Any academic philosophers visit this forum?
I was wondering if any academic philosophers visit this forum as I am interested in some content that can be provided by them.
I am somewhat saddened that the logic and philosophy of mathematics and philosophy of science categories never receive much attention or forum posts.
What can be done about that?
I am somewhat saddened that the logic and philosophy of mathematics and philosophy of science categories never receive much attention or forum posts.
What can be done about that?
Comments (134)
@Pfhorrest is an academic philosopher. He writes interesting articles in his main page: The Codex Quaerentis.
I remember that a few years ago he posted some consistent and philosophical threads but I think he is off from TPF or he is just taking a break.
In the other hand, Guest Speakers was a good idea to ask academic philosophers to join TPF and answers some questions.
Right! Sorry for forgetting you... If I am not wrong you hold a PhD on philosophy at Comillas right? Well, I remember it because I attended to Nebrija which is in front of your university. :sweat:
Yes, I remember seeing Nebrija. :cheer:
No worries, it's actually not important.
If having a PhD in philosophy and teaching philosophy courses counts as an academic philosopher then I am or was an academic philosopher before I retired. But the logic and philosophy of mathematics and philosophy of science is not my area of interest.
I, on the other hand, am not surprised at all. I never attended to so many talks and in such frequency about science in any philosophical forum or community that I have participated in other than here. In fact, when I joined TPF, since 1.5 years ago, I was surprised to see that TPF allowed topics in which the subject was purely scientific, instead of removing them. Now, I got used to it of course!
Sure, I think I was wrong regarding threads that are about physics even though very little of them are actually scientific or conducted according to what academia might require.
I can understand this well. What I cannot undestand is how can science --and more specifically, talking about purely scientific subjects-- be so à la mode in here!
Science is by its nature conventional, so its concepts
are more accessible to the average person than are philosophical ideas. As a result, people are forced to use their knowledge of science to extrapolate abstract philosophical notions. For instance, they may know what physicists have to say about time and space, but have no idea what philosophers have written on the subject and how it may differ from the scientists.
Good point! :up: This explains a lot.
I dunno that I'd really call myself "an academic philosopher", as that sounds like I have a PhD and publish papers in journals and stuff. I just have a BA in the subject. But I appreciate that someone here remembers me fondly!
I found a philosophy chat server on Discord that I enjoyed more than here, where I was quickly thrust up the ranks of staff and now basically run the place. It's probably against the rules to link to it here...
(We do have quite a number of actual academic philosophers of higher educational attainment than myself, PhDs and Masters and so on, and many graduate students working toward those goals).
I always find the two disciplines fascinating in blend -- in fact that's what I was thinking with respect to philosophy of science as to why it gets less attention: you need to know not just one discipline, but two -- and, in practice, a lot of philosophy of science relies upon a philosophy of history, so you get to have that thrown into the mix as well.
So it's just a larger barrier to entry than [s]a lot of the other sub-fields of philosophy[/s] the standard topics one encounters that turns one onto philosophy. Not that there aren't people who really can pick up on all of these things at once, just that it's less likely to find a person who does simply by the number of things you need to feel confident about to do it.
The philosophy of mathematics is largely foundation theory, and this is a very technical subject. I was a math prof but beyond naive set theory I know little of foundations. In the past the forum had several participants who seemed quite knowledgeable in the subject, but, apart from Tones in a Deep Freeze they don't seem to be active. Beyond foundations I suppose one looks into the historical origins of the subject, arguing what Aristotle really meant by something attributed to him, etc. Not much there in my opinion.
As for science, threads on quantum theory spur a number of posts, many of which appear authoritative, but I have my suspicions. We have had a few actual physicists active here, but they seem to have at least momentarily fled the environment. It's an arena of discussion that beckons those who enjoy batting around the quaisi-woo some actual luminaries lay out - seriously or frivolously.
I've posted maybe a dozen times on Physics Forum, which is a fantastically well-run and professional forum, but they give very short shrift to anything deemed 'too philosophical' which covers a very wide range of topics. I posted a question about philosophy of maths and the ontological status of number, which was frozen because, the moderator said, there was no-one there qualified to address it.
I wonder what would happen if this were posted on a math forum. Probably the same result. There do seem to be ontological questions arising about sets, and numbers can be interpreted as sets.
I wonder what you would make of this blog entry by Colin McGinn. It's quite short. Does he have a point, or is it not even wrong?
https://www.colinmcginn.net/what-is-mathematics-about/
I would never visit a math forum. My school maths was terrible. My interest in the philosophy of math came later in life. I have enough interest in and knowledge of physics to visit physics forum very occasionally.
I think it's muddled. But then I was never impressed by 'mysterianism' either.
Well, I would say the "intrinsic character of numbers" is irrelevant to the subject, and an unfruitful environment for agnosticism. Can philosophy bring any clarity to something that exists only within its practice?
Fair enough.
It's kind of the only label I identify with comfortably, but I do recognize that McGinn is not for everybody - he can be too opinionated and this can sometimes say things which are doubtful. But being a Mysterian myself, I can't help but like him.
I can certainly understand that, if there is such an "intrinsic character", but it plays no role in the development of the field, then this is not something of concern for a Mathematician. This applies to physics too, I think.
If you have in mind ethics, political philosophy and the like, there is a lot of interesting material. But as to the sciences and math, there is no neat distinction between philosophy of any field in science and the science itself. We call it philosophical when the question sounds deep.
Other problems: the self, free will, monism, knowledge and the like, don't look promising, because we've been debating them for thousands of years. Branches of science developed out of philosophy, but a set of important questions (to a good deal of the founder of these fields) have been left behind.
Could be a clue of questions which we don't have the intellectual capacity to solve.
Have you ever happened across Wigner's essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences? It's atrocious prose, but I found the gist of it compelling when first introduced to it via the previous Forum.
Also Mario Livio Why Maths Works, and Jim Franklin The Mathematical World. (The latter explicitly addresses the question of what maths is about.)
Quoting Manuel
"although I can't say exactly why" :lol:
And there are numbers outside that domain, like the imaginary number [math]\sqrt -1[/math] which is used in renormalisation procedures in physics.
