would be just like other wild animals hunting for food for survival.
Must it be that mathematics must be embedded in the universe, or could it be that regularities to the way things occur in the universe result in it beng adaptive to have mathematical cognitive faculties?
It might seem that way to someone who hasn't worked in the subject. But mathematicians are very imaginative people. What they have done goes far beyond what you describe. I've published a number of papers having no connection to measurement and the world of physical objects. If I had been restricted from doing so I might have become a philosopher. :cool:
I have long thought that mathematics is both invented and discovered. If it is embedded in the human understanding of nature, then that is an existential fact about the part of nature that is the human/ environment interaction or relation. So, it is there within at least our natures to be discovered, which from another perspective can be seen as us inventing it.
I don't know where that "empriricist objection" is quoted from, but it is the lamest. most hand-wavy of objections.
Quoting Wayfarer
Of course, numbers are not physical objects. But it seems unarguably true that number and quantity is everywhere manifest in the physical world. And this would seem to be logically necessary in any diverse world. That numbers are not physical objects does not contravene physicalism, per se, although it obviously contravenes your conception of physicalism.
Any attribute of, or relation between, anything at all would seem to contravene your model of physicalism since attributes and relations are not physical objects. I think it's fine to disagree with physicalism, but it seems to me that the claim that it is incoherent or self-contradictory relies on a strawman version of the position.
That's how I see it also. When a researcher flexes their imagination and comes up with a new definition or concept, there immediately comes into existence all that can logically follow from this - and be discovered.
Sure. Last time I did math was in my high school days, a long long time ago :D I was describing it in the simplest manner.
However, you seem to agree with the idea that math is not embedded in the universe, but it is a human language type tool working from reasoning, if I am reading you correctly.
My thoughts exactly. I did link to that essay, What is Math, which gives to context for the quote.
Symbolic language.
Mathematics
Yes, mathematics is one example of a symbolic language. I see mathematics as being an elaboration of the basic, prelinguistic ability to count. I say prelinguistic because apparently some animals can do simple counting. Mathematics would be impossible without language, because it relies so much on naming. The numerals are names of quantities.
Wow really? Heard first time. Which animals can count?
Anyhow simple counting is not mathematics. Mathematics can give (birth to) answers for complex problems. In that way it is not like exactly literal language either.
Can counting be viewed as mathematics? This could be another topic.
https://www.bbc.com/future/article/20121128-animals-that-can-count
https://www.newscientist.com/gallery/mg20227131600-animals-that-count/
Quoting Corvus
I didn't say that simple counting is mathematics, I said that mathematics is an elaboration of simple counting. Perhaps it would be better to say that mathematics is an elaboration of simple arithmetic, which in turn is an elaboration of counting.
I didn't mean to suggest that I think mathematics is embedded in the universe. I think that there are regularities to the way things occur in the universe, due to the universe having such regularities biological evolution could and did occur. Another consequence of the universe having regularities is that the sort of symbolic processing we call mathematics can have a strong correspondence with those regularities in many of the ways that we see that it does.
As far as difference between humans and chimps goes, that can only be speculative. However, one thing to consider, is that events in evolutionary history are often tradeoffs. For example, penguins seem to have traded off flying, for the better access to fish that comes with swimming.
This four minute BBC video suggests a possibility. Perhaps the ancestors of humans gave up the greater working memory of chimps, for a greater facility with symbolic thought, and differences in environmental niches determined whether the tradeoff was worth it or not.
I think the regularities in the universe is the same nature as the perception of cause and effect (the cement of the universe), time described by Hume. They are just the products of mental operations.
Seems like six of one, half dozen of the other. If the regularities are there, then "what mathematics describes," is everywhere in the universe, even if "mathematics" is not. If we take mathematics only to be the descriptions, not the things described, then mathematics is still "embedded in the universe." It's just that the only place "mathematics" is embedded is within living animals. Then our problem seems to be "how did this totally new thing come to be embedded only in animals?"
Well, to my mind, the obvious answer is "because of the regularities in the universe," which is, of course, partly what mathematics is used to describe. And so, we've gone in a circle. But the insight that a sheep is not the sound of the word "sheep," nor our drawings of sheep, nor the mental image of a sheep we can call to mind," does not suggest that "sheep are not in the world." By the same token, it seems like what mathematics describes quite often is as readily apparent in the world as sheep.
Contra this position, we could say that humans are separate from the universe, e.g., . But how are they separate from the universe?
We don't seem causally separated from the universe. Falling trees kills us, we die without food, our thoughts vary depending on how much food and water we get, if we ingest certain substances they can have a huge effect on our cognitions, etc. Our capabilities for language, mathematics, etc., the things that are supposed to make us distinct from the world, can be radically reduced or essentially destroyed depending on how we interact with the world.
If we grow up locked in a dark room, and somehow survive, we'll have severe cognitive deficits and not exhibit these distinct phenomena. If we get a bad head injury, we can lose all these distinct abilities. If we are given a high dose of drugs, we might temporarily lose all these distinct attributes. These unique attributes then, seem to be causally dependent on our interactions with the world. At some point, when the anesthesia mask goes on and you start counting backwards, you stop counting because of what you're inhaling.
But all this close mind-body interaction seems to suggest to me that we aren't "distinct from the universe" in the sort of way that would allow us to develop mathematics, language, etc. in any of the acausal ways that would allow us to discount the question of: "how did the world cause us to have these abilities if they only refer to special things that are only accessible to human beings?"
The close link behind mind and body is, to my mind, one of the best arguments for naturalistic explanations of apparently "unique" human capabilities, some of which have proved to be less unique than we originally thought (e.g., arithmetic capabilities).
:up:
I see nothing worth quibbling with. :grin:
Quoting Janus
(Access to this article is behind a paywall, so I copied most of it here)
The Animals Are Talking. What Does It Mean? by Sonia Shah
Language was long understood as a human-only affair. New research suggests that isnt so.
Inside these murine skills lay clues to a puzzle many have called the hardest problem in science: the origins of language. In humans, vocal learning is understood as a skill critical to spoken language. Researchers had already discovered the capacity for vocal learning in species other than humans, including in songbirds, hummingbirds, parrots, cetaceans such as dolphins and whales, pinnipeds such as seals, elephants and bats. But given the centuries-old idea that a deep chasm separated human language from animal communications, most scientists understood the vocal learning abilities of other species as unrelated to our own as evolutionarily divergent as the wing of a bat is to that of a bee. The apparent absence of intermediate forms of language say, a talking animal left the question of how language evolved resistant to empirical inquiry.
When the Duke researchers dissected the brains of the hearing and deafened mice, they found a rudimentary version of the neural circuitry that allows the forebrains of vocal learners such as humans and songbirds to directly control their vocal organs. Mice dont seem to have the vocal flexibility of elephants; they cannot, like the 10-year-old female African elephant in Tsavo, Kenya, mimic the sound of trucks on the nearby Nairobi-Mombasa highway. Or the gift for mimicry of seals; an orphaned harbor seal at the New England Aquarium could utter English phrases in a perfect Maine accent (Hoover, get over here, he said. Come on, come on!).
But the rudimentary skills of mice suggested that the language-critical capacity might exist on a continuum, much like a submerged land bridge might indicate that two now-isolated continents were once connected. In recent years, an array of findings have also revealed an expansive nonhuman soundscape, including: turtles that produce and respond to sounds to coordinate the timing of their birth from inside their eggs; coral larvae that can hear the sounds of healthy reefs; and plants that can detect the sound of running water and the munching of insect predators. Researchers have found intention and meaning in this cacophony, such as the purposeful use of different sounds to convey information. Theyve theorized that one of the most confounding aspects of language, its rules-based internal structure, emerged from social drives common across a range of species.
With each discovery, the cognitive and moral divide between humanity and the rest of the animal world has eroded. For centuries, the linguistic utterances of Homo sapiens have been positioned as unique in nature, justifying our dominion over other species and shrouding the evolution of language in mystery. Now, experts in linguistics, biology and cognitive science suspect that components of language might be shared across species, illuminating the inner lives of animals in ways that could help stitch language into their evolutionary history and our own.
For hundreds of years, language marked the true difference between man and beast, as the philosopher René Descartes wrote in 1649. As recently as the end of the last century, archaeologists and anthropologists speculated that 40,000 to 50,000 years ago a human revolution fractured evolutionary history, creating an unbridgeable gap separating humanitys cognitive and linguistic abilities from those of the rest of the animal world.
Linguists and other experts reinforced this idea. In 1959, the M.I.T. linguist Noam Chomsky, then 30, wrote a blistering 33-page takedown of a book by the celebrated behaviorist B.F. Skinner, which argued that language was just a form of verbal behavior, as Skinner titled the book, accessible to any species given sufficient conditioning. One observer called it perhaps the most devastating review ever written. Between 1972 and 1990, there were more citations of Chomskys critique than Skinners book, which bombed.
The view of language as a uniquely human superpower, one that enabled Homo sapiens to write epic poetry and send astronauts to the moon, presumed some uniquely human biology to match. But attempts to find those special biological mechanisms whether physiological, neurological, genetic that make language possible have all come up short.
One high-profile example came in 2001, when a team led by the geneticists Cecilia Lai and Simon Fisher discovered a gene called FoxP2 in a London family riddled with childhood apraxia of speech, a disorder that impairs the ability of otherwise cognitively capable individuals to coordinate their muscles to produce sounds, syllables and words in an intelligible sequence. Commentators hailed FoxP2 as the long sought-after gene that enabled humans to talk until the gene turned up in the genomes of rodents, birds, reptiles, fish and ancient hominins such as Neanderthals, whose version of FoxP2 is much like ours. (Fisher so often encountered the public expectation that FoxP2 was the language gene that he resolved to acquire a T-shirt that read, Its more complicated than that.)
