This post is interesting because it so clearly shows just how far our common points of reference are, and why, perhaps, we're simply speaking across each other. I mean, to play your game of sampling:

1) 'Sensible/Intelligible': The intelligible/sensible distinction is thoroughly Platonic in provenance and refers to the sensory ('feelings/affects') and the rational/conceptual. You can find it in Plato, Averroes, Descartes, Kant and Sellars, among other places. It's pretty much among the most basic and classic distinctions in all of philosophy. That your first associations were with - of all people and things - Austin, Tarski and 'coherence theory' - just speaks to, well, the completely different universe of discourse that you occupy. An entirely idiosyncratic one, at that.

2) 'Measurement': Sorry, but this one really is just pure and unadulterated sophistry. Leaving aside the obvious fact that 'measurement' in the context it was used was clearly a synonym of 'assess' or 'evaluate', the idea that 'measurement' belongs exclusively to a scientific vocabulary is only something a non-native speaker of English could ever think. When Protagoras declared that ἄνθρωπος μέτρον - man is the measure of all things - do you think he meant that humans are scientific instruments? That this has to be even pointed out is embarrassing for us both.

3) 'Necessity': you think necessity refers to deflationary theories?? Really? Really really? You think necessity has not been thematized with truth in philosophy until a bunch of boffins in early 1900s decided to do it? Try Plato.

So yeah, if I sound frustrated it's because I am. The very terms in which you read me belong to an entirely alien discourse, one in which philosophy suddenly sprang up out of nowhere just over a century ago or something. Most of what you say is not even wrong, it's just... irrelevant and uneducated.

Ignorance as principle it is then.

Well if it's out of your understanding then you can't object to it because you'd have no grounds to do so, by your own lights. I suspect you want to argue something like: these things are constitutively out of our range of understanding. But that would be voodoo - ignorance elevated to the rank of principle.

The thing about God is that God is always invoked as an unexplained explainer: God doesn't explain anything at all, he's nothing but a stand-in - a synonym even - for ignorance. Explanations in terms of societies don't, or rarely do, function like this: to say that such and such can be explained in societal terms is (usually) to say that such and such is a response to some kind of societal problem. 'Society' rarely names an 'answer' so much as a problem to itself be explained: what are the conditions which made society respond in this way? And those answers will generally be local, historical, and concrete (even as they can play a part in broader anthropologies).

Or, err, A COMPLETELY REASONABLE AND STRAIGHTFORWARD APPROACH TO THINGS I MEAN HONESTLY ITS NOT SO BAD.

Mistakes, yes. But falsity? A note can 'ring false', I suppose, but theres no intentionality there; its not false about anything. A machine can break, be useless: is the machine false? And no one has ever needed philosophy to speak truth.

and while it's true that we all look at things from a particular frame of reference — Sam26

This isn't it. Its not: 'we look at things from a particular frame of reference'; its: 'the frame brings out the very things we can see to begin with'. I should mention, one of the reasons I called Psuedonym's post a piece of sophistry - which it remains, and yours tends in the same direction - is that the very terms 'subjective' and 'objective' and mostly meaningless: 'framing' - and the vocabulary isn't great because it leads to misunderstandings of the kind in your post - is not merely a 'subjective' act, if by 'subjective' is meant something like 'arbitrary'. A particular framing is always motivated in part by whatever it is that is being framed - it is never arbitrary, nor a matter of whim and fancy. I tried to explore some of this in my more recent 'math' post where I tried to thematize the question of motivation more thoroughly. But yeah, this kind of objection almost entirely misses the mark. This is symptomatic of it:

It seems that Bryant, or at least the way you've portrayed him, is saying there is no such thing as truth, or that truth doesn't matter, or that the word truth somehow doesn't apply when observed from the view of framing; which seems to be nothing more than one's own subjective view.