I'm sure a logician might wanna include some of what we say in here in their book as exercises (find the fallacy).
Quoting jgill
I wrote a paper (published in the Journal of the British Society of Phenomenology) titled What is a Number: Rethinking Derridas Concept of Infinity. It deals with Derridas deconstruction of mathematical idealization as it is found in Husserls and Kants works. This is certainly technical in the sense that it relies on a thorough familiarity with writers like Derrida and Husserl.
Quoting jgill
Im trying to think of an example of something that exists only within philosophys practice (or doesnt exist only within its practice). Put differently, isnt the aim of philosophy to address within its practice such inclusive concepts as world, existence , reality and truth?
A lot of academic philosophy is focused more on itself than on concepts of "world, existence, reality and truth." Much of what is taught and published is exclusively devoted to the study of philosophers and their texts; in essence, it is philology of philosophy. History and sociology of philosophy are often also included into the same discipline.
It is for some the former via the latter.
Of course.
Entities in thought experiments? Swamp man, twin earth, brains in vats, grue and bleen, the utility monster, Gigantor...
Why is much philosophical focus devoted to the study of philosophers and their texts? Perhaps in order to use the work of others to articulate fresh concepts of world, existence, reality and truth. One could make the same argument for the purpose of historical analyses of philosophy.
For a student of philosophy, sure.
Quoting Joshs
Except that for many, studying philosophers and their texts is not a stepping stone towards future practice, but the practice itself. Not that there is anything wrong with that - I didn't mean what I wrote as criticism of academic philosophy. It is what it is, but I suspect that many people don't realize that. They may think, when choosing their major at a university, that they would graduate to write about world, existence, etc. But chances are that if they pursue philosophy as a career, they will be doing something else.
Other academic disciplines are different in that regard. For example, philosophy, history and sociology of science are not considered to be part of science itself and wouldn't be studied in the same departments with scientific disciplines. On the other hand, your typical scientist probably never read any science text published earlier than 70 years ago.
Aristotle, for example? This is not the whole of his work but still an important part.
Commentary has always been used as a rhetorical strategy. A way of minimizing resistance to something new and different or controversial. It is not uncommon for philosophers to misrepresent those who came before them.
Philosophy is self-reflexive and dialogic. What others have said is not separate from what one says about world, existence, reality and truth.
Original ideas and concepts have always been the exception.
Yes, some time ago, but nothing stuck, so I guess I wasn't moved by it.
Quoting Wayfarer
You must be referring to integral domains, commutative rings, generalized from the properties of natural numbers. From natural numbers one enlarges to rational numbers, then real numbers. And then extending this to complex numbers. Complex numbers are used as a powerful tool in QM.
Is there a question here?
The word domain has several meanings in math. In number theory you have integral domains and when speaking of functions of one sort of another it refers to a set, let's say, of x's for which f(x) is defined.
Basically, it's just a set of objects defined in some sort of space. Not meaningful by itself.
Thank you for this moment of clarity. In math what has come before is a stepping stone to advancements. The actual words of the pioneers are immaterial.
Yep. What is variously said about world, existence, reality and truth manifests the limited number of ways in which humans can model those ideas, which in turn is mediated by language and its limitations. As I recall having read Hegel somewhere say: "it is the same old stew, reheated".
So it is not surprising that there is very little conceptually new under the sun.
More often than not that sparing only occurs in a formal setting - via books, papers, and conferences. The free flow of ideas is stymied by the desire to establish and maintain one's territory and reputation. Professional jealousy is common. The number of contingent faculty is increasing. Adjuncts often feel isolated and are regarded as second class citizens.
Not to mention the creation of small circle of cliques of similar minded people who go around saying the same thing to each other in different settings...
It becomes narrow and repetitive quite soon. One finds interesting views in many places.
I did a Ph.D. in philosophy, taught philosophy at degree level for a long time, ended up in edmin (education administration), and finally jumped into retirement before I was pushed. I don't know whether I count as a professional philosopher or an academic philosopher or both.
I'm a bit hesitant about "coming out" because I found academic philosophy tends to reduce itself to a dance around a small number of doctrines with very little illumination at the end of it. Not knowing the background of members encourages an open mind. So I value the anonymity that this environment provides. Though I suppose I had better update my profile now.
The relationship between philosophy and other disciplines has been fraught for as long as I've been involved. People in other disciplines are seldom comfortable with interventions from philosophy; I think they think that they are best qualified to pronounce on anything to do with "their subject" and it seems reasonable to expect that a philosopher knows something about it before pronouncing on it. Some philosophers seem to manage it. Moreover "I don't know anything about *** but ..." is not a good starting-point for a discussion with a specialist. On the other hand, it seems reasonable (and even inescapable) that people outside the specialist walls, including philosophers, will have opinions about *** and should not be prevented from discussing it and making sense of it in their own way.
Philosophy struggles to define its own field and methodology. This presupposes that the model of other disciplines, like mathematics and science. But that model doesn't necessarily apply There is a version of the history of philosophy that identifies it as the chaotic starting-point of all other disciplines, which have spun off from it as they have developed through the chaotic discussions of philosophers.
Philosophy is not unlike mathematics or science in some ways. But it is also like disciplines such as Literature or History, and like them, a small number of texts function as canonical. These texts open the field of philosophical discussion and show what it is like; they also provide common reference points for discussion as well as a mine of philosophical mistakes - and since there are so few philosophical successes, the mistakes are all the help we are going to get. I have even heard it said that in philosophy, getting it right is less important than being wrong in interesting ways.
Perhaps, philosophy struggles to defines its own methodology because one of the main causes of this discipline is to be critical against methods used in previous academias or groups. Despite the fact that there were been many philosophers among all Western world, I think most of the doctrines and theories root from the same starting point: Ancient Greece.
If we look at Asian philosophy or culture, the scheme switches. It is different the disciplines of Confucianism and Daoism because these have as a cause the aim of pursuing wisdom and connection with nature. We will not see discussions on the verses of Tao Te Ching but just interpretations to get the meaning of our lives.