The search for an exclusively human vocal anatomy has failed, too. For a 2001 study, the cognitive scientist Tecumseh Fitch cajoled goats, dogs, deer and other species to vocalize while inside a cineradiograph machine that filmed the way their larynxes moved under X-ray. Fitch discovered that species with larynxes different from ours ours is descended and located in our throats rather than our mouths could nevertheless move them in similar ways. One of them, the red deer, even had the same descended larynx we do.
Fitch and his then-colleague at Harvard, the evolutionary biologist Marc Hauser, began to wonder if theyd been thinking about language all wrong. Linguists described language as a singular skill, like being able to swim or bake a soufflé: You either had it or you didnt. But perhaps language was more like a multicomponent system that included psychological traits, such as the ability to share intentions; physiological ones, such as motor control over vocalizations and gestures; and cognitive capacities, such as the ability to combine signals according to rules, many of which might appear in other animals as well.
Fitch, whom I spoke to by Zoom in his office at the University of Vienna, drafted a paper with Hauser as a kind of an argument against Chomsky, he told me. As a courtesy, he sent the M.I.T. linguist a draft. One evening, he and Hauser were sitting in their respective offices along the same hall at Harvard when an email from Chomsky dinged their inboxes. We both read it and we walked out of our rooms going, What? Chomsky indicated that not only did he agree, but that hed be willing to sign on to their next paper on the subject as a co-author. That paper, which has since racked up more than 7,000 citations, appeared in the journal Science in 2002.
Squabbles continued over which components of language were shared with other species and which, if any, were exclusive to humans. Those included, among others, languages intentionality, its system of combining signals, its ability to refer to external concepts and things separated by time and space and its power to generate an infinite number of expressions from a finite number of signals. But reflexive belief in language as an evolutionary anomaly started to dissolve. For the biologists, recalled Fitch, it was like, Oh, good, finally the linguists are being reasonable.
Evidence of continuities between animal communication and human language continued to mount. The sequencing of the Neanderthal genome in 2010 suggested that we hadnt significantly diverged from that lineage, as the theory of a human revolution posited. On the contrary, Neanderthal genes and those of other ancient hominins persisted in the modern human genome, evidence of how intimately we were entangled. In 2014, Jarvis found that the neural circuits that allowed songbirds to learn and produce novel sounds matched those in humans, and that the genes that regulated those circuits evolved in similar ways. The accumulating evidence left little room for doubt, Cedric Boeckx, a theoretical linguist at the University of Barcelona, noted in the journal Frontiers in Neuroscience. There was no great leap forward.
One of the thorniest problems researchers sought to address was the link between thought and language. Philosophers and linguists long held that language must have evolved not for the purpose of communication but to facilitate abstract thought. The grammatical rules that structure language, a feature of languages from Algonquin to American Sign Language, are more complex than necessary for communication. Language, the argument went, must have evolved to help us think, in much the same way that mathematical notations allow us to make complex calculations.
Ev Fedorenko, a cognitive neuroscientist at M.I.T., thought this was a cool idea, so, about a decade ago, she set out to test it. If language is the medium of thought, she reasoned, then thinking a thought and absorbing the meaning of spoken or written words should activate the same neural circuits in the brain, like two streams fed by the same underground spring. Earlier brain-imaging studies showed that patients with severe aphasia could still solve mathematical problems, despite their difficulty in deciphering or producing language, but failed to pinpoint distinctions between brain regions dedicated to thought and those dedicated to language. Fedorenko suspected that might be because the precise location of these regions varied from individual to individual. In a 2011 study, she asked healthy subjects to make computations and decipher snatches of spoken and written language while she watched how blood flowed to aroused parts of their brains using an M.R.I. machine, taking their unique neural circuitry into account in her subsequent analysis. Her fM.R.I. studies showed that thinking thoughts and decoding words mobilized distinct brain pathways. Language and thought, Fedorenko says, really are separate in an adult human brain.
At the University of Edinburgh, Kirby hit upon a process that might explain how languages internal structure evolved. That structure, in which simple elements such as sounds and words are arranged into phrases and nested hierarchically within one another, gives language the power to generate an infinite number of meanings; it is a key feature of language as well as of mathematics and music. But its origins were hazy. Because children intuit the rules that govern linguistic structure with little if any explicit instruction, philosophers and linguists argued that it must be a product of some uniquely human cognitive process. But researchers who scrutinized the fossil record to determine when and how that process evolved were stumped: The first sentences uttered left no trace behind.
Kirby designed an experiment to simulate the evolution of language inside his lab. First, he developed made-up codes to serve as proxies for the disordered collections of words widely believed to have preceded the emergence of structured language, such as random sequences of colored lights or a series of pantomimes. Then he recruited subjects to use the code under a variety of conditions and studied how the code changed. He asked subjects to use the code to solve communication tasks, for example, or to pass the code on to one another as in a game of telephone. He ran the experiment hundreds of times using different parameters on a variety of subjects, including on a colony of baboons living in a seminaturalistic enclosure equipped with a bank of computers on which they could choose to play his experimental games.
What he found was striking: Regardless of the native tongue of the subjects, or whether they were baboons, college students or robots, the results were the same. When individuals passed the code on to one another, the code became simpler but also less precise. But when they passed it on to one another and also used it to communicate, the code developed a distinct architecture. Random sequences of colored lights turned into richly patterned ones; convoluted, pantomimic gestures for words such as church or police officer became abstract, efficient signs. We just saw, spontaneously emerging out of this experiment, the language structures we were waiting for, Kirby says. His findings suggest that languages mystical power its ability to turn the noise of random signals into intelligible formulations may have emerged from a humble trade-off: between simplicity, for ease of learning, and what Kirby called expressiveness, for unambiguous communication.
For Descartes, the equation of language with thought meant animals had no mental life at all: The brutes, he opined, dont have any thought. Breaking the link between language and human biology didnt just demystify language; it restored the possibility of mind to the animal world and repositioned linguistic capacities as theoretically accessible to any social species.
The search for the components of language in nonhuman animals now extends to the far reaches of our phylogenetic tree, encompassing creatures that may communicate in radically unfamiliar ways.
This summer, I met with Marcelo Magnasco, a biophysicist, and Diana Reiss, a psychologist at Hunter College who studies dolphin cognition, in Magnascos lab at Rockefeller University. Overlooking the East River, it was a warmly lit room, with rows of burbling tanks inhabited by octopuses, whose mysterious signals they hoped to decode. Magnasco became curious about the cognitive and communicative abilities of cephalopods while diving recreationally, he told me. Numerous times, he said, he encountered cephalopods and had the overpowering impression that they were trying to communicate with me. During the Covid-19 shutdown, when his work studying dolphin communication with Reiss was derailed, Magnasco found himself driving to a Petco in Staten Island to buy tanks for octopuses to live in his lab.
Reisss research on dolphin cognition is one of a handful of projects on animal communication that dates back to the 1980s, when there were widespread funding cuts in the field, after a top researcher retracted his much-hyped claim that a chimpanzee could be trained to use sign language to converse with humans. In a study published in 1993, Reiss offered bottlenose dolphins at a facility in Northern California an underwater keypad that allowed them to choose specific toys, which it delivered while emitting computer-generated whistles, like a kind of vending machine. The dolphins spontaneously began mimicking the computer-generated whistles when they played independently with the corresponding toy, like kids tossing a ball and naming it ball, ball, ball, Reiss told me. The behavior, Reiss said, was strikingly similar to the early stages of language acquisition in children.
While experimenting with animals trapped in cages and tanks can reveal their latent faculties, figuring out the range of what animals are communicating to one another requires spying on them in the wild. Past studies often conflated general communication, in which individuals extract meaning from signals sent by other individuals, with languages more specific, flexible and open-ended system. In a seminal 1980 study, for example, the primatologists Robert Seyfarth and Dorothy Cheney used the playback technique to decode the meaning of alarm calls issued by vervet monkeys at Amboseli National Park in Kenya. When a recording of the barklike calls emitted by a vervet encountering a leopard was played back to other vervets, it sent them scampering into the trees. Recordings of the low grunts of a vervet who spotted an eagle led other vervets to look up into the sky; recordings of the high-pitched chutters emitted by a vervet upon noticing a python caused them to scan the ground.
At the time, The New York Times ran a front-page story heralding the discovery of a rudimentary language in vervet monkeys. But critics objected that the calls might not have any properties of language at all. Instead of being intentional messages to communicate meaning to others, the calls might be involuntary, emotion-driven sounds, like the cry of a hungry baby. Such involuntary expressions can transmit rich information to listeners, but unlike words and sentences, they dont allow for discussion of things separated by time and space. The barks of a vervet in the throes of leopard-induced terror could alert other vervets to the presence of a leopard but couldnt provide any way to talk about, say, the really smelly leopard who showed up at the ravine yesterday morning.
Toshitaka Suzuki, an ethologist at the University of Tokyo who describes himself as an animal linguist, struck upon a method to disambiguate intentional calls from involuntary ones while soaking in a bath one day. When we spoke over Zoom, he showed me an image of a fluffy cloud. If you hear the word dog, you might see a dog, he pointed out, as I gazed at the white mass. If you hear the word cat, you might see a cat. That, he said, marks the difference between a word and a sound. Words influence how we see objects, he said. Sounds do not. Using playback studies, Suzuki determined that Japanese tits, songbirds that live in East Asian forests and that he has studied for more than 15 years, emit a special vocalization when they encounter snakes. When other Japanese tits heard a recording of the vocalization, which Suzuki dubbed the jar jar call, they searched the ground, as if looking for a snake. To determine whether jar jar meant snake in Japanese tit, he added another element to his experiments: an eight-inch stick, which he dragged along the surface of a tree using hidden strings. Usually, Suzuki found, the birds ignored the stick. It was, by his analogy, a passing cloud. But then he played a recording of the jar jar call. In that case, the stick seemed to take on new significance: The birds approached the stick, as if examining whether it was, in fact, a snake. Like a word, the jar jar call had changed their perception.
