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?

Insults and yet no argument. Curious that.

As befitting an intellectual Curious George.

... and your insults are so lame as well.

Quit complaining and put up a counter argument if you have something to say.

I really don't understand what your project is here. It just comes across as someone labelling all the parts of a car down to the last bolt but refusing to actually drive it anywhere.

If you're interested in problems within a post-structuralist framework there are a large number of really interesting ones to tackle (so I'm told), but what you seem to be doing here (and others too, I'm not singling you out specifically), is expecting answers from within a broadly post-structuralist framework to apply to the structures which themselves contain that framework. There's a reason why academic philosophers work, and publish, almost exclusively on problems set by their chosen field (ethics being a typical exception). The analysis simply doesn't make sense outside of that field until it is 'translated' into whatever language the reader/critic speaks.

All that's happening in this whole thread, and dozens of others like it on this forum, is that ideas are presented within one framework which are, by and large, fairly routine (not uninteresting, just sequential) and they will be met by others from within that framework by an overabundance of cross-referencing proofs, or by others outside of that framework trying to do the 'translation'. That's what @schopenhauer1 is trying to do here (and @csalisbury, to an extent), but instead of helping with that translation, you're just responding like the clichéd English tourist refusing to speak the native language. You're saying the same thing louder and slower in the hope they get it, in your language.

I can really only see three reasons why anyone would want to post ideas on a general philosophy forum. Either they carry such inductive weight that they are virtually impossible to deny and so are useful out of the box (... is that a flying pig?), or they're promising but unfinished and could benefit from critique within the framework of the problem they address (in which case, if you don't clearly specify that you're going to get nowhere), or they're ready for others to 'try on' to see how they work, like taking the car for a test drive.

With obviously varying degrees of skill, that's all people here are trying to do, test-drive the ideas presented, within their framework, the fact that their feedback isn't then going to be in terms of the problem the post set out to solve is not a flaw, its inevitable. If an idea is going to be of any use to anyone (surely the only reason for posting it) then it's going to solve a problem they have, which is going to take quite a bit of collaborative translation.

can really only see three reasons why anyone would want to post ideas on a general philosophy forum. Either they carry such inductive weight that they are virtually impossible to deny and so are useful out of the box (... is that a flying pig?), or they're promising but unfinished and could benefit from critique within the framework of the problem they address (in which case, if you don't clearly specify that you're going to get nowhere), or they're ready for others to 'try on' to see how they work, like taking the car for a test drive.

With obviously varying degrees of skill, that's all people here are trying to do, test-drive the ideas presented, within their framework, the fact that their feedback isn't then going to be in terms of the problem the post set out to solve is not a flaw, its inevitable. If an idea is going to be of any use to anyone (surely the only reason for posting it) then it's going to solve a problem they have, which is going to take quite a bit of collaborative translation. — Pseudonym

Hey great post.. One of the best arguments on this forum for the principle of charity and collaboration in general. That should be in a guideline or something :up: .

I'd actually like to thank you for taking the time to construct this post.

Note here that the creative element, the innovatory aspect occurs before a single line of the proof is formulated. — StreetlightX

I get it- the creativity before any formal proof is written. 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. The constraints are as limited as you want to make it in philosophy.. The constraints are very tangible in math and dictate certain outcomes and legitimate moves which are even possible within its confined scope. This constraint in creativity, in a way, creates a confined area that I am claiming is more deterministic (the outcome shall reveal itself). The creativity is not nearly as boundless as other subjects, thus the creativity is more dictated by the game at hand. The proof after this constrained creativity, is just more constraint- this time on what a legitimate explanation (in the community) can be- another difference but at a more concrete level.

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.

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

Thanks, glad it made sense to someone at least.

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

But this is the game, do you not recognise it?

If you say so.

What then of the points that make the circle. Are they not the smallest possible straight edges? — apokrisis

Neither can a point have an edge, nor can a circle be made up of straight lines. So this idea is contradictory in two ways.