I don't want to diminish the great value of Western philosophy but I always wished I had more clear concepts and information about buddishm or the Analects of Confucius.
Delightful! Thanks for a glimpse into the profession. :cool:
One of the most interesting features of the modern world, to my mind, is the interpenetration of the great traditions of the world. Western science seems to travel better than Western philosophy. Buddhism has, and still is, very attractive to many people in the West, but also great interest in Confucius and Daoism. Islam, of course, is also very present. Hinduism less so. I don't anticipate some great confluence where all are absorbed into one, but there are certainly influences at work.
Beyond that, it's very difficult to say anything coherent about what's going on. It would be wonderful to be able to see what has happened in, say, 50 years time.
Can we not approach the subject of the value of philosophy in a different way than done usually in the forum? Usually the question asked is what philosophy is. Then discussions degenerate into some defense of philosophy's claims against some objecting that philosophy has made so little progress in comparison to science. The question then turns to whether philosophy should adopt some sort of scientific method or abandoned altogether. What if we just accept that philosophy is as philosophy does, that its method is what defines it? Just entertain the thought and accept for a moment that philosophy is actually its method. That browsing the ancient texts up to the new ones and that picking apart the arguments made and retracing the lines of thought is philosophy and that it is immutable.
What then can we expect from philosophy? If approached in this way we can see affinities with law, with history and theology. Its method is scholastic. It takes concepts to their extremes, using conventional points of view in various hypothetical situations and tests their limits. it uncovers assumptions we have to make when settling disputes about truth, beauty, justice and what not. When we consider its method immutable we see that it is not an empirical science and will never be. It therefore cannot yield any observable empirical truths about the world. What it can do is examine the concepts we use to think about the world. It can show us their relations, their mutual support or their antinomies. Philosophy then, is thinking about thinking, because the concepts we use to examine the concepts are the very same concepts themselves. It is a circular activity of reflection.
What is the worth of such an activity? The answer to that question depends on whether one holds on to the identity of thinking and being. i.e. the proposition that all that is, must be able to be thought and that being thought entails in any case the potential to be. If one holds on to that notion, the conceptual world is the same as the material one and by conceptual analysis philosophy explores the world as it is. The empirical sciences are simply the other eye which we use to look at the world. I would call this the idealistic position.
If one does not accept the assumption the role of philosophy is much more limited. Philosophy simply cures us for our bewitchment by language and works tirelessly to clear the debris of our thinking. The material world though is broader and always escapes our thinking about it. The more we discover the material world, the richer our concepts become. I would refer to that as the materialistic position.
I think both approaches may well be viable. I think it is illusory though to want something from philosophy that it cannot provide, empirical knowledge of the world. That claim is significant. For instance. Philosophy may teach us how we use the concept of justice, but cannot provide us with empirical knowledge of whether an act is just or not, not in the idealistic conception of in the materialist one. The idealist would maybe hold that justice exists and that some acts indeed are just and unjust. A materialist would have to either fold on the question or translate justice to some sort of material term like benefit. Such an excercise, here undertaken in a very ramshackle and shorthand way about justice, does reveal something though. It reveals the origins of our commitments and ay explain different usages of the term and therefore also the miscommunications surrounding it.
That is what scholastic science may do, retrace the history of our thoughts and our arguments. The exact value you attach to such an activity rests on your commitments, but it can only clarify itself and noting else. If that is enough for you, by all means do philosophy. If not, go ahead and do research in the laboratory or society at large and become a scientist.
I'm not a philosopher, but I tend to think that there is 1) reflecting on one's beliefs and values and the limits of knowledge and 2) philosophy which does this and much more. I tend to privilege the first and have never privileged philosophy as such (not because I disregard the enterprise, just that I don't think the average human brain can do much with it - time limits, capacity, access to mentors, etc.).
Quoting Tobias
Totally agree. And this kind of reflective practice, if you like, is invaluable in understand the various frames or world views people hold and how much these shape awareness and the meanings of ideas.
Quoting Tobias
if philosophy is circular then so is science , since the empirical world it strives to represent is already prefigured in its theories. But for both science and philosophy, this circle may be seen as a spiral. We construct hypotheses which determine what and how we see, and the world talks back to us in the language we invent for it, triggering transformations in our conceptions. Through this reciprocal movement thought develops. As far as yielding an immutable method, this is neither true of philosophy nor science. In both cases , the methods change as ideas develop in their spiral fashion. In fact, the methods of science and philosophy evolve in parallel, since the difference between what science and philosophy supposedly do is somewhat arbitrarily defined in the first place. They are more of an inseparable mesh than discrete categories and evolve together over the course of history.
What about human soul/spirit/self/identity BEFORE the person gets born and/or acquires it?
------------
EDIT: Sorry, that was actually stupid of me to ask that. And I can't delete the post.
Theres a book or two to be found in these contributions. Forgive me if I dont reply in detail.
For what its worth, Im very taken with Wittgensteins remark that a philosophical problem has the form I dont know my way about. That fits with his idea that what he is looking for is an oversight (Übersicht) which I take to mean something like a map. Perhaps when one has a starting-point and a map, one moves into another mode of thinking which is more like other disciplines. Unfortunately, the world we live in changes, confusion returns and so philosophy continues. It may not look like progress, but that doesnt mean there is no point.
Some further observations:-
The priority given to science (which is usually taken to mean the hard sciences) and mathematics is not universal in philosophy but is local to analytic philosophy. There are plenty of other kinds of philosophy.
It seems to me that the most helpful characterization of philosophy is reflection; this doesnt mean just anything that might be called reflection but means a disciplined reflection disciplined by the examples of other philosophers. Too narrow a conception of philosophical method risks (and usually falls into) a narrow focus, which, I think, is almost always fatal, except, perhaps, as a temporary tactic.
The institutional environment for philosophy and other disciplines has been revolutionized in the last hundred years of so by the its institutional context. Unfortunately, the search for a definition of philosophy has too often been weaponized in pursuit of the inevitable struggles within academia, in which it is necessary for each discipline to stake out its own territory and claim on resources. Philosophy suffers if it is too closely confined in that way.