Cat Hobaiter, a primatologist at the University of St. Andrews who works with great apes, developed a similarly nuanced method. Because great apes appear to have a relatively limited repertoire of vocalizations, Hobaiter studies their gestures. For years, she and her collaborators have followed chimps in the Budongo forest and gorillas in Bwindi in Uganda, recording their gestures and how others respond to them. Basically, my job is to get up in the morning to get the chimps when theyre coming down out of the tree, or the gorillas when theyre coming out of the nest, and just to spend the day with them, she told me. So far, she says, she has recorded about 15,600 instances of gestured exchanges between apes.
To determine whether the gestures are involuntary or intentional, she uses a method adapted from research on human babies. Hobaiter looks for signals that evoke what she calls an Apparently Satisfactory Outcome. The method draws on the theory that involuntary signals continue even after listeners have understood their meaning, while intentional ones stop once the signaler realizes her listener has comprehended the signal. Its the difference between the continued wailing of a hungry baby after her parents have gone to fetch a bottle, Hobaiter explains, and my entreaties to you to pour me some coffee, which cease once you start reaching for the coffeepot. To search for a pattern, she says she and her researchers have looked across hundreds of cases and dozens of gestures and different individuals using the same gesture across different days. So far, her teams analysis of 15 years worth of video-recorded exchanges has pinpointed dozens of ape gestures that trigger apparently satisfactory outcomes.
These gestures may also be legible to us, albeit beneath our conscious awareness. Hobaiter applied her technique on pre-verbal 1- and 2-year-old children, following them around recording their gestures and how they affected attentive others, like theyre tiny apes, which they basically are, she says. She also posted short video clips of ape gestures online and asked adult visitors whod never spent any time with great apes to guess what they thought they meant. She found that pre-verbal human children use at least 40 or 50 gestures from the ape repertoire, and adults correctly guessed the meaning of video-recorded ape gestures at a rate significantly higher than expected by chance, as Hobaiter and Kirsty E. Graham, a postdoctoral research fellow in Hobaiters lab, reported in a 2023 paper for PLOS Biology.
The emerging research might seem to suggest that theres nothing very special about human language. Other species use intentional wordlike signals just as we do. Some, such as Japanese tits and pied babblers, have been known to combine different signals to make new meanings. Many species are social and practice cultural transmission, satisfying what might be prerequisite for a structured communication system like language. And yet a stubborn fact remains. The species that use features of language in their communications have few obvious geographical or phylogenetic similarities. And despite years of searching, no one has discovered a communication system with all the properties of language in any species other than our own.
For some scientists, the mounting evidence of cognitive and linguistic continuities between humans and animals outweighs evidence of any gaps. There really isnt such a sharp distinction, Jarvis, now at Rockefeller University, said in a podcast. Fedorenko agrees. The idea of a chasm separating man from beast is a product of language elitism, she says, as well as a myopic focus on how different language is from everything else.
But for others, the absence of clear evidence of all the components of language in other species is, in fact, evidence of their absence. In a 2016 book on language evolution titled Why Only Us, written with the computer scientist and computational linguist Robert C. Berwick, Chomsky describes animal communications as radically different from human language. Seyfarth and Cheney, in a 2018 book, note the striking discontinuities between human and nonhuman loquacity. Animal calls may be modifiable; they may be voluntary and intentional. But theyre rarely combined according to rules in the way that human words are and appear to convey only limited information, they write. If animals had anything like the full suite of linguistic components we do, Kirby says, we would know by now. Animals with similar cognitive and social capacities to ours rarely express themselves systematically the way we do, with systemwide cues to distinguish different categories of meaning. We just dont see that kind of level of systematicity in the communication systems of other species, Kirby said in a 2021 talk.
This evolutionary anomaly may seem strange if you consider language an unalloyed benefit. But what if it isnt? Even the most wondrous abilities can have drawbacks. According to the popular self-domestication hypothesis of languages origins, proposed by Kirby and James Thomas in a 2018 paper published in Biology & Philosophy, variable tones and inventive locutions might prevent members of a species from recognizing others of their kind. Or, as others have pointed out, they might draw the attention of predators. Such perils could help explain why domesticated species such as Bengalese finches have more complex and syntactically rich songs than their wild kin, the white-rumped munia, as discovered by the biopsychologist Kazuo Okanoya in 2012; why tamed foxes and domesticated canines exhibit heightened abilities to communicate, at least with humans, compared with wolves and wild foxes; and why humans, described by some experts as a domesticated species of their ape and hominin ancestors, might be the most talkative of all. A lingering gap between our abilities and those of other species, in other words, does not necessarily leave language stranded outside evolution. Perhaps, Fitch says, language is unique to Homo sapiens, but not in any unique way: special to humans in the same way the trunk is to the elephant and echolocation is to the bat.
The quest for languages origins has yet to deliver King Solomons seal, a ring that magically bestows upon its wearer the power to speak to animals, or the future imagined in a short story by Ursula K. Le Guin, in which therolinguists pore over the manuscripts of ants, the kinetic sea writings of penguins and the delicate, transient lyrics of the lichen. Perhaps it never will. But what we know so far tethers us to our animal kin regardless. No longer marooned among mindless objects, we have emerged into a remade world, abuzz with the conversations of fellow thinking beings, however inscrutable.
Thanks for posting that!
Thanks for the article. Interesting.
Yeah, some other non-human species definitely seem to possess some level of linguistic abilities for sure, but their level is rudimentary. It is not really up to the level of the human languages.
Maybe their linguistic abilities will evolve to our standards after 2-3 million years? Who knows?
I have seen some intelligent animals such as the black birds such as the Corvus (?) and Magpies demonstrating good reasoning abilities, keep posting pebbles into a water bottle, until the water level reaches to the depth where their beak reaches in order to drink the water etc.
Again, although not high enough reasoning for making electronic or computing devices, but there is no reason to deny the possibility that their reasoning might evolve to ours or even to par excellence in the future.
The philosopher Eugene Gendlin described the empirical world as a responsive order. By that he meant the evidence we receive from the world is a response to the way we formulate our inquiries toward it. It can respond very precisely to different formulations, but always in different ways, with different facts. This is why the evidence ( and regularities) changes with changes in scientific paradigms. We can think of the responsive order as a kind of dance or discursive conversation. The assumption here is that our perceptions, observations and models are not representations of something. Instead they are forms of action on the world. We make changes in our environment and anticipate how it is likely to respond and talk back to our instigations, based on channels of expectation we erect from previous interactions with it. This is like a dance that I teach someone, in which my moves have built into them expectations concerning how the other will respond to my actions. Their actual response will never precisely duplicate my expectations, and so I adjust my next move to accommodate the novel aspect of their response.
Through this continual reciprocal process of action, feedback and and adjustment, not just between me and the world but between me and a discursive community of other scientists, I come to see a world of predictable regularities. I may even convince myself that these regularities are embedded in the world itself rather than being the product of a particular interactive dance that I initiate according to certain rules. In order to form this belief, I must formulate the dance in such a way that I abstract away my intricate adjustments to the continually changing qualitative feedback the world answers my actions with. To do this, I construct logico-mathematical idealizations that force changes in kind into changes of degree. Out of a flowingly changing experiencing I abstractively construct idealized objects that I can then compare and contrast calculatively through methods of quantification. But then to claim that these mathematical structures are embedded in the world is like saying that the actual dance that results from the reciprocal back and forth adjustments between me and a partner are embedded in that partner. In fact they are embedded in neither the subject nor the object, but in the in-between interaction guided and constrained by the subjects normative expectations.
What mathematics addresses is in the world, but it is no more a description of that world than my initiating and participating in a dance is a description of the dance. What mathematical structures describe, then, is the idealizing objectivating comportment of a subject toward its world, that way in which it conditions the world to talk back to it in the form of self-identical objects and quantitative relations. Having a world to idealize ( even if the aspect of that world one is idealizing derives from imagination) is is as essential as having a subject to do the idealization. Each side is in partnership with the other.
I will say this. It is no accident I used the metaphor of the dance , rather than something like a chaotic flux, to describe our relation to the world. I believe ongoing structural regularities are intrinsic to our experience of the world, but I also think logic-mathematical reasoning is derivative and secondary in comparison with the reciprocal, pragmatic kind of regularity exemplified by a dance.
I do want to say more regarding your response.
I'd have to say, "Of course mathematics is in the world.", in the sense you communicated so well. Do you have any thoughts, on whether that sense of mathematics being in the world is a perspective that is commonly held by those who ask, "Is maths embedded in the universe ?"
Most often I've encountered the question from people motivated to use the fact that there is math in the world, as evidence for the necessity of a God.
Mathematics is the world to the same extent that French or German is in the world, as a peculiar grammar by which we organize it for our purposes.
Logic is relationships which always replicate; a subset of science.
Math is relationships of quantity; a subset of logic.
Quantity is recursive boundary conditions - the extent to which you can divide something into equivalent parts.
Do relationships which always replicate exist in nature?
Yes, I would agree with that.
No, there are no a priori things. Or did you mean the replication occurs in the context of nature? Rephrase?
Quoting Joshs
The way we formulate our enquiries towards the world is in response to the way the world appears to us. We have no control over how the world appears to us.
What would you consider conscious control? Remember those magic eye puzzles with the embedded 3-d object? Or what about optical illusions where you can switch between tow images within the same picture? Isnt that analogous to how well science can reconfigure the way that world appears to us though a gestalt shift?
So do you think ordinary languages, like French and German, would have facilitated equal progress in physics and cosmology since the 17th C, in the absence of mathematics?
I will add that the expression that mathematics is 'in the world' is meaningless, just as it would be to say that a carton of eggs contains the number 12. Mathematics gives us a common symbolic means to describe, quantify and understand the world in a way that is not just based on individual perception but is grounded in a shared understanding and inherited knowledge.