But - Bryant: "Every philosophy is able to produce truths. No philosophy has ever suffered from an inability to produce truths. Rather, on the one hand, philosophy should be approached like a machine. The question posed to a philosophy should not be “is it true?”, but rather “what does it allow me to do?”, “can it do any work?”, etc. Just as we don’t ask whether or not a lawn mower is true or false, but rather “what does it do?”, we shouldn’t ask “is the philosophy true or false?”, but rather: what does this frame allow us to do? how does it allow us to remake ourselves? how does it allow us to remake the world in which we find ourselves? how does it allow us to relate to each other differently, etc?". To speak of 'subjective' and 'objective' here is not even wrong; just a misuse of grammar - language idling...

For one thing, this metaphor of a frame he uses, when you cash it out and ask a philosopher what frame they are working with, the answer is presumably a set of propositions — jkg20

Never propositions. Propositions are the worst possible way to understand how philosophy operates. If propositions are understood as something like 'bearers of reference which are truth apt', then this is precisely what is in question here.

Fuk that was awesome.

I think I agree with Pseudonym about Bryant's philosophy. All this seems to say is that one is looking at philosophy from one's own frame of reference, and while it's true that we all look at things from a particular frame of reference, what's correct or incorrect doesn't depend on any one frame of reference. For example, how we talk about reality is dependent on language, and there are rules of use that have nothing to do with your own frame of reference, but are dependent on how we use language as a society and a culture, so one can't talk or philosophize about things simply from one's own perspective apart from correct and incorrect uses of particular words. It seems that Bryant, or at least the way you've portrayed him, is saying there is no such thing as truth, or that truth doesn't matter, or that the word truth somehow doesn't apply when observed from the view of framing; which seems to be nothing more than one's own subjective view. — Sam26

@Csalisbury: look - it's the Kuhn reception.

Heh, completely different take it is. I'm invoking him in support of my position, not against it! Well, perhaps not completely different. I think Witty drew the wrong conclusion from his own argument, which ought to point to what it means to formulate good, well articulated philosophical questions - not reject philosophy altogether. He didn't recognize that philosophy - any worthy of the name - already operates according to the strictures he rightly understood language to abide by. Which is what happens when one has as poor a grasp on the history of philosophy as Witty, unfortunately.

Wittgenstein, king of sass:

"How do I recognize that this colour is red? One answer would be: 'I have learnt English.'"

You can almost hear the "you imbicile" tacked on to the end of that.

I actually meant to ask what you thought an incomplete problemscape would look like in philosophy. The point being that I'm not sure how such a process would apply in philosophy even though I'm sure it does in maths. — Pseudonym

If I may, the entirety of Wittgenstein's Philosophical Investigations can be read as nothing but a critique of incomplete problemscapes; its alternative title might have well been: A Critique of Pure Problems. Every single word in that book can be considered a critique of badly-posed questions, and as a hand-guide as to how to pose questions well.

§380: "How do I recognize that this is red? a “I see that it is this; and then I know that that is what this is called.” This? a What?! What kind of answer to this question makes sense? (You keep on steering towards an inner ostensive explanation.) I could not apply any rules to a private transition from what is seen to words. Here the rules really would hang in the air; for the institution of their application is lacking".

And then there are the Lectures on the Foundations of Mathematics: "The mathematical proposition says: The road goes there. Why we should build a certain road isn't because the mathematics says that the road goes there - because the road isn't built until mathematics says it goes there. What determines it is partly practical considerations and partly analogies in the present system of mathematics."

This may go back to something you said in the OP about the fundamental metaphysics/epistemology of math- is it invented or discovered? I haven't thought about it much, but whether numbers themselves are invented or discovered, the logic/processes/patterns involving them seem to have a "discovered" aspect to them. — schopenhauer1

But if you follow the example, it's clear that invention and discovery are not so clearly separated; the paper referenced in the OP speaks of (mathematical) creativity as "fall[ing] somewhere between 'invention' and 'discovery'", but I think it's possible to be more precise: we invent because we discover, and we discover because we invent; there's a reciprocal dialectic here; again, follow the example: we 'discover' the irrational, but we're not sure, at first what to 'do' with it. All we know is that it's causing us 'problems': it is a problem (for our understanding of things). And by 'doing' - let me be crystal clear - I'm talking about what kind of sense we want to impart to it (the irrational), how we want to classify, categorise, and think about it: It is a number, or not?