At PI 122 Wittgenstein talks about an übersichtliche Darstellung, a surveyable representation, (alternatively translated as perspicuous representation):
It is surprising how little he says about it, given that he says that a representative overview is of fundamental significance.
A few key ideas touched on at PI 122:
seeing connections
the way we represent things
how we look at matters
At PI 126 he says:
and at 90:
Elsewhere he says:
An additional key idea:
possibilities
A representative overview helps make it possible to see connections, to look at things in a new way:
Thank you for that collection.
Typical, isn't it? He mentions a metaphor and passes on, as if it was transparent. Then elsewhere, you find another metaphor from which he passes on. And another and another...
Yet they all seem to work together somehow.
I may have missed something - "surveyable representation" does not sound familiar - that's not a criticism - but "perspicuous representation" does. Is there a translation other than Anscombe's around?
Integers are outside the naturals.
Rationals are outside the integers.
Reals are outside the rationals.
Complex numbers are outside the reals.
Quaternions are outside the complex numbers.
The table of number systems at the bottom of the quaternion hyperlink might help you! There's lots of sets that have the integers inside of them.
I think he wants us to see and draw the connections, or not. In an early draft of a forward for Philosophical Remarks he wrote:
The fact that there are things he deliberately hides is deserving of our attention. That there are locked rooms hidden in the pages of his work is an intriguing confession and interpretive challenge. The question of where these rooms are and what is hidden in them, is not something that is even asked in the secondary literature that I am aware of.
Quoting Ludwig V
The 4th Edition translates it this way.
Quoting Fooloso4
I dont interpret him as meaning that he deliberately hides things from readers, but rather that if one isnt ready to recognize what he is saying, no amount of explication will help. It is not a matter of choosing the right words and phrases, for these will be misunderstood. The last thing he wants is to limit beforehand who has access to his thinking. On the contrary, he was desperate to share his ideas with as many as possible, and to write in such as way as to achieve this goal . The key to understanding Wittgenstein ( or any philosopher) is provided by the reader as much as the writer.
While there is always interpretative indeterminacy, when he says:
I take putting a lock on the room that they do not have the key to to be a deliberate act.
Quoting Joshs
I agree.
Quoting Joshs
It is not that he selects the reader but that the readers are self-selective, they are able to understand it or not. It is for the benefit of these readers who cannot that certain things are kept from them.
Quoting Joshs
In the preface to the Tractatus he says:
He doubts he will be understood by most. But his concern is not simply that he will not be understood, but that he will be misunderstood, his thoughts will be watered down or mangled. I don't think he writes despite the fact that he will be misunderstood but strategically so that what is most important will not even be noticed.
Thanks. My question was about the sense in which a domain, such as the domain of natural numbers, is real, but not phenomenally existent. I notice that nowadays it is commonplace to say of anything considered real that it must be 'out there somewhere' - but even though such a domain is not anywhere, it is nevertheless real. See this passage.
Maybe I can put this another way. If one tries to dilute or dumb down their ideas in order to reach a wider public, one may end up not only failing to achieve the hoped-for understanding among the masses, but making the work incoherent for those most inclined to comprehend it. The only way forward is to write for an imagined kindred spirit, which will have the secondary effect of alienating a wider audience. We see the symptoms of such a choice all
the time on this site, as participants here complain about the deliberately obscure writing style of various philosophers.
Is the "Quus" argument an explanation of Wittgenstein's thinking, or a derivation from it? But more, can such a distinction, between understanding Wittgenstein and extending him, be made?
The supposition here is that there is a something that is the real meaning of Wittgenstein's work, that we might try to understand.
But is that right?
And of course, the answer we give for Witti applies to any other philosophical text. The question is not what did Plato really mean, but does it make any sense to talk of his work as having only one meaning?
In a regulative sense I think it makes sense to talk of the real meaning -- at least somewhat historically grounded, roughly responding to this or that idea -- but then as you try to find the real meaning, so as to say "yes, this is it, for these reasons", especially with the usual philosophical texts which attract us: it is fairly judged as a multiplicity.
An interesting thing about Wittgenstein is that he has always attracted an audience and that audience over time has been quite diverse.
There are various reasons why an author might be or seem to be deliberately obscure. But there is a difference between an obscure writing style and deliberately hiding something.
When Wittgenstein says, as quoted above, that he has been frequently misunderstood, it is clear that there is something that he means, otherwise there could be no misunderstanding. We may never be able to establish a definitive interpretation, but that does not mean we should not attempt to determine what it is he means.
I do not regard interpretation as merely a way of determining what someone else is thinking but as a way of thinking. As Wittgenstein says in the preface to PI:
And in Culture and Value:
For Wittgenstein philosophy is an activity not a theory or doctrine or set of principles that we must find the meaning of.
From your link:
It may be ancient and unsolved, but that doesn't mean it holds the interests of those involved. What appeals to most mathematicians is the exploration and creation (or discovery) of new ideas - new theory. I was a rock climber for over half a century and what compelled me in both math and climbing was finding out what lies around the bend or over the overhang, whether it's creating or discovery - an argument that few in the profession care diddly about - and this seems to be a major difference between what is being said about philosophy in this thread and what is true of mathematics, save for those few in math foundations: Philosophy is concerned with what was said or printed or argued in the past, whereas mathematics (with the exceptions of a few math historians) always looks toward the future, even when analyzing the present lay of the mathematical landscape.
From "what is new is the exception" to "what is new is the rule".
Foundations and set theory, overlapping philosophy and mathematics, are out of my bailiwick. :cool:
Not in my view, obviously, but I won't try and persuade you.
:100:
Isn't that what you are talking about? The issue of the "reality" of mathematical objects. Over two millennia have passed with no consensus. When we speak of Platonism isn't that something from ancient times?
However, quantum theory may ultimately bring some clarity as physicists explore the mysteries between mathematical entities and physical reality. Where in a process does actualization occur? Virtual particles appear to be Platonic rather than physically real - they cannot be observed and yet they are convenient in certain procedures. In QT is where I might expect to see progress in understanding the nature of mathematics, here is where the subject may morph into a kind of neophysical existence. Who knows?