A point is the limit to a line - the zero-D terminus that has greater local symmetry than the 1D line which is having its own symmetry broken by being cut ever shorter, and eventually, infinitely short. A point is simply a line that can't be cut any shorter. — apokrisis

A point marks the limit to a line segment. It is contradictory to say that a point is a line segment which can't be cut any shorter, because a point and a line segment are fundamentally different. The two are incompatible. A point has zero dimensions, while a line signifies a dimension. A point has absolutely no spatial extension. It's relation to space is limited in a most complete way such that it cannot have any shape or spatial form. A line, despite the fact that it continues infinitely, has a very specific, and limited spatial extension, limited to what we call a dimension.

Then for a line to be either straight or curved is itself a question embedded in the 2D of a plane at a minimum. So curvature, or its lack, is determined by the symmetry breaking of a more global (2D) context. A line becomes "straight" as now the locally symmetric terminus of all possible linear wigglings. — apokrisis

I agree that a plane is two dimensional. But a line, by definition cannot be two dimensional. Therefore, "curved line" is itself a contradiction. To express two dimensions with lines requires two distinct lines. The relationship between the lines is expressed as an angle. You cannot have a curved line. That's why pi is irrational, it tries to establish a curved line, but a curved line itself is contradictory, irrational.

My argument is that it is not the curved line itself which produces the irrationality, it is the relationship between two dimensions which is what is truly incommensurate, just like the relationship between zero dimensions and one dimension, described above, is incommensurate. That is why the square root of two is irrational as well. What this indicates is that our spatial concepts, in terms of dimensions, are incorrect. The concept of dimensions of space produce an unintelligibility and therefore must be incorrect.

Straightness is defined in terms of the least action principle. A straight line is the shortest distance to connect two points. You may be familiar with that story from physics. — apokrisis

I think that the application of the theory of general relativity has proven this to be false, the shortest distance to connect two points is not actually a straight line. This is further evidence, that our dimensional modeling of space employing lines and angles, vectors, is incorrect.

They are minimal length lines. But are they straight or are they curved? Or would you say the issue is logically vague - the PNC does not apply? No wiggling means no case to answer on that score. — apokrisis

I answer this question by saying that the entire conceptual structure which models space in terms of distinct dimensions is inadequate and therefore incorrect. This conceptual structure leaves us with an unintelligible, irrational relationship between dimensions. The relationship is modeled with angles, but the concept of "angle" doesn't allow for the true nature of curvature. The "angle" is something totally arbitrary, inserted into spatial conceptions as an attempt to alleviate the described problem of an incompatibility between linear dimensions. When something fails you insert a stopgap to deal with the problem. That is the "angle", but the stopgap is supposed to be temporary. The only real thing that the "angle" represents is the limitations of linear geometry. Pythagoras was perplexed, that there was irrationality inherent within "the right angle", as right and useful as it had proven to be. In reality, as useful as it may have proven to be, no angle is the right angle because "the angle" represents nothing, it is a falsity.

I'm interested in how you're thinking of 'accuracy' of an idea. If you apply it to the steps of proving a theorem, that's usually pretty banal; people who can read the language the proof's written in will usually be able to see if it's right or not, if the general idea is right etc. There's a derived sense in which a theorem can be accurate; if its proof is. But I don't see that this sense of accuracy applies to mathematical objects or ways of thinking about mathematics in the same way.

There are probably, to borrow from Austin, felicities and infelicities in how theorems are proved and how people think about/imagine mathematical objects. I tried to highlight this with the Dedekind Cuts vs Cauchy sequences thing. Street's article highlights it in a more accurate way; a particularly felicitous way of thinking about the problem lead readily to its solution.

An apocryphal quote (might be real, couldn't find a reference when searching though) attributed to Grothendeick is that 'don't try to prove something until it is obvious'. Similar one by Riemann 'if you give me the theorem I'll give you the proof'. Mathematicians seem to think about creativity in mathematics this way; a certain 'accuracy of ideas' which doesn't immediately reduce to the accuracy of a proof.