We make a choice. And in so doing, we invent, we create a new, modified concept of number, a concept that might have been otherwise (B&C: "We – users of mathematics, members in a wide sense of the mathematical community – take certain aspects of mathematics to be thus-and-so rather than otherwise"). And now the tricky bit to understand: this inventiveness exerts retroactive effects on the very status of 'discovery': we can only say we have discovered an irrational number to the degree that we have invented a new concept of number that allows the class of irrational numbers to be designated as numbers to begin with (cf. Sauvagnargues: "a contingent irruption (chance) unleashes its own logic, its virtual problem, from which the supposed linearity of prior history is retrospectively configured").

Discovery and invention are co-implicated with each other, each conditioning the other according to a temporal circuit in which discovery prompts invention which in turn conditions the very status of discovery. So the question is not 'is math invented or discovered?', but 'what is the status of invention and discovery when it comes to mathematical concept determiniation?' (or any concept determination whatsoever, I want to argue). What this account is so far missing - what it is necessarily missing - are the pragmatic conditions which 'sway' the choices 'we' (the community of math users) make in one way or another. And these cannot be 'given'; there is no theorem that dictates - within the math - how math ought to be used. So the question which then needs to be addressed is what accounts for the/your intuition - and so far it is only an intution made without proper argument - that "if the game was run again things would work out roughly the same".

First, I think this intuition is probably correct, but perhaps for different reasons to you. 'My' reason would be that the concerns of humans - the things that matter to us, the the things we find significant in life - are probably rather uniform, and would themselves be roughly the same if you 'ran the game again': I can do things if I can figure out the hypotenuse of a right triangle and make it amenable to calculation - perhaps build a house a bit better, construct a rocketship with that much more precision. What would be 'invariant across histories' is not some deep, transcendental structure written in the stars as if by divine diktat - no matter what theologians and pretend-naturalists/fake pragmatists like Apo tell you - but the concerns of living beings with fine-span metabolisms and the need to keep warm: concerns which condition necessity.

Which would work if and only if causality is restricted to operating on the microphysical realm, which is contentious to say the least. It also displaces causality from being an intra-worldly phenomenon to an inter-worldly one, which is a displacement of the question. We generally ask the question to know about changes or entities in this world, and not others.

If you take the sufficiency rider seriously, then any answer in terms of causality needs to answer the further question: but why 'this' cause and not another? (+ further question re: individuation of causes; what makes a cause a cause and not another...).

, Hume and Kant, for example, made it their mission to articulate and argue for a world-view structured around the claim that the PSR is simply false. — Michael Della Rocca

Hmm, my impression is that transcendental philosophy - Kant and his successors - has a more complex relation with the PSR than is generally acknowledged. After all, the transcendental was invoked precisely to secure the necessity of thought with respect to the world; that is, the transcendental was invoked in order to stave off the spectre of arbitrariness with respect to thought, so that truth would find itself on a more secure footing than Hume could give it. And for the post-Kantians - Hegel and Maimon in particular - the problem with Kant was that the very categories of thought were themselves considered to be too arbitrary, and in need of further grounding - hence the various 'philosophies of the Absolute' that followed in Kant's wake (Schelling, Fitche, Hegel).

All of which is to say that there is a more subterranean hewing to the PSR - rejigged and reworked - than I think is commonly acknowledged.

If you say so.

If you don't like the game, don't play.

But I am trying to say that the creativity is still dictated by the limited scope and content of math itself contra philosophy where the game is much wider. — schopenhauer1

Sure, and I acknowledged this: but the relevant question is what accounts for this difference in scope. The obvious answer seems to be that math is constrained by its subject matter: it deals, roughly - very roughly - with with numbers and their operators. Philosophy is obviously subject to no such restriction; or at least, it is subject to restrictions of a different kind. But regardless of their respective fields of inspiration - one narrow, one broad - the point is simply that the dialectics of necessity and contingency function in the same way. Again, I think you're massively underplaying the way in which, once a philosophical problematic is set out - a concept developed, a problem articulated - the moves are just as constrained as they are in math.