OK, I'm on board with that. :up: :smile:
That is what I would describe as a jaundiced view. Platonism one of the wellsprings of Western culture which I think still maintains both relevance and vitality.
Jesus. No disrespect, but if this is all you could say about philosophy, then you don't fit in philosophy. People who summarize the thousands of philosophical posts in forums like this with a statement such as above, has not learned anything but cliché.
I agree. It is. On rare occasions in my career when the nature of the reality of numbers and math came up amongst a group of my colleagues invariably eyes would roll and the topic would disintegrate shortly thereafter. Had I been among foundationalists reactions might have been different.
So, you are saying there has been consensus about the reality of numbers and whether math is created or discovered? I'm not addressing other aspects of Platonic philosophy.
So, are you saying you did not get the gist of what I just said? Do you really need me to explain to you what I said in english? There are things you could say with depth about the subject besides "Over two millennia have passed with no consensus".
Will you be satisfied with a consensus, just to have an agreement? A population could have a consensus on something and they're still ignorant or wrong. I'd rather read philosophical writings having differing views, but well argued, than seeing a consensus for the sake of stopping all philosophical arguments.
The study of mathematics is not the same as the study of philosophy.
Why not the divinity of Jesus Christ indeed? I think this signifies a deep confusion about the nature of transcendentals. And I think that is because empiricism, as a philosophical attitude, has conditioned us to believe that only what is phenomenally existent, only what science can validate, ought to be considered real. So despite the fact that science in general, and physics in particular, has been so utterly reliant on mathematical reasoning for its discoveries, the philosophical framework in which it operates cant actually accomodate the kind of insight mathematics represents - hence those declamatory statements!. And that has many vast philosophical implications.
Consensus is vital to mathematics, but from what you say a hindrance to philosophy. When one argues about the reality of numbers, that is not an argument in the realm of mathematical practice. It may have great meaning for philosophers but is seen as incidental to the subject by most math professionals. On the other hand, a philosopher might have difficulty explaining philosophical implications of a theorem picked at random.
Maybe in English. And I'm sure you are correct. I suspect most of those things "said in depth" have relevance in philosophical circles rather than in mathematics communities - or anywhere else. It's good to know the limitations of one's reach. I have created and proven perhaps two hundred theorems - but they are virtually worthless, lost in millions more. All said in depth. :cool:
No. I meant to say "with depth" -- meaning, with deeper understanding than the lack of careful thought on your part by saying over 2 millennia and no consensus. Not "in depth" where one demonstrates a comprehensive knowledge of something, such as you and the two hundred theorems you proved.
I hope I've made this clear.
Quoting jgill
Wrong again. I did not say this. Consensus is not a hindrance to philosophy, but if this is what you think is the pièce de résistance in philosophy; then you've missed the mark by a mile.
Thanks for that link. It's nearly as good as Christmas. But I was thinking that perhaps it was time I read it again, so it is well timed.
We seem to have two quite distinct threads running through this thread. Never mind.
I get quite worried about Wittgenstein's hints that there are things hidden in the Investigations. He does the same thing in the Tractatus in that he says that we cannot speak about the really important things. But at least I understand why. It's less obvious what is going on in these bits of the Investigations.
But then I remember that I'm rarely satisfied with anything I write for longer than about five minutes and if I worry about misinterpretations I get absolutely paralyzed. If Wittgenstein felt the same way, I can understand that.
One has to accept that text (or speech) is never all that we would like it to be. Communication is always subject to noise and distortion - there's no way of escaping from that. One does one's best and that's all there is.
As I see it is, there is really no question about the reality of thoughts, ideas, concepts and abstractions. Very few people would deny the reality of such things. The problem arises from how we talk about these things. The words we use which facilitate such communication often do not properly represent the way that we understand (or fail to understand) these things. Notice for example, I've referred to thoughts as "things". I really do not believe that thoughts are even similar to material objects which I also call "things". With talk like this, we create an environment where ambiguity and equivocation are highly probable.
So, we talk about mathematical "objects" and we also talk about physical "objects". What is implied by this talk is that there are two types of objects, one type having the properties which mathematical objects have, and the other type having the properties which physical objects have. Then we need principles to distinguish one type of object from the other type, and this is where the difficulties arise. When we try to separate two distinct types of objects we employ a reductive analysis, and they end up "converting" into each other.
What is implied by this, is that we cannot maintain a separation between two distinct types of objects. There is not any real principles to separate the two. The separation of two types of objects is not supported by reality and our attempts to create such a separation are fraught with problems because it is a fictional categorization.
Now we are left with a choice, which of the two types of "objects" provides us with a real representation of what an object is. What Plato argued, with the cave allegory, is that the intelligible objects, thoughts, ideas and abstractions, are the real objects. The supposed physical objects are really just the reflections of the true objects which are the intelligible. However, the majority of human beings, the masses, live in a world directed toward fulfilling their bodily desires. Therefore they prioritize their bodily senses, and they refuse to follow what the intellect demonstrates to them. Accordingly, they reject the guidance of "the philosopher", who has come back from his journey into the intelligible in an effort to disillusion them, returning to the cave where the others are imprisoned by their sense inclinations. They refuse to be led toward the truth.
Yes, and I think most of the authors people complain about on this site are neither deliberately nor accidentally obscure. They are trying to be as clear and comprehensible as possible in their writing , and it is the inability of many readers to grasp the originality of the ideas that is the source of the mistaken impression of obscurity. The authors are hiding something from these readers, not deliberately but as a consequence of the difficulty of the concepts.
This is true of Wittgensteins work. I think that it is a mistake to assume he is deliberately hiding something. Rather than contemplating the ways in which the average reader was likely to interpret him, and then proceeding to craft a style which deliberately hid ideas from them, I suggest he put all his focus into optimally communicating to an idealized kindred spirit, knowing that if he succeeded in doing that it would automatically have the effect of hiding his thinking from those who would be inclined misunderstand it under any circumstances.