No, I don't think so. Science observes, and then attempts to explain what is observed. I see fire, for example, and I explain it in terms of phlogiston, then later I explain it in terms of oxidative combustion. I continue to see the fire the same way; its appearance does not change regardless of the theory about its cause.
No. However, I don't see what that has to do with the sense in which mathematics can be said to be in the world.
Quoting Janus
Do you think you would see a group of lines the same way if you recognized them as just a pile of sticks compared with seeing them as forming a familiar Chinese character? Would your eye follow the shapes in the pile the same way? If you had never seen a computer before would you recognize the tower, mouse and screen as belonging to a single object? If you didnt know what a bus was for would you interact with it in the same way?
I think I sent this to you before, from Francisco Varela, but Ive always found it provoking.
I agree. It seems obvious to me that number is in the world, as least in the world as it appears to humans. It is hard to imagine any world without more than one thing in it, and our world obviously is replete with a vast multitude of things.
Not in my experience, but it might be selection bias. Certainly it is sometimes used to challenge the plausibility of "the universe is necessarily meaningless and valueless and anyone ascribing any sort of teleology to nature is necessarily deluding themselves." But this doesn't entail arguments in favor of any sort of explicit theism.
The best example of this view I can think of is Nagel's "Mind and Cosmos," which looks at significant problems in the "life is the result of many random coincidences and looking at them as anything other than random is simply to give in to fantasy," view. But Nagel is an avowed atheist. Likewise, Glattfelter's "Information, Conciousness, Reality," Winger's "Unreasonable Effectiveness," etc. don't seem particularly theistic to me.
They just seem to challenge some of the dogmas of a particular type of atheism popularized in the 20th century, which has made some pretty stark metaphysical claims about meaning, value, and cause. These claims are, IMO, more grounded in existentialism than many people acknowledge, and I think equating challenging them with "theism" has become a bit of a strawman in atheist infighting.
IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"
I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no.
I think there is a parallel to this phenomena in history actually. Prior to the advent of the Big Bang Theory, popular opinion was that the universe must be eternal. Evidence for an origin point was itself considered to reek of a sort of corrosive theistic influence. But of course, that evidence piled up, and today I don't think most people think acceptance of the Big Bang Theory in anyway precludes atheism. I think it's possible you could see a similar thing with teleology, although I can't say for sure. Teleology doesn't seem to contradict atheism, just a particular brand of it.
Quoting Count Timothy von Icarus
One can trace a Platonism beginning in Greece, making its way through religious Christian thought and finally arriving at a humanism which retains the idea of the uncaused cause and the pure immanent identity of what presents itself to itself, but transfers these from God to mathematical idealities such as identity, pure quantitative magnitude and
extension.
Mama say what? :yawn:
Definitely selection bias on my part.
Quoting Count Timothy von Icarus
As modern philosophers go, Nagel is a bit too far to the scientifically naive side, for my taste. Wigner's argument is what I've encountered the most, but it seems like puddle thinking to me. I'll have to look for Glattfelter.
Quoting Count Timothy von Icarus
:up:
Dont tell Sokal
:up:
And of course the regularities of our world, the seeming logos for lack of a better term, certainly can be used to make an argument about the divine, either regarding its existence or its nature. That's the project of natural theology after all. However, I do not think the recognition mathematics, etc. as, in a way, existing in the fundamental fabric of being, at least as much as we can say anything exists, or even the recognition of some telos at work in nature, necessarily entails any particular theistic or religious attitude.
Like you say, any apparent all encompassing logos can perhaps be paired down into fairly sterile mathematicological idealizations. I don't think you get religion qua religion without the mystical/experiential elements, and that the fear of religion "creeping in the door," of the sciences is greatly overblown, at times a cover for religion-like dogmas.
For one example of an excellent effort on this front, there is Saint Bonaventure's The Mind's Journey Into God.
What exactly is wrong with the puddle's thought in Adam's analogy? The idea that the hole was made for the puddle is the most obvious target. But the puddle is still in the hole because of what the puddle is and what the hole is, and those seem like phenomena a sentient puddle might well strive to understand.
I don't know how well the analogy generalizes to things like the Fine Tuning Problem though because there the comparison cases seem to be as wide as "all conceivable, describable objects, and maybe inconceivable ones too." And I don't think the pivot to multiverses solves this problem in the least. You just move from, "why this precise universe," to "why this precise universe production mechanism." Because if all possible universes are created, a host of follow on problems show up. I think FTP actually gets at a broader set of problems with naturalism when it is stretched into the realm of infinite abstractions, problems which are currently very poorly defined, rather than being a simple fallacy.
To my mind, this is more akin to the puddle trying to get its bearings by asking, "what is a hole and why is it here? And do puddles make holes (which, to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism)?"
Augustine on Intelligible Objects (clearly showing his Platonist influences):
Cambridge Companion to Augustine.
Snap
But nicely said. Perhaps puddles are aliens in disguise. Clever little buggers.
Going back to Wigner's argument, and considering how reasonable or unreasonable the effectiveness of mathematics is...
Our being here (from a naturalistic evolutionary perspective) is only possible because there are regularities in the universe. The theory of evolution only makes sense in a world with regularities. So the anthropic principle applies. If our thinking is the result of biological evolution, then it is not unreasonable to find that we are in a world with regularities. With that in mind, it is not so remarkable that we have found a way (mathematics) for utilizing our symbolic cognitive capacities, to discuss such regularities with some degree of accuracy.
So why think it is anymore remarkable that mathematics is in the world, than that a puddle has the shape of the hole it is in? What is wrong with the puddle's argument is that it doesn't consider the possibility of having the causality backwards.
Quoting Count Timothy von Icarus
Well, we still might want to take a closer look at the causality. Do puddles cause heat to be removed from themselves in order to freeze, or is the hole the cause of the movement of heat?
Quoting jgill
Yes, our math is axiomatic. The initial axioms drive the succeeding mathematical formula.
https://www.amazon.com/World-Beyond-Physics-Emergence-Evolution/dp/0190871334/ref=mp_s_a_1_2?dib=eyJ2IjoiMSJ9.85qJ-oJohxHqrtzQatdovH7-dUrh6pZfdaShFwzJL6StLg9LlVDShzZjYaBGq2UlzvY3W1Jfo48PeDf-v8J_mKZqjwwbDWBD-XwFeDf0YRYrAY3HnM4NimmMvWVMqArNN6vktkI1IER1IcSHpgx_ML5gzRem52uJukbXLbObn0sLoDoIW2H92N7pPYYxbb7a1PZSBd-tyHJDmWRCnUy0Nw.vRTBcrPAUfePwOIC_XkMsJF7AFsT_G81TdGX-P53OF8&dib_tag=se&keywords=Stuart+A.+Kauffman&qid=1708716213&s=audible&sr=1-2-catcorr
That summation should put an end to this thread. But of course, we can argue about the pertinent meaning of each word in the last sentence. The short answer is "Yes". But what do you mean by "in", or "embedded", or "grounded"? :wink:
Quoting Lionino
The universe isnt math unless the same thing different time applies to natural phenomena rather than our pretending to hold it still so as to calculate it.
The universe is not math unless the regularity of the laws of physics is true? I have not read "Our Mathematical Universe" but I am convinced Tegmark addresses that.
Quoting Lionino
The truth of the regularity of the laws of physics is not relevant to the question I raised. Truth as correctness comes from comparing a model of the phenomenon to the phenomenon. If they correspond then the model is true to the observed phenomenon. What is at issue in my question is whether an abstraction may be involved in treating the model and the phenomenon as self-identical during the comparing process. There is no question we have produced a large collection of true mathematical statements in physics, and that these true statements of mathematical physics make many technologies possible. The question is whether we can come to a more fundamental understanding of modeler and phenomenon, subject and object than that which begins from the assumption that both hold still during the comparing process. Such an understanding does not invalidate mathematical truths , it shows them to be derivative and opens up new possibilities for understanding the world and ourselves
We can go with that.
Quoting Joshs
I can't know exactly what you are referring to here, as there is no concrete example of what 'abstraction' would mean; but it seems to be connected to Tegmark's concept of baggage, explained in the link biology has more of it than physics, sociology has more than biology. The way we explain a physical theory in English is an abstraction of the phenomenon, while the mathematics of the phenomenon is pretty much the phenomenon itself lato sensu when a neutron decays into a proton and an electron, the only things happening are numbers changing.
Quoting Joshs
I don't understand this.
Quoting Lionino
Think about what is happening when a number changes. In the first place, what must be assumed about a phenomenon such that a number can be assigned to it? The phenomenon must be assumed to have a qualitative core that remains the same while we count increments of change within it. We usually think of numeric change in terms of the model of motion. When we measure the movement of a ball we count changes in degree of spatial displacement of something that is assumed to remain continually self-identical as the qualitative meaning this ball throughout the countable changes in its location. But what if the quality we label as this ball never persisted from one moment to the next as the same qualitative thing?
There would be nothing self-identical about which to count increments of change. Put differently, numeric quantification depends on our ability separate difference in degree from differences in kind, qualitative change from quantitative change. This is what same thing, different time means. What poststructuralist authors argue is that it is only by abstracting away, that is, by not noticing, the continual qualitative changes in the substrates of our counting that we end up with a universe of objects which appear to behave mathematically. They argue that in fact every change in degree is simultaneously a difference in kind. And this applies not only to objects in the world, but our cognitive schemes. It is not simply that there are no perfect shapes in nature, but that even in our own imagination there are no perfect shapes.
As Heidegger writes:
It is only as a result of our own conjuring trick that we produce a world that is remarkably amenable to numeration.
This does not at all mean that our physics is incorrect, that we have to go back and change all our calculations. It just means that there is a more intricate kind of behavior taking place in what the physicists observe and model , a behavior the requires a non-numeric language in order to understand it. The need for this language, and its advantages over mathematical forms of description become more clear in the social sciences than in the natural sciences. This is not because we understand these phenomena less well than we do the physical realm. On the contrary, newer approaches within psychology reveal an understanding, still lacking among most physicists, of the qualitatively shifting dynamics underlying mathematical objectification.