As befitting an intellectual Curious George.

Where you see math as not being dictated by the internal mathematics itself, I do see this, through the constraints of what math is trying to investigate. — schopenhauer1

So this means you think math dictates the uses to which math is put? Is there a theorem for that?

Mm, a shock indeed that anyone could be so philosophically backward in their interpretation of the results.

A word on proofs: proofs (and with them, truth) are trivial, they're bureaucratic grunt work, the labour of pencil-pushing; proofs are only ever the product of getting the concepts right in the first place, of drawing up the right kinds of distinctions and correctly distributing the right categorizations of sense. Consider the recent proof of the Gaussian Correlation Inequality, as detailed in Quanta. It discusses a problem more than half a century old, recently solved.

The relevant question is: what did the 'solving' involve? A: It involved forumlating the problem correctly, posing it correctly: "Royen hadn’t given the Gaussian correlation inequality much thought before the “raw idea” for how to prove it came to him over the bathroom sink. ... In July 2014, still at work on his formulas as a 67-year-old retiree, Royen found that the GCI could be extended into a statement about statistical distributions he had long specialized in. On the morning of the 17th, he saw how to calculate a key derivative for this extended GCI that unlocked the proof. “The evening of this day, my first draft of the proof was written,” he said.

...Over the decades other experts had been attacking the GCI with increasingly sophisticated mathematical methods, certain that bold new ideas in convex geometry, probability theory or analysis would be needed to prove it. Some mathematicians, after years of toiling in vain, had come to suspect the inequality was actually false. In the end, though, Royen’s proof was short and simple, filling just a few pages and using only classic techniques. Richards was shocked that he and everyone else had missed it." Note here that the creative element, the innovatory aspect occurs before a single line of the proof is formulated, a proof which took him a day or so to write.

People have this incredibly naive idea that 'problems' (not just in philosophy, but also and especially in math) are always well-defined and it's all just a matter of going through the motions to find the right answer. But the 'answer' is almost always a case of getting the problem itself right, of understanding the very nature of the problem at hand; proofs 'fall out' of this prior conceptual work, which is where the real effort of grappling with the problem lies; proofs are the crust of bubbles on a wave, they are everything that is unimportant and trivial about solving a problem because the 'solution' to a true problem is always in the very way the problem is articulated. As a philosopher I was reading recently put it, "[Truth is] the outcome of an infinite process of sense-production. Truth is the limit object of a production of sense."

--

Fdrake was also tellinng me about the proof for the 'Classification of Finite Simple Groups', which apparently is 17 volumes long, and which is one of the most important theorems in all of statistics. I'll simply quote what he wrote to me about it: "During its finalisation tonnes of slips in logic and rigour were found, only one or two blokes who served as the coordinators for the research program of finishing the book knew how to direct things globally, to this day (afaik) no one has a comprehensive understanding of the proof in every detail. It would take a lifetime, then you'd die. The best part of the story is that no (exaggerating here) pure mathematicians doubted the whole theorem because they already knew the idea was the right one and the logic was almost an irrelevant detail. These kinds of details gets derisively called 'casework' a lot of the time."

'Next-step analysis', the kind I'm not ready to do, even though still general: "Nevertheless, from the moment when capitalism crystallised, when it occurred, it unleashed a necessary and constraining process. This is why history must be theorised as a mixture of the aleatory and the necessary, proceeding by contingent leaps, determining a problem that retroactively produces a prior history without emerging from it. ... What is at stake is a transductive crystallisation in the strict sense that Simondon uses it, even though he did not think of applying this concept to the history of capitalism: a contingent irruption (chance) unleashes its own logic, its virtual problem, from which the supposed linearity of prior history is retrospectively configured. This is why ‘there is no good reason but contingent reason; there is no universal history except of contingency...