Quoting Fooloso4
Do you think that in my scenario where his focus is entirely on an imagined kindred spirit, the way in which he composed his work would have been different than in your scenario where he not only writes revealingly for such a spirit but at the same time, in a calculated fashion, deliberately hides things from others?
Lets take On Certainty as an example. His main interlocutor here was G.E. Moore. Would you agree his overwhelming focus was on having Moore (and others who agree with Moore) think about certainty in a new way?
if he kept things from some other readers, how do you imagine the work would have looked like had he put those thing back into the work? Given that , as he himself admits, he was surprised and disappointed when his earlier efforts were widely misread, do you think he even would have had the confidence to know what to hide from them? How can we choose to deliberately hide things without anticipating ahead of time what things are likely to be misunderstood? I suggest that it is only in hindsight that Witt could know what in fact ended up being hidden from readers in specific writings of his.
I could not help noticing that the results of my work (which I had conveyed in lectures, typescripts and discussions), were in |x| circulation, frequently misunderstood and more or less watered down or mangled.
The above quote displays a surprised realization in hindsight that his ideas were hidden from many. I think what Witt learned from this disappointment was to no longer expect to reach more than a handful of people with his writing. This preparatory insight is, I believe, the only deliberate thought that pertains to what in hindsight turns out to have been hidden and locked.
This is often the case.
Quoting Joshs
Prior to talking about something hidden he does say in the forward:
and then adds:
If those who understand are automatically separated then why go on to talk about locked rooms? He says:
But isn't this what he is doing? Doesn't the text tell most readers that something they do not understand? And doesn't he say they will not be able to understand it?
I am reminded of something else he said:
Perhaps in his attempt to help the philosopher escape what goes unnoticed is something quite different.
And you did. My mistake.
Quoting Metaphysician Undercover
Yes, and in the quantum world those distinctions could be imperiled. The problem of actualization of potentia brings science and philosophy forcefully together IMO.
So it seems. So is Kripke's argument a rendering of Wittgenstein's, or a misinterpretation which is nevertheless philosophically interesting?
Is the Quus argument what Wittgenstein had in mind, or a variation from it?
I'm suggesting that this question need not have an answer.
I don't think Kripke understood Wittgenstein. He took PI 201 and ran with it. He thought it was a new form of philosophical skepticism. In response to Kripke one might ask, given his skeptical solution, why he still maintains that there is a skeptical problem at all? If our ability to follow rules correctly and consistently is not dependent upon the application of a privately held conceptual understanding of the rule (the justified mental fact), but can be explained in terms of training and conformity to standard practice, then what remains of the skeptical problem?
The skeptical problem arises only as a result of the theory that there must be some fact which meets some particular set of conditions to which we must have access in order to justify that we are acting in accord with a consistent meaning for a particular term or rule. Far from introducing a new form of skepticism, Wittgenstein is calling to our attention the fact that in our actual practice of learning and using rules no such demand needs to be met.
Kripke intimates that Wittgenstein deliberately obscures his skeptical position that there is no fact as to whether I mean plus or quus ( On Rules and Private Language, 69-71). What Kripke fails to see is that by denying just such a fact Wittgenstein is not agreeing with the skeptic, but rather calling into question the very assumption that there is such a fact.
See Quantum mysteries dissolve if possibilities are realities.
Interesting, basic and to the point. It may be, that reality is far different from the way that it is conceived by scientists.
I believe the key to understanding this principle is to recognize the reality of time. If the future consists of possibilities, and the past consists of events which have been actualized, then the present must be conceived as the time when possibilities are actualized. This "present" would need to be be a "time period" which consists of some duration, during which possibilities from the future become actualities in the past. For reasons demonstrated by some philosophers, this transition can not be instantaneous, the present is not a "moment", not a non-dimensional division between past and future. "Actualization" itself implies an act which requires some amount of time for possibilities to be actualized at the present time.
Time is measured as it passes, so all measured time is in the past, necessarily, requiring action (actual motion) to make a measurement of time. As we move toward measuring faster and faster motions (pure energy) in our experimentation and practise, we deal with shorter and shorter periods of time. When the present is conceived as having temporal duration, then part is future-like, and part is past-like. In dealing with extremely short periods of time we deal with the part which is future-like, consisting of possibilities, just starting to become actualized. Moving further into the future-like part of the present in our practises provides us with more "power" over how possibilities are actualized at the present.
As the article states, this "new" perspective is not actually "new". It is as old as philosophy itself, and has manifested as the theological perspective. It is from this perspective that moral principles, and our understanding of free-will is derived. The human mind partakes in the future-like part of the present, that part which is immaterial, being prior to the measurable physical activity which occurs as time passes. From this position it has the capacity to direct the actualization of possibilities as time passes. This is the Aristotelian biology, which places the soul as the first actuality of a living body. All the capacities (potencies or powers) that the living being has, are understood as possibilities for actualization (potentials), under direction of that first actuality.
Quoting Fooloso4
My memory may be fallible, but I'm not sure W directly confronts the sceptic. He certainly thinks that many of the philosophical questions that he does address contain mistakes and he certainly does philosophy in a unique way.
Hacker, in his categorial framework, mentions with approval the idea that philosophy is conceptual, or rather grammatical, in an extended sense of the word. That's helpful in some ways, but still gives a purchase to the idea the philosophy should make progress.
My suggestion to understand this is to look more widely at the intellectual and cultural world that we live in. There are many disciplines that can be said to change and develop, but are misunderstood if one supposes that they should or could progress. It seems to me that the Arts, by which I mean music painting dance drama stories etc. are all like this; the obvious explanation is that they have no goal or purpose, because they are done for their own sake. They are done in their cultural and historical traditions, but add to them rather than superseding them. Mathematics, it seems to me, is like them in that respect - it adds to its traditions without superseding them. It is true, of course, that mathematics often turns out to be useful, but I can't accept that that is its point. Science seems more like an outlier in that it seems to have a goal, though I'm not absolutely sure that is the whole story. In this context, our question becomes how philosophy fits in to this collection of activities. It's probably best to think of them as a family united and divided by family resemblances.