You likely will not agree with any of this, but at least it may give you a better sense of why postmodernists have a bug up their ass about the mathematical grounding of science, truth as correctness and propositional logic.
For [hide="Reveal"][s]Tegmark[/s][/hide] my understanding of a mathematical universe, the qualitative is emergent from the quantitative when a mind interprets it, baggage, which the human mind is full of. Numbers are not assigned to things, but they are all that things are, and our scientific theories seem to support this to a certain extent. Fundamental particles are in fact a collection of numbers, among which mass, electric charge, isospin, weak hypercharge, spin, lepton number. You may say these are the qualitative core(s), but that is a simple rebuttal that suffers from the same gaps as just stopping at the fact that they are quantitative.
Quoting Joshs
Ball would be a human label (baggage) emerging from a collection of things (atoms and such). It is always changing as everytime it bounces it loses atoms off its surface, but then we end up not in metaphysics but in a discussion of semantics what is a chair?
Quoting Joshs
?: I imagine what poststructuralists think we are not noticing qualitatively about electrons or photons specifically.
Everytime we think about A, A is different from the previously thought A. A only exists as it is different from B. These are useful ways of thinking about our cognition. But a lot of philosophy relies on the validity of the idea of repetition and of identity. We can throw those out at a very fundamental level, but at some point we will have to grant them if we want to progress.
There is no such thing as tissues, just a collection of cells that are made of molecules. Yes, but we can't derive biological laws from chemical laws due to the sheer complexity and also to possible emergent features. We must grant that there is such a thing as tissues if we want to come up with medicine.
Quoting Joshs
A very big issue with that view is that you could say sociology comes from psychology, which comes from neurology, which... from physics. But you can't say the converse, that physics comes from biology or that chemistry from neurology. The more derivative a field is, the more baggage it has, specifically because it goes away from the foundations of the universe. Another issue is that sociology and psychology are very unreliable (papers have very low reproducibility) while physics is almost always reliable.
Quoting Joshs
Oh no, I acquiesce to almost all of it, I just think that lots of it is playing the ultimate skeptic without providing a better framework to operate with; which is fair, but it does not stop us from making theories about the world around us. There is no such thing as qualities or quantities, as objects or science, as balls or speed, it is all derivative of the great Monad that is the Spinozean God, of which my solipsistic experience is a mode. Voilà, science is fake, and so are late Picasso's ugly paintings. Ok, but let's say all is not a Spinozean God...
The poststructuralist can claim all he wants ("every change in degree is simultaneously a difference in kind"), but until he proves ?, I can just ignore him on this topic because it has explanatory power for me to do so. Mathematical universe is a theory about the universe, it takes our perceptions as they are, without doubting our modes of cognition as they appear, without taking phenomenology into account.
Quoting Lionino
Numbers wouldnt be assigned to things, but since number implies a process of identical repetition, it would commit things to a certain structure, that a thing repeat some attribute or property identically. Why does quality suffer the same gap as stopping at the fact of quantity?Doesnt quantity require quality but not the reverse? Can there be a quantity without a quality, category, whole, entity, species to be counted? Put differently, when Tegmark says mass, electric charge, isospin, weak hypercharge, spin, lepton are numbers, dont we have to ask what it is that continues to be the same again and again ( number) in these entities, qualities , categories, properties?
Quoting Lionino
This isnt just semantics but the fundamental basis of number as the repetition of same thing, different time. As soon as we say something is a number, we have committed ourselves to a certain way of defining that something, as persisting self-identity. If Ball is a human label, what is a collection of things in themselves? The ball may change every time it bounces, but, what do we say about the atoms it loses off its surface? Are these not treated like the ball , as self-identical objects in motion? Or as fields of forces with assigned properties which are enumerated as identical repetitions of the same entity?
Quoting Lionino
Quoting Lionino
A main reason why we cannot reduce the higher order sciences to the lower ones is that typically, the lower ones , such as physics, use a more traditional scheme of understanding than the higher ones. Physics today for the most part stays within a model of realist causation , although there are strands of newer thinking within the field, such as Karen Barad, which are allowing physics to catch up with the thinking that has been available within philosophy and psychology for a while now. For a long time, physicists, including Hawking, denied the relevance of time for the understanding of physical phenomena. But Lee Smolen and others, thanks to their embrace of ideas from biology and philosophy, are showing the absolutely central importance of time for understanding physics. So while it should in theory be the case that we can reduce philosophy to cognitive psychology , cogsci to neuroscience , neuroscience to biology, biological to chemistry and chemistry to physics , it turn out to be a circle , where the most complex human sciences come up with new ways of thinking that eventually make their way down to the natural sciences, which are reliable precisely because they are so abstractive. But the broad, simplifiying abstractions of physics have their downside, such as pushing into the convenient category of randomness whatever their simplifications cannot model.
We can progress in different ways. One form of progress relies on repetition of identity. Another form of progress relies on showing how the repetition of identity is derivative from differences upon differences. The first form of progress leads to normative ethics based on an empirical realism that assumes we are all living in the same natural world, thanks to the grounding of empirical certainty in the identical repetition of properties within natural objects. Since it assumes a verifiably same world for everyone, there are correct and incorrect, true and false understandings of this same world for all. As a consequence, political polarization, holocaust, atrocity and other forms of social violence must often be explained on the basis of wayward intentions and motivations of individuals and groups ( greed, dishonesty, evil, immorality, hunger for power, sadism) or ignorance (drinking the Koolaid), rather than the result of an ethically legitimate worldview askance from ones own.
Quoting Lionino
Again, Im not denying that physics has explanatory power. Accepting poststructural thinking doesnt take away any of that power. It leaves it completely intact, but enriches it. My mode of perception makes things appear for me exactly as I described it to you. Since we are accustomed to seeing our world in terms of self-identical objects , it take a bit of practice to make ourselves explicitly aware of what is already implicit within that perception. Husserls method of phenomenological reduction through bracketing our naive naturalistic attitude ( which physics remains stuck within) is one way of gaining entry into this implicit intricacy hidden within the abstraction of self-identical persistence that we place over what presents itself to us as a continually qualitatively changing flow of sense.
Is it? I think it starts wherever depending on your pressupositions are, or perhaps they are intrinsic to each other? Tegmark seems to be of the idea that it is mathematics that rules all. Whether we want to equate mathematics with quantity is perhaps the root of the issue.
Quoting Joshs
And can there be quality if it is not instantiated and thus exemplifies the number 1? If a quality does not instantiate itself, and thus show itself countable (being 1 if limitless or many if limited), does that quality even exist?
Very importantly, as a matter of empirical fact, we have not found anything in the universe yet that cannot be reduced to numbers. "If you accept the idea that both space itself, and all the stuff in space, have no properties at all except mathematical properties," then the idea that everything is mathematical "starts to sound a little bit less insane."
From the quote above by Tegmark we start to see that it is less about quantity being fundamental and more about whatever qualities there being quantifiable.
Quoting Joshs
If we find a preon or a string, isn't everything in the world different numbers of this repeated fundamental quality that is preonness or stringness? The numbers through which something is quantified are "alloted" to a certain "slot" that will be our quality. But then I pose the same question, how can we determine preonness to be more fundamental than quantity if, for preonness to exist, it must first show itself quantifiable, which is to exist in a number of 1, 2, 3? What even is preonness? What is that quality? To pose that question is also to ask what it is made of, and that question will stumble upon quantification at some point. Whatever it is, we might as well call it 'pure existence', and it gives rise to the world through its repetition.
Quoting Joshs
Many people say many things. Time will tell them wrong or right.
Quoting Joshs
This one I didn't say.
Quoting Joshs
Anyone would be hard-pressed to prove that physics, or natural sciences, is better off without naïve realism.
Quoting Joshs
Of course, la différance. My point is that the subject that the mathematical universe approaches is not about human cognition, it takes that for granted, but about what we perceive as a naïve realism. It is a philosophy of real world, not of mind or phenomenology, so it does not wrestle with those latter two.
The mathematical universe goes beyond enumeration, it is not just about repetition of something which we denote with natural numbers, but that there are possibly infinitely many universes that manifest different mathematical structures. Isn't a 2x2 matrix different from a 4-vector only in quality? The mathematical universe does not deal with that question.
Quoting Lionino
Let's say there are things, we observe those things through the senses, here is how they work.
Should we submit structural engineering to différance too? What do we stand to gain there? Anyone would be hard-pressed to prove that engineering is better off without naïve realism.
Your point is that these considerations are true, mine is that here it doesn't matter whether they are true.
Think of 3 dogs, 3 apples, and 3 cups. They are all 3s, but denoting the different objects.
How do we know whether quality or quantity is fundamental? Or rather two sides of the same coin? Does a quality, to exist, need not to show quantity too, being either one or many, zero being not existing?
The idea of the mathematical universe is not that quantity or quality are fundamental, but that all the properties that there are are mathematical. There are no non-mathematical properties, science seems to support this.
The mathematical universe does not address matters such as solipsism, différance, phenomenology or idealism. It takes our perception of things as they are and goes from there, just like science does. Just like the correspondence theory of truth assumes there exists an outside world to which beliefs would correspond to.
https://space.mit.edu/home/tegmark/mathematical.html
Quoting Lionino
There are, of course, widely varying ways of understanding the relation between quality and quantity. For instance, one could follow Henri Bergson, who distinguishes between non-numeric qualitative duration and the empirical multiplicity of magnitude.
I think Tegmarks idea of a mathematical universe is tied not just to the simple idea that we can locate cardinal and ordinal numbers in everything in the universe, which I think Bergson would agree with. Rather , he is wedded to a specific theory concerning how number applies to things in terms of mathematical concepts. Tegmarks theory cannot allow Bergsons idea that matter goes back and forth between qualitative and quantitative multiplicity. Instead, he wants to enclose qualitative differences within the platonism of fixed mathematical structures and schemas. For Tegmark, platonic schema has the last word, where for Bergson qualitative change in nature does.