...This is why, in the third chapter of Anti-Oedipus, Deleuze and Guattari write that there is no universal history except that of capitalism. This does not mean that capitalism is inscribed in an all-encompassing, universal history, but, on the contrary, that it creates the conditions of possibility of such a history: there is no universal history without capitalism. There is no universal history of civilisations except that of capitalism, just as there is no universal history of Reason except that of philosophy. It is not that the two determinations are teleologically programmed in advance, but rather that from the moment when they occurred (as a contingency), their emergence retrospectively unifies all prior attempts, through the construction of the universal. From the moment when capitalism emerged, it unified prior histories because it configured itself as universal, acting pragmatically as an instance of domination. But this universal is contingent (it is not necessary that it crystallises at a particular moment)." (Anne Sauvagnargues, Artmachines)

The history of math proceeds in this way too...

Maybe, maybe not, but that's just displacing the conversation again; you're talking about something else. That's what I keep tying to tell you.

No, as to what counts as more useful. That one needs a lever to move a weight does not make the lever 'true'. That's just bad grammar.

No, 'accuracy' is not at issue, never was, never will be, not even in principle.

The fact in math how some concepts can overtake (as more accurate) than previous versions, and this can be agreed upon by the math community. — schopenhauer1

No, wrong. Explained already.

I don't know how else to explain that I'm concerned with concepts and not proofs. This is the third time now, and you keep talking about something else.

t’s a step past Derrida (as stereotyped) because it’s concerned with creative construction, rather than deconstructive handwringing in the face of the void left by metaphysics. — csalisbury

Yes. I mean I haven't mentioned him at all here but yes, 'how to step beyond Derrida' is massively written across all of this. Because yeah, it's actually a question that really messes me up, like, how do you move beyond the formalist promise of the à venir, of the 'mere' always-already opening to the future? (especially because I think it's entirely correct?). And I'm finding in this language of 'choice' precisely that way to think beyond Derrida's 'undecidables', those moments that both belong and do not belong to a system (like Godel statements...); But I'm also trying to think that move beyond in a very specific way, a way that isn't just a fall-back into a Russellian 'theory of types' where you simply avoid self-reference (even as you self-refer to do it), but in a way that affirms the productivity or the generativity of paradox, where this moment of two co-existing incommensurables force a leap of creativity to diffuse the tension.

Is this academic? I mean, yeah a little, especially since I keep circling back to 'philosophy' as my object of analysis, rather than anything else in particular. And I admit that that's out of a sense of comfort and ease, soothed also by the fact that the individuation of philosophical concepts is no different to the individuation of anything else in the world. So the 'next step' is to try and think about all these ideas in terms of 'worldly things', bodies, ecologies, economies, political organization, etc, etc. But that shit's really hard to do, and I'm still (obviously) wrangling with the basics. I mean, at least give me credit for bringing the math into it, I thought that was pretty novel, even for me. But yeah, okay, paganism, you're not entirely wrong, but then, I'm still working through shit man, and I'm allowed to do it because you're not my thesis advisor and I'm taking the leisurely route and attack a small area from different angles even if you think it's all a bit samey.

The point is that the reason why philosophy is a wider field is to do with significant, categorical (non-scalar) differences in its approach to concept determination. Specifically, it's criteria for both the selection of commitments it is interesting to follow and its criteria for testing the degree to which they have been followed. The difference being that maths has reasonably strict criteria for both, where philosophy has virtually none.

Give any work of maths to an educated layman. What are the chances they'll correctly identify it as maths? Give a potential work of philosophy to a group of philosophy professors and even they won't agree on whether it is one or not. — Pseudonym

This is a comforting opinion to hold I guess, but as it stands there's nothing here but assertion and some cute imaginative scenario posing.