Interesting link. It's not quite what I had in mind, but probably more reasonable. I had thought of a continuum between the world of ideas and the physical world.
Thought-provoking. Thanks. Goes back to constituting mathematical (and physical) reality from the continuum to the discrete, not the other way around. Traces of Bergson.
Quoting Ludwig V
That's the way it usually works. Math people "create" or "discover", building more or less on preceding results, sometimes obviously but at other times seemingly "new".
Quoting Ludwig V
Bingo! :clap:
There are various forms of skepticism and it is misleading to conclude that Wittgenstein either accepts or rejects it. In On Certainty Wittgenstein addresses examines claims about such things as knowledge and certainty. He denies certain claims and argues in favor of others.
Quoting Ludwig V
Good point. What are we to make of this?:
Is there a Philosophical Investigations, or are there only un-detached Philosophical Investigations parts?
Given a rejection of
it seems not.
It is not that there is a categorical or unqualified interpretation but rather that problems with a particular interpretation can be identified. That a strong case can be made that this or that interpretation is wrong. This does not mean that there is or ever will be an interpretation without problems. As I said above, there is always interpretive indeterminacy. There are also different interpretive practices. There is an attempt to understand what an author means, as well interpretations based on the assumption that this is not possible. There are interpretations based on what the text means for a reader. There is the attempt to situate the text in time and place or in response to something or other. There is deliberate appropriation in which the text is used to present the interpreters own story. There is the attempt to deconstruct or uncover the author's unspoken assumptions. Interpretation that points to the fact that an interpretation is itself interpreted. And so on.
It seems that there is something of a consensus here.
Quoting Fooloso4
What I was getting at it that Wittgenstein doesn't say "Here is scepticism. This is my solution." in the way that Descartes, Berkeley, Hume &c. &c. He seldom does that. I think there are reasons, even good reasons for that. It doesn't mean that I think that nothing that he says is relevant to scepticism and intended to be relevant to it.
What I make of the itch and scratch metaphor is that what progress means can be different in different contexts. My point was that the despair about progress in philosophy depends on a particular definition of what progress is and that definition does not apply in a lot of other cases - including, of course, scratching an itch.
Quoting Banno
I'm not sure I want to answer that question. I think the point is that the themes in the Investigations are linked and interwoven. That's one of the strengths of his writing.
Quoting Fooloso4
In addition to the different practices you mention, there is also the point that interpretations will vary to work in different contexts - which will include questions and interest that the author could not have had in mind.
Haha! Certainly not after a career in philosophy... :lol:
I started down that road long ago, only to opt for the safety of more mundane pursuits. I admire your courage.
Quoting Ludwig V
Of course he can't provide explicit answers; he must show how to think about the problems at hand. If he is to be consistent in wanting us to look to use instead of meaning, that's the only consistent approach he could take. The meaning of Philosophical Investigations is the use to which it is put, so the book must show us how it is to be used.
It doesn't matter if "gavagai" is a rabbit or an undetached rabbit leg. What counts is making the stew.
How very pragmatic of you. :smile:
That's just rude. :wink:
No, not pragmatism. It's just preferable to argue about the meaning of "gavagai" on a full belly. That's pretty much the reason i decided not to pursue academia.
You must have had a feeling of knowing what was in store. Or was it more than that? :smile:
The result is apparent in this forum. Folk think philosophy easy, a topic for dabbling dilettanti.
To it's credit, the Department still exists.
The one-eyed king surveys his blind subjects.
And inflate grades. And be prepared to be held responsible when students fail. And go along with the pretense that you are not dumbing things down.
We (mathematics) were mostly a service department, with courses we designed for liberal art majors, business majors, engineering tech majors, etc. We occasionally had run-ins with those departments about grades and standards, and we could adjust those without abandoning our self-respect. I mostly became responsibly involved in these things when I headed up the department for a couple of years.
Because of the service factor we were able to keep courses for our majors at a reasonably high level, with me designing and teaching the senior level offerings in real analysis (intro), complex variables, and topology. I was considered the most demanding, but mostly about giving a B instead of an A. :cool:
Quoting Banno
I plead guilty. I am learning slowly about what makes a philosopher tick. My one senior level course in the subject in 1958 was more of a survey and little was said about the practice of philosophy.
I agree about the full belly. However, having started another career which would have provided considerable comfort as well as a full belly, I had to put up with feeling like a fish out of water. In the end, I decided that a full belly had too high a price and started postgraduate work to put off making another choice between unappetising options and see how it went. Somewhat to my surprise, in the end, I got a job.
I see from later comments that others had experiences similar to mine. I compromised, because what I was doing was better than any alternative that I could think of and it kept my belly (and my family's belly) full, though holidays tended to be on the cheap. Perhaps I was just hooked on philosophy. But it was all a severe disappointment; I started with idealistic ideas about philosophy being available to everyone and working closely with other subjects. Some of that has happened, but a great deal of it has not. My Department no longer exists, in spite of trying hard to adapt to the changes; the University decided it could not afford any luxuries. We did try arguing that philosophy was not a luxury, but no dice.
Quoting Banno
Yes. But. I knew some quite annoying professionals. In any case, philosophy, like sport and classical music benefits from a lively fan base and surely should be available to as many people as possible.
The truth is, that although I have some regrets, I don't regret my career. What surprised me most was that when I retired, I had had enough and I turned my back on philosophy for some years. But gradually I found myself drifting back to it, and now here I am - obsessed with it again and much happier for it.
I recently came across the term philosophunculist.
Philosophy is like a broken tooth that you cannot prevent your tongue from prodding. Or Midgley's plumbing, where you can't ignore that smell or the constant dripping.
To be more specific, It's clear that there are folk here with little formal education, yet they are engaging with material outside of the forums, and growing in their understanding of philosophical issues. Ire should perhaps properly be reserved for those who drop in to the forum supposing themselves to have the answers, which are of course obvious and simple and we should have already seen them, silly us.
Quoting Banno
:up:
Quoting Banno
:up: There are two things about philosophy that are not quite polite to mention. But they are important, nonetheless. Answers are not the point, and in fact are the death of philosophy. Similarly, agreement about the answers are welcome as an episode, but disagreement is what keeps us going.