Quoting Lionino
Husserls position on the relation between qualitative and quantitative change is more radical than Bergsons. His phenomenological project aims at taking our perception of things as they are after we have bracketed our presuppositions. For instance ,Husserl would ask you, when you look at a table in front of you, what do you actually see, a three dimensional object or one perspectival view of that object which hides the back of the table from you? Do you see an unmoving thing or one whose appearance changes as you move your head and eyes, or walk around to the back of it? How do we come to think of this thing we only ever see in perspectively changing dimensions in terms of a fixed set of properties Tegmark would say that , yes, we construct these objective properties , but that doesnt mean that what we construct doesnt correspond to the real mathematical nature of physical matter. Husserl depicts Tegmarks realist view in the following way:
But Husserl argues that the above description does not take our perception of things as they are for us in the most primordial sense. Once we have bracketed all of the presuppositions we draw from memory to fill in for what we dont actually experience in front of us, what we actually experience is devoid of the quantitatively measurable constancies that Tegmarks mathematical universe depends on.
I agree. I noted in a You Tube "documentary" recently that there is a tribe in the Amazon that counts by 2s. Was that embedded? I think math, like Language, and everything else accessible to human mind/experience is a posteriori constructed by Mind and accepted if functional, rejected if not.
Sure thing.
For example, every number is predefined, so when we build an equation or a formula, each one of the terms have already been defined -- and no wonder the equation works! :scream:
One of the things that we like to use as math object is the circle or a sphere because of the circumference, diameter, and arc angles. So, from this, we claim that math is out there waiting to be discovered and the proof of this is that circle and sphere exist in nature. We are obsessed -- no we lose our mind to it. In our mind the circle signifies antiquity and wisdom. It signifies disciplined and scholarly thoughts. Hey, the solar system is full of round things!
Agreed. I like your example regarding circle.
I wish I was proficient enough in math to dig deeper for artifacts of math's artifice. But I chuckle at where it may have taken off: this idea that Math pre-exists our constructions.
When Plato has the slave draw the triangle proving forever the pre-existence of that Form. As if the slave didn't figured it out because he was born into a culture that had triangle constructed as a useful signifier.
But more questions follow: "is math only in us? If so, where does it come from? What causes it?"
I guess this would probably depend on your views on perception. If we see apples because apples exist, then it doesn't seem to be much of a stretch to say we see numbers because numbers exist. But if we construct our apples out of an inaccessible noumena, then perhaps there are no apples or numbers or other people to discuss the existence of numbers with for that matter.
Constructed out of what? Or is it creation ex nihilo?
Short reply: Constructed (like everything else displacing Nature with Consciousness) out of images stored in memories, developing over maybe hundreds of millennia by the same or a similar Darwinian process familiar enough that it requires no describing. What is functional is adopted and input then revised by future generations , so far, reaching the extremely functional stage it has today.
No, not ex nihilo, yet, ultimately empty and nothing. A useful Fiction, like the rest of Mind and its constructions.
Why not that?
I guess I'm not understanding, "out of images stored in memories." Is Mind ultimately empty because everything in comes out of images and memory and these aren't part of Nature?
Normally Darwinian processes are described as occuring in and through nature to natural things. There is actually a somewhat pathological insistence that "Mind" not he allowed to enter the picture, so I don't know if I [I]am[/I] familiar with how you mean it.
How does conciousness "displace" nature? Could we also say it emerges from or is embedded in nature? Or is it something wholly different?
Short reply:
Unless I misunderstand, (in which case, sorry) a pathological insistence that Darwin cannot be applied to Mind is only evidence of folly, or at best dogma, not evidence that it cannot be.
And, yes, Mind is ultimately empty. It is not Natural, but being empty, it ultimately is not Real, either. It's a Fiction made of fleeting images, applied as Signifiers to code the Body to feel (not as in emotions, as in those organic process which we organically sense) and act. Not dualism or physicality, but a qualified physicalism: Body/Nature real, Mind exists as a separate "entity" but is Ultimately empty and fleeting.
And as for how does it displace Nature? That's exactly what it does. There was a now mythical, time when a human might have looked at an apple and seen what a (mythical) equally intelligent animal sees. But you and I cannot see apple without it being structured by the chains of Signifiers, images in your memory, structuring that experience for you as seeing an apple. In Nature I.e. in Reality, you or that mythical animal wouldn't see apple; as a Real Being, you would just be be-ing; not seeing apple, just see-ing, an incessant present, not chopped up by the structures of Mind into successive objects and moments of time.
In fairness to this post, our experiences, all of them including MATH, as amazing as they are, are Fictional constructions which, in effect, displace Reality. There's no essence, Spirit or being behind Mind, nor its constructions. You already are that Being, as a living body. We just want it to be the Fiction that's real. We want it to be Mind. Hence everything from Plato to Hegel.
A quick addendum, and I'll leave it.
One of the ways we arrive at truths, as you know, is by convention. This is a powerful structure for triggering the settlement commonly called belief.
I don't know about you, but when it comes to math beyond a Senior highschool level, I cannot test my beliefs, and must rely on convention.
If you were in the same boat, (l accept likely not,) and you and I agreed, Math has some essence of The Truth of The Universe to it, what the hell would we even be talking about?
And, my point is not what you think. It's not to say we should stay out of things we cannot be certain about. My point is tgat is what we all do, necessarily, all the time.
We construct Fiction, and settle upon the functional places, whether because of convention, reason, or fantasy; all of them also Fictions.
Hmm, I find the issue more intimately entwined with whether or not quantity in fact occurs within the cosmos. I find the stipulation that it does not hard to even fathom, much less entertain. But if quantity does occur within the cosmos, then the means of addressing this quantity in the cosmos is, and can only be, what we term maths. Maths is a language with quantity as its referent. No quantity, no maths.
It is only when we humans get into axiomatized maths that maths can be deemed to become fully relative to the axioms we humans concoct.
No lesser animal has a clue about axiomatized maths, but some lesser animals can and do engage in rudimentary maths just fine; again, with quantity as their referent.
Hence, to my mind, the only way of appraising all maths as strictly within us and thus as having nothing to do with the quote unquote "real world" is by appraising the "real world" to be fully devoid of quantity.
If you replaced the word math, with symbols, or representations, would the above also hold true for you?
As I tried to explain, to my thinking quantity can only be represented via math - such that at the very least rudimentary math is a representation of quantity (I should add, and its relations). Because of this, my answer will be "yes".
Bear with me then, I might need to think it through. But it seems, that while I recognize the contradiction of submitting Mind cannot know Reality, but only construct a (Fictional) reality, still I'll state a hypothesis about Reality, at least as I understand that fiction.
Is the so called real world, Reality, and not the world I am submitting we construct in Mind? And if so is Reality devoid of representation, as you are suggesting?
Isn't it devoid of representation by so called definition? Isn't Reality present, by "definition" (the past has vanished, the furure has not happened). Reality is necessarily that which is, and not that which is re-presented? The instance of re-presentation is the irretrievable loss of presence, and Reality.
And you might say, I meant that within Reality, representations exist, the lion's roar, etc. But the simplest way to adress that is we run from a lion's roar, its a drive, a bird is attracted to another's "dance," it's a drive. The representation status is a construction of mind. While the so thought of, "real world" of Mind may have math and representations, and we are inescapably attuned to that, Reality does not anywhere have representations and math hiding in it somewhere, waiting, like everyone from Plato to Heidegger have said, to be gleaned out by us through some real process of becoming. We are not a special species with a God given spirit (who else then, but God?) called consciousness. Consciousness is a structure of Fiction, in perpetual construction of Fiction with effects on Nature through the human body and human culture.
We're that super weird conceited ape who somehow evolved its internal sense of imaging and memory, into an autonomous System which has taken over our organic aware-ing. So much are we attuned with that system that we invent theology, create civilizations, and math too, and insist that they are real, that uniquely we discovered them in Nature, instead of proudly admitting we made them all with our brains.
Quantity only exists in Nature because we displace Nature with quantity, etc. Think of quantity without reference to any form of representation, but on its own, in its allegedly pure and essential form as it supposedly inhabits Reality. You can't, that's absurd, right? The very thinking utilizes representations. Then why do we shy away from acknowledging that our uniquely human Conscious experiences are structured by representations and as such, they are not ultimately Real?
I should start with the observation that we don't share the same ontological models of reality. That mentioned, I think of it this way when I put my ontological/metaphysical cap on:
If there happens to be two or more coexistent psyches, then quantity necessarily is existentially in the cosmos in an objective manner: for here there factually co-occur a plurality of psyches (if absolutely nothing else). If, on the other hand, there is no quantity in reality, then this will entail the fact that there is no plurality of coexistent psyches: with this directly resulting in solipsism - wherein the one solipsist by unexplained means "fictionalizes" everything, quantity very much included. I in no way uphold the possibility of solipsism - though I'm not here to argue this out. Because I don't, I then conclude that it is logically impossible for quantity to be illusory, or fictional - again, this because at the bare minimum a plurality of psyches co-occur.
------
I'll also add that, as I so far interpret them at least, representations are such precisely because they re-present that which is present. Without that which is present, no representations could obtain.
Getting back to the thread's topic, our representations of present quantities might well be deemed mental constructs, but the quantities themselves (which our representations re-present) are not (unless one starts entertaining notions such as that of objective idealism wherein everything is mind stuff, but even here quantity would yet be a staple aspect of the universal effete mind ... which is not the fully localized and active minds that you and I are, individual active minds which represent portions of this same universal effete mind which all coexistent active minds share).
:up:
These considerations would be valuable in a thread about the nature of time.