*waves hands in the other direction*

But nowhere did I say that 'math and philosophy are the same'; I simply said they share the same approach to concept-determination. That philosophy is a field of wider breadth is, well, duh.

it's that commitments of almost any sort can be made (and followed) and still constitute 'philosophy'. This is not the case with maths, — Pseudonym

But of course it's the case with math. The history of math is nothing other than the history of commitments made one way - and not another. And even this too is unfair, because plenty of mathematicians do explore those paths less travelled as well. The only thing to add to all this is the pragmatics: what motivates the commitments. But this is not something that can be given a priori, nor argued to be the unfolding of some divine plan a la our resident theologian Apo.

But my sentiment I'm trying to convey here is that the models and demonstrations you speak of have a lot of constraints as to what kind of methodology can be employed to solve a particular mathematical problem. Philosophy does not have these constraints — schopenhauer1

See, this too I think is just wrong. That is, any close attention to philosophy shows it to be an incredibly constrained practice. I quoted Deleuze in a previous thread as saying that philosophy is nothing but the pursuit of the implications of a problem posed; a 'great philosopher' being one who is equal to the task of that pursuit, doggedly following it wherever it goes. I mean, everything in Plato unfolds according to a certain committent to Reality of Ideas (εἶδος) and their status as surpa-sensible; everything in Leibniz unfolds according to a commitment to a conception of the principle of sufficient reason; everything in Bergson follows from a commitment to the primacy of duration, etc.

I'm simplifying a little of course, but these commitments - exactly alike the commitments made in the determination of mathematical concepts - force upon a philosophy the kinds of contours it takes; To 'learn Hume' or to 'learn Plato' is not to learn simply what they said, but also why they said it, as well as the ways in which the distinctions they draw commit them - 'constrain them' - to saying certain things and not others. This is why there are - or rather can be - 'schools' of philosophy - as you said, 'Wittgensteinians', 'Platonists', etc; this would not be possible if not for that fact that philosophy sets it's boundaries - its distinctions, its categorizations - out in incredibly precise ways. As I said, to be a Wittgenstienian (for example) is not to 'say what Wittgenstein did'; it's to accept a manner in which problems are posed, problems which may be other than those even conceived of by Wittgenstein himself.

Might be worth mentioning here that while I despise say, Plato and almost everything he said, I accept that his project was a rigorous, well-drawn one for all that; one doesn't have to like a philosophy to recognize and respect its consistency and power. In fact I find him all the more dangerous for it.

To a tin ear, I'm sure all sorts of sounds can be heard. So much the worse for that ear.

The issue here is SX calling particle physics use of symmetry breaking "arbitrary". — apokrisis

Your illiteracy has reached new heights I wasn't sure possible.

That was part of it's attraction for me; it describes wheels spinning without ever engaging, an aspect of much of philosophy. — Banno

Fair enough. I suppose it's that very distinction, between the engagement and not, that interests me. Some here seem to think that philosophy per se is wheels in the void; I want to defend its friction - while avoiding at the same time a certain positivism, ugly and moribund.

Lol, 'who are you to disagree with my contentious reading of mathematical physics'. Asks me to get over myself. Love it.

This is what I get for playing grumpy leftie on my phone.

This appears to be the same point I have made at various times with that silly philosophical game in which players make up the rules of the game as they go along. — Banno

Heh, kind of. But that game was too arbitrary: it wasn't made for a purpose. The distinctions articulated within it were not posed to solve anything in particular. It's closer to say, what Apo generally attempts to do than what I'm trying to do here.

It is precisely the kind of contingency that I am generalising away as the differences that don't make a difference when the intent is to reveal the basic structural mechanism at the heart of existence. — apokrisis

But this here is the very move that is unmotivated: it responds to no imperative other than your 'will-to-system', which, as Nietzsche rightly observed, simply lacks integrity. It is an intra-systemic imposition that responds to no genuine, worldly problematic; it's less the revelation of a 'basic structural mechanism at the heart of existence' than a transcendent, theological principle posited from above. It breaks with the demand for immanence, and, like I said, confuses description for prescription.