Quoting Ludwig V
I suppose it depends on what you mean by answers. A given philosophical position can be seen as an answer to a question that a previous philosophy stimulates. It does this by offering a way of understanding that allows us to clear up confusions or problems that are generated from within the history of philosophy (skepticism, nihilism, dualism and the Hard Problem). An answer can resolve by dissolving rather than solving.
What Ive said about philosophy is true of science. The power of a scientific theory is not in the specific answers its predictions give, but in the way it re-poses problems relative to the theory it replaces. Questions and answers pre-suppose each other in philosophy, not just in the sense that an answer is a response to a question but in that philosophy must offer answers in order to generate new questions.
Quoting Joshs
I agree with that. But then, an answer that is correct, job done, doesn't generate new questions.
Perhaps we should distinguish between answers (2+2=? Answer 4) and responses, which do. Or perhaps we can just rely on disagreement and elaboration to keep the conversating going?
My perception of the nature of philosophy keeps changing.
I can't resist the urge to reply "No it isn't!"
Does this mean that you think answers are unhelpful? I guess one might ask, about what matter?
I agree that questions are important but do we need to take from this that answers are always anathema?
What exactly is an answer to a philosophical question - is it a solution or dissolution? Or the best available, but tentative hypothesis?
I'm not a philosopher, I'm wondering is there a single philosophical question that has been 'answered' definitively for eternity?
Yes and No. ;)
:rofl:
On the surface, the answer is probably No.
But that depends on how you define the questions. Arguably, what happens is that an answer that works in one cultural and intellectual environment will seem inappropriate or inadequate in another and so the question is re-framed and re-interpreted.
There's an old saying - or possibly a quotation whose source I've forgotten - that it is differences of opinion that make horse races. And when there's a winner, the race is over. My point is that it is differences of opinion that make philosophical dialogue - and reflective dialogue is the heart of philosophy.
I'm opposed to people who think that the questions must have a final answer - especially when they think they have found it. It leads to dogmatism and squashes dialogue. Perhaps I should have distinguishes between answers, which shut down dialogue, and responses, which don't.
There seem to be a lot of people around who worry about the lack of "progress" in philosophy. I'm suggesting that the demand that philosophy makes progress by providing conclusive answers is only one view and that there are alternatives that perhaps should be better developed.
I don't know how philosophy will develop, but I'm sure that it will continue in one way or another - for better or worse.
Quoting jgill
I'm not clear whether you think that's a bad thing or a good thing. I suppose it could be either, depending on why it changes.
It is also possible that philosophy can be seen in more than one way at the same time.
I can't resist replying "Yes, it is!"
As a math person (retired) sitting on the sidelines, I am beginning to appreciate the dialectics, the vitality of the practice. The thought of being wrong in an interesting way has a charming appeal. :smile:
Quoting jgill
It certainly stuck in my mind. It also gives on another target to replace the ever-elusive Truth and helps with destructive anxiety.
So let me offer you another insider remark that I've never forgotten. A professor well known for his contributions to logic once confided in me that he understood Gödel's famous argument, but didn't believe it. (!) Thst's a consolation for people like me who find logic very difficult.
Years ago when I was still somewhat active in the research community I published a paper on an unexplored topic. I proved a theorem, but with heavy hypotheses. A year or so later a colleague published a similar paper, based on mine, and proved a much, much nicer theorem - minimal hypotheses. So, in a sense, I was "wrong" to assume more than was needed, but wrong in an interesting way.
Quoting Ludwig V
My first grad course in math back in 1962 was an introduction to foundations and set theory. It was pretty neat how we (doing homework exercises) started with the empty set and ended the course with a definition of the exponential function. But beyond that, only perhaps two students out of a class of maybe 25 found the remainder of the subjects attractive. Even the young and enthusiastic professor recommended most of us stay away from the topics in the future.
Gödel's results are reflected in only a very small number of research themes.
Yes, that would be a good example.
Quoting jgill
I'm not surprised. Those results, in my uneducated view, are pretty devastating for mathematics as we know it. Philosophers are probably more inclined to take his theorem seriously. But most of them are inhibited because they don't want to grapple with and are not qualified to grapple with mathematics (or should that be metamathematics?)
The point that I've not forgotten is that the orthodox philosophical claim that logic provides arguments that everyone will agree to is false. Yes, there is a penalty, supposedly. If one withholds assent from a sound argument one is guilty of inconsistency or something. Which is true. But that professor did not seem to be suffering any serious ill consequences.
In fact, a large majority of mathematicians go their merry way, ignoring the incompleteness thing. Although it's in the background - like being struck by a meteor while playing golf - it is inconsequential to most research. I think you are correct in that it is a more important concept for analytic (set theory/foundations) philosophers.
What you say reminds me of what Hume says about radical scepticism - he calls it Pyrrhonic. Everybody will continue on their merry way, despite not being able to disprove it. Indeed, he recommends everyday life as a good cure for it.
-I hope not....except of course if we they are Naturalists(methodological).
Quoting Shawn
-That's so true! Since your mentioned Philosophy of Science( I love this category), are you familiar with Paul Hoyningen's work on the Philosophy of Science(Systematicity, the Nature of Science). If yes, could you share some thoughts on his ideas on Science not being something special but still enjoying such an epistemic success!
Thanks for the mention. Yes, my degree is in theoretical physics, but I have published more in philosophy. A new paper was recently accepted: "The Hard Problem of Consciousness and
the Fundamental Abstraction," which will appear in the Journal of Consciousness Exploration & Research.
I'd seriously recommend moderators look into this idea. It wouldn't even need to be something they create an account for, there could be a guest account set up by moderators for the occasions these guests are here. Almost like having a guest on a YouTube live pod or something where people can engage in discussion with them. Maybe a specific topic that the guest philosopher is an expert in or published a paper on and the discussion starts out with people reading that before engaging in the discussion.
That would, in my opinion, be a seriously good use of a forum like this that elevates the philosophical experience for everyone.