Quoting Count Timothy von Icarus
Good links for that topic:
https://plato.stanford.edu/entries/platonism-mathematics/
https://plato.stanford.edu/entries/platonism/
https://plato.stanford.edu/entries/philosophy-mathematics/
Quoting ENOAH
This may be so, but every language we know of has words for one and two and some, just like all have words for live and die.
https://intranet.secure.griffith.edu.au/schools-departments/natural-semantic-metalanguage/what-is-nsm/semantic-primes
Solipsism--only one psyche exists (in Reality)
What about the position that psyche--including its constructions--doesn't exist at all in Reality? Nihilism? No. Nature exists in/is Reality. Mind is a system "reflected" in the organic body, which functions as it does because it evolved, inter alia, a logic that it must be real. But it is not. So no one mind only; but rather, no mind. Just the be-ing body.
And we intuitively "know" this. If we didn't, there wouldn't be these challenges in philosophy, particularly epistemology and metaphysics including ontology.
I guess I'm just not understanding why you say Nature exists at all. If all we ever have access to is Mind, and this is empty fiction, wouldn't Nature just be another of our fictions? Can we know anything of Nature? If not, why suppose the body and nature? Is it an article of faith?
Shankara similarly has it that all is illusion, Maya, part of the infinite creativity of Brahaman. But in Advaita Vedanta, being is one, a unity, and we are not cut off from the recognition of Brahman and recognition of our true nature. I'm not sure if this works in a case where there isn't knowledge of the Absolute, since we end up with no grounds for the fiction/reality distinction.
Well, in an important way, it doesn't seem to. Everything bleeds into everything else, there are no truly discrete physical systems. We have a "bloboverse." There is one universal process, and this would seem to preclude quantity.
Indeed, it's unclear what it would mean to have multiple things "be" without them interacting (and thus forming a unity). In what sense totally discrete things all "be" and be part of the same singular category of "being?"
But processes necessarily change. A toy universe needs at least some variance to have content. A world that consists of just a single undifferentiated point is essentially the same thing as nothing. It's like how a signal of just 1s or just 0s cannot transmit any information. Floridi has a good proof of this in his "The Philosophy of Information," and Spencer Brown's Laws of Form and Hegel's Logic get into similar territory.
For something to be, there has to be some variance, as sheer indeterminate being reveals itself to be contentless. And in variation, you get the seeds of quantity.
For what would it mean for something to have unity if plurality is not a possibility? From the one comes the many.
To answer briefly,
1. 'nature" in whichever way we define/understand it through mind, is included as one of the fictions. I cannot know that Nature is real. It's just that I think most philosophical pursuits of the problem make it worse when they focus on MInd/Form/Spirit/Dasein as real when for every other member of our universe, it is Nature alone that is "present". Descartes, after his impressive acrobatics, concluded I think...But he started in the place which poses the problem in the first place, not the presence of his breath, but in the re-presentation of his thoughts. The "I" thinking is already a fiction.. He should have concluded, Body breathes, Body is.
2. Sankara, though closer, also got lost in the fiction with the necessity of Brahman to "oppose" maya. "Oppose" is only necessary in the system regulating Mind. And yes, how do we even dare to speak of a Reality vs Mind when, as you say, there isn't knowledge of the Absolute, since we end up with no grounds for the fiction/reality distinction? We cannot speak. Speaking belongs to the Fiction. I am not suggesting that our "access" to the reality, like everything else, be mediated through the Fiction. I am suggesting that the Reality cannot be "known" in the sense that we understand knowledge. If we "want" to "access" Truth or Reality, as distinct from our constructions, we must, and can only, do so in be-ing. Don't expect me to be able to answer the question further, because, as it turns out, I'm already just reconstructing fiction. But if anything, don't look to Sankara, don't even look to Mahayana epistemology and metaphysics. Look to Zazen, not Zen philosophy, but the actual sitting in Zazen.Maybe that process allows for brief, timeless (because free from the construction of time) "moments" of Real be-ing.
Thank you.
But for your reference to be effective in demonstrating what appears to be your position on this, you'd have to accept that all of the primes are inherent in Nature and none are derived from post-lingual human constructions. Are you? Some of those primes seem to be questionable as to their "ontologies."
:up:
It brings up the same question as the "What Is Logic?" thread. We have our formal systems, mathematics as a field of inquiry; we have the possible universe of all such systems we might create (our potentiality for math?); and then you have the apparent instantiation of mathematics in nature. Yet our math and this math are clearly not the same thing.
Are these all the same thing in some way? Is there a general principle that connects them? For, from the naturalist perspective, it seems like the easiest way to explain our and other animals' ability to fathom quantity is that quantity exists "out there" in some way, but obviously there are arguments against this intuition.
In the logic thread I proposed "logos" for the logic-like function of the world. I wonder what a good term would be for "the apparently mathematical in nature?" Quantos? Mathematicularity? Máth?ma? Quanticularity?
Quoting Count Timothy von Icarus
We could always dust off mathesis universalis.
Mathematicality is the closest existing (this one barely exists) word for that meaning. To be more specific, inherent mathematicality.
Quoting Count Timothy von Icarus
:worry:
Would you deprive us from a future where articles in metaphysics discuss "quanticularity qua quanticularity?" :cool:
With words such as "transcriptomics" and "eusociality", we are already at a point of no return towards that future.
I wish I still had the philosophy of math anthology book that featured the math philosophers who argued for the construction of mathematics as an empirical endeavor.
I think of Newton, developing calculus to describe physical phenomena. And perhaps some math is created in this fashion today. But by and large it's not an empirical process. Although math is called the Queen of the Sciences, it is not really a science.
Youre saying math is not empirical for roughly the same reason that a novel or poem is not empirical, right?
Sounds right.
Leibniz :^)
Quoting L'éléphant
Lakatos?
What could that being possibly be?
What does it look like? Have you seen it personally in real life or even in your dreams?
Berkeley said "to exist is to be perceived." No perception means no existence at all.
Isn't logos the beginning of everything humans experience, and therefore not inherent/imbedded in Nature? (And I'm not referencing so-called St. John). Isn't math, computer science, the periodic table, grammar, logic, the rules of Football, and so on, just numerical or other modified formations of the original word, Language? I say, in the beginning of the becoming of human Consciousness and History, was, the "word," all strictly human things were made by the word; and without the word was not any thing human made that was made.
I think Berkeley was (unwittingly(?)) referring to human Consciousness. For human Consciousness:Quoting Corvus; anything not perceived in/by Human Consciousness, does not exist for Human Consciousness.
The "you" which continues to exist in the dream state, is still Human Consciousness.
The you in deep dreamless sleep, is not "you" but the Real Organism which exists in Nature, independently of Consciousness, which "you" have displaced with your experiences constructed out images which must be perceived to exist.
That "you" the one presumably in deep sleep never goes out of existence, but for the dreaming or waking human, that Real You is overshadowed by the shadows in the cave; that is, by things (which must be) perceived.
And, to tie it back to the OP, math is one of those things, restricted to human Consciousness and, therefore, only "real" insofar as constructed and perceived.
Actually it is not that straight forward. Berkeley as you might know is an empiricist and he is against rationalist ideal. Therefore he clearly want to establish perception and sensation as the method of knowing. He also wanted to establish God. So he goes on to say that when we asleep we are perceived by God.But that argument is followed by the question who perceives the God. Clearly that is contradiction. Consciousness is clearly established by Kant if I am not wrong. Contrary to popular belief mind and consciousness are two different things. Berkley for sure is an idealist and there is an importance for mind but that doesn't mean he talked about human consciousness.
Thank you for clarifying, and sorry for my recklessness. I know far too little about Berkeley to justify my claim above. I was admittingly using it as a stepping stool.
When you differentiate Mind and consciousness, I'm not saying I disagree. But when you have a second, can you provide me with a brief explanation. Do you mean human Mind and Human Consciousness? Are you being technical as in Mind is the proper subject of psychology and consciousness of metaphysics? And in my post, if I, as I believe, am referencing one, which one am I imprecisely or unknowingly referencing. What is Berkeley's focal point regarding his inqury into Reality for humans? Mind? Consciousness? The Brain? Or, (some privileged, none of the above) Being? Again, I'm seeking information. If and when...
Consciousness and mind are really problematic. Different philosophers have different approach towards both. You could refer philosophy of mind if you are interested in it. Jaegwon kim wrote it if I am not wrong. It explains about these aspects in detail. You could check that if you are interested.
No. They're not that fancy. They're practicing math scholars and philosophers.
According to Hume, idea of self doesn't exist. What did Berkeley say about SELF?
But the real question here was, how do you know the existence of the being which,Quoting Abhiram ??
Agreed. Human consciousness applies math to all the objects in the universe, but some folks think that math is embedded in the universe.
Is Modern Greek a lot different from Ancient Greek? It would be advantageous to know Ancient Greek for reading philosophy.
Are there anything more than matter and motion in the universe?
[hide="Reveal"]I wouldn't say that Lakatos is fancy because I think he sucks from what I've read, but[/hide] gotcha.
Attic Greek for Plato, Aristotle, etc? Yes. Hellenistic/Roman Greek for neo-Platonists and theologians? Not that much.
Both of those spaces use real numbers, but attempts to combine quantum mechanics and relativity have come up with alternatives, like a discrete space with very small but non-zero lumps of space time that cannot be subdivided. Another such attempt posits that the universe is on a curved 2-D space where information affects act mathematically to mimic the behavior of 3-D gravity inside the curve. Even our 3-D visual perception of the world is manufactured in the brain from 2-D input by specialized neural processes that have to be visually triggered in infancy. Evolution gave us a brain that presents a 3-D world to us because it is a good approximation that helps species' survival, not because it is real.
Some quantum theoretical interpretations posit that the universe is really google-dimensional, perhaps with even the number of dimensions changing, and 3-D space is a good approximation due to information effects.
Another alternative to real-valued dimensions comes from non-standard analysis - see (https://www.wikiwand.com/en/Nonstandard_analysis), which expands the reals to include infinitesimals, which are smaller than any real number but greater than zero, and their reciprocals, unbounded numbers, which are larger than any real but less than infinity = 1/0. See (https://www.researchgate.net/publication/330751668_Infinitesimal_and_Infinite_Numbers_as_an_Approach_to_Quantum_Mechanics).
Another QM interpretation holds that the quantum field is a Hilbert space, not just mathematically but actually, which would make the physical world part of the set-theory universe, reversing the question this thread raises. I personally find this non-appealing for a few reasons. One is that the 3-D Euclidean space of Galileo is also a Hilbert Space, but no one ever thought his universe was part of the set theory universe. Another is that you would then have to consider the reality of the set-theory universe, which would be an interesting thread in itself but is a lot to insert into physics.
In the end, how the universe is modeled mathematically is still up in the air. Inserting the mathematical universe into those physical models would not be very helpful.
I recall reading somewhere, that in Platonic era of ancient Greece, there was no Greek word for "truth". Is this correct?
Imagine that you are reduced down to being a "brain in a vat" but you also have eyes. Now imagine that you are floating in a universe that is devoid of all matter and all energy. Your only "experience" is that of complete and total darkness.
To me, this is a conceivable state of affairs and suggests that numbers are not independent of the real world - as a brain-in-a-vat, where would you "get" any concept of numbers? You have no fingers to count, nothing to touch or see that discloses "multiplicity": 2-ness, 3-ness. 4-ness and so on. By contrast, in the real world we actually live in, I suggest we get the concept of, for example, 3-ness, by seeing 3 apples, counting 3 fingers and so forth.
In summary, I suggest there are conceivable universes in which there is no reason to believe numbers exist as "things" in any sense at all, no matter how abstract - we need a real world that demonstrates 2-ness, 3-ness, 4-ness, etc. to stimulate us to create the concept of numbers.
The closest ancient Greek word for truth is "aletheia", which can be analysed etymologically a (negation) + lethe (concealment, forgetfulness, escape) = aletheia.
It doesn't quite reflect a word for truth, does it?
It does, because there is no such contrived meaning for alithia, it comes from alithis which means true. Truly in English means "really" all the time, does that mean English has no word for truth? "True" originally meant "in good faith".
Truly can mean truthfully and rightly too. Truth is an English word for truth. :D
Anyway, "aletheia" is a Greek word for "truth", but it comes from the etymology "Not"+"Concealment" = a+lethia = alethia. I thought it was an interesting word. Would it imply that truth is hidden by nature?
He says due to the fact it is difficult to translate "aletheia" into the English word "truth". He also points out the word "aletheia" had been used by Heidegger to describe the character of the world.
It is also difficult to translate "truly" into the Greek word "alithinos", for the reason I brought up above. It is also difficult to translate "demokratia" into the English word "democracy". Despite not having read the article, I don't think Jan Szaif's point is that Greek had no word for truth.
Quoting Corvus
500 years from now I will come back from the dead and use the word "Heidegger" to describe break-dancing at a beach. Hopefully the academics will talk about that in 600 years.
I think his point is that aletheia in ancient Greek meaning is different from modern day meaning of truth.
I will read the article again when I am freer, and will try to update further.
Quoting Lionino
Do you believe in eternal resurrection? That would be a Nietzschean idea, wouldn't it?
It is called existential experience. You know you exist ?right? It is simply the experience of your existence. You are experiencing it you can't deny it. It is simply that experience. If you are not aware of it then I suppose you might have to wait for an existential crisis to happen. Then you will be aware of your existence.
Initially when you were describing about the being, I thought you were talking about some other being than yourself. But from your post above, it appears that you must have been describing you yourself as a being encompassing Quoting Abhiram
Is it correct?
Truth in ancient Greek meant concrete existence opposed to mere appearance or beliefs. In Plato truth was not available in the material world, but truth belonged in the world of idea. Aristotle's truth was truth deducted from his syllogism. They had no idea of verified truth from observation and experiment.
Therefore even if they had a word aletheia which is closest meaning for todays word "truth", it wasn't identical meaning to today's concept of truth.
First you said it means unconcealed, now this. Which one is it?
Quoting Corvus
Really?
????? ??? ????? ????
the truth of this story
Aeschin. 1 44
??? ??? ??? ??????? ?? ??? ??? ??? ????????? ??? ??? ??? ????? ????? ?????????? ?? ??? ?? ????? ??????? ??????? ??? ????? ???????
Take a rare word or metaphor or any of the others and substitute the ordinary word; the truth of our contention will then be obvious.
Aristot. Poet. 1458b
?? ? ?????? ????????? ??? ??? ????? ???? ???????????, ??????? ???? ?? ?????????? ???????, ??? ?????? ?????
but the current story that Hippias made the people in the procession fall out away from their arms and searched for those that retained their daggers is not true
Aristot. Const. Ath. 18
???? ????????? ??? ???? ?????? ?????, ???? ?? ??? ???? ?????? ??? ?????? ????????? ????????, ????? ??? ??????? ?????.
????????
??? ????? ??, ?? ??????, ?????. ???? ????? ???? ?? ?????; ????? ?? ???????????;
he had with him, which was well worth hearing, and he said he would surely become a notable man if he lived.
Terpsion
And he was right, apparently. But what was the talk? Could you relate it?
Plat. Theaet. 142d
??? ?? ?????? ???? ??? ????????: ???? ??? ?? ??? ????????? ????? ???????
for then the truth of your statements would have been ascertained by the very persons who were to decide upon the matter.
Lys. 7 22
??? ????????, ?? ?? ???, ????? ??????????.
Then the report, I replied, is pretty near the truth.
Plat. Charm. 153c
???? ?? ??????, ?? ?? ????? ??????, ??? ??? ???????? ???? ????? ?? ??????? ?????;
Come now, let us make out, if what you say is true, where these second-best men are also useful to us
Plat. Lovers 136c
?????? ????? ?? ?? ????? ???????, ???? ????? ?? ????? ?????????, ????? ????? ???? ??? ?????? ???????.
And, you know, friends are said to have everything in common, so that here at least there will be no difference between you, if what you say of your friendship is true.
Plat. Lysis 207c
Quoting Corvus
What today's concept of truth? 'Veritè' also does not have the identical meaning of 'truth'.
Greeks did not have theories of truth like we have today, but many philosophers back then talked about what truth is. How can they not have a concept of truth? Greeks knew that "the sky is blue" is true and "the sky is green" is false. That "true" does not match "alithís" is a mootpoint, there is no such thing as a perfect translation, because every language imparts a worldview onto its speakers (the likelihood of two worldviews being identical is close to 0).
Unhidden and unconcealment was the Etymology, and concrete existence opposed to mere appearance or beliefs is Epistemology.
Quoting Lionino
Today's concept of truth is vastly broader with the modal logic, fuzzi logic and dynamic, epistemic logic ... etc etc and Science has many different concept of truth too.
Quoting Lionino
The sky is blue is not always true. The sky is black at nights, and grey in cloudy days. The sky is green is true if you wore a green sunglass and look at the sky. Hence, the sky is blue is only true when the sky is blue. The sky is green is true when you wear a green colour lensed sunglasses and look at the sky, or through the green glass of the window.
Quoting Lionino
That sentence is false.
Talking about true things and truths doesn't verify that they had real concept of truth. It just means that they were expressing their psychological state or intention to indicate that they agreed to something, they feel something is right, or they have unconcealed something from the hidden.
These seem like concepts of truth to me. Maybe they hadn't developed certain vocabularies about truth that modern philosophy has, but... if they agree with one statement about the world and disagree with another one, does that not imply at least a most basic concept of truth?
I thought you could be a Greek, but don't appear so.
The question had been raised due to the comment in Szaif's article. But I also believe that ancient Greek had concept of Truth. It was just Szaif's point that the ancient Greek's concept of truth was much different from modern concept of truth mainly due to the peculiarity of the Etymological origin of truth. I was wondering if that comment could be further elaborated and proved with some evidence by a native Greek folk.
I am not, but I know many Greeks. I think they would stand by that there is nothing different between Greek's and English's 'true', etymology nonwithstanding.
If truth is something that is unconcealed, that sounds like an implication for the existence of truth in the empirical world. Truths are hidden in the world, and you have to look for the truths, and disclose them from the hidden into your mind.
That view certainly contrasts the belief that truth is a product of perceptions and reasoning in human mind.
From ChatGPT 3.5:
Maybe this will get the thread back on original tract. Thanks for your comments. I agree that Hilbert spaces are useful for the manipulations of Q Theory, but are more descriptive than fundamental.
Of course you always have to be careful with AI - it makes stuff up so needs confirmation. I asked one once about that and it said its defined task is to generate plausible responses. I said "Doesn't that make you a BS artist" and it said that they are similar but being an inanimate machine it does not have the capacity to have an intent to deceive, so it is not a BS artist. I consider that a BS answer that confirms my view, but didn't press it. Certainly making a distinction like that, however poorly, makes it somewhat like a philosopher.
I have adequate knowledge of two areas of thought and/or practice: mathematics and rock climbing. Yesterday I asked ChatGPT about a close friend of mine in the latter, what he is best known for. AI produced a reply that was entirely wrong, stating my friend was famous for a certain climb, while in fact he never did that climb and is known for an entirely different accomplishment. Made up facts.
I'm more interested in arguments that the quantum field is itself physically real. It turns out that Faraday had a similar issue with trying to make the case that electric and magnetic fields were real. Kant was an opponent of this. He favored "the unmediated action at a distance of gravitation that would yield an epistemic ideal to which the alternative model of continuous action, with its hypothetical constructs, could not aspire. Easier far to treat such constructs as no more than mathematical devices, aids to the imagination, not to be taken in any way seriously in ontological terms." This is pretty much now how classically oriented physics talk about the quantum field.