Grothendeick really, really thought of stuff this way:

I can illustrate the ... approach (to mathematics) with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.

First, I'd ask what an un-set-up problemscape looks like. In order that some job of work needs to be done to set one up, I think it's reasonable that you should be able describe an unfinished one. Second, you say "allow" the problemscape to be navigated. I'll skip over "navigated" for now lest you literally start tearing your hair out, but "allow" intrigues me. Again, by the same method, what would an approach which did not "allow" navigation look like, how would we know we were engaged in such a method? — Pseudonym

You said you're unfamiliar with math. An un set up problemscape for you might be solving this integral:

$\int\limits_{-\infty}^{\infty} e^{\frac{x^2}{2}} dx$

and I can give you a couple of hints to its usual solution:

• you can't solve the integral through standard methods (no plug and play algorithms)
• you need to see the integral as equal to a 2 dimensional integral
• you need to learn something about the transformation of Cartesian to Polar coordinates

I think if I gave that integral and the hints to some math undergrads with university level calculus experience on a homework assignment, a good chunk of them would be able to solve it. In less than an hour. With no Wolfram Alpha. An un-setup problemspace, to you, might be me just giving you that integral to compute with no hints. It has a certain impenetrability, you need to spend some time on the contours of the problem before finding a way in. When you're about the solve the problem, if you're anything like me, you'll be like 'oh god... I can do this*? This will actually work? Holy shit that's cool'. By * I mean 'I can use some details of bullet points 2 and 3 to solve it? Wow.'.

Of course, you could google that integral if you know how to use Google to search equations (standard internet equation notation), then you'd find the standard solution to it. You'll discover that the problemscape for that problem is very well studied, and there are lots of avenues of study leading to and from it.

I imagine whenever you post something on here, you have an opinion on the topic. If the topic's something you've studied before and you're regurgitating pre-articulated thoughts it doesn't require much thinking except in how to communicate what you've already thought. You know your way around the problemscape; the imaginative background you have for the problem; and all that remains is to beam it into your readers' minds with sufficiently good writing.

I don't think you're doing that here, you seem to be in a similar discursive position to me, you've got some intuition on the structure of philosophical problems in general, you see what I'm saying as a flawed instance of that structure (at least on the forum), and you're struggling to find the words to articulate in response to what I'm saying to communicate a disagreement or difference in emphasis. [You've got to wrap up what you think into a neat package; which perhaps can be identified with thinking about the problems in the thread and in your head; then translate the package into a common language.] The stuff in the [] seems to occur all at once.

If you relax the assumption that we're 'beaming things into eachothers' heads' with language use, and instead inhabiting a vast terrain of communal ideas, we get a more interesting location for the problemscape. To be sure, it's something we're doing, but it's also just as much something that's already been touched on by countless others in different contexts. Sure, what we're doing isn't going to be inscribed in the canon of philosophical discourse since we're on a forum, but that doesn't matter that much. It's like we're both on a knitting forum and sharing patterns.

So, I resist your claim what we're doing is mostly driven by psychological peculiarities - we're navigating some abstract space of problems that we share but have our own different copies of. I see the claim that we're driven by psychological peculiarities as misguided: it's like saying the knitter is driven by psychological peculiarities; sure, they are in a sense, but they're also following a pattern or making one up.

I'd like it if one of our few academic philosophers could chime in on their experiences of dealing with philosophical problems. @Pierre-Normand, do you have any input on what it feels like and how you address philosophical problems as an actual academic philosopher?

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. — StreetlightX

Ok, so we are essentially accusing each other of the opposite thing- you think I am making philosophy too broad and overlooking its constraints, and I think you are making math too broad and under-emphasizing its constraints (and the outcomes there of).

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. The limited rules dictates next moves more than it is simply synthesized by the "limitless" inspiration of the mathematician. In other words, if this game was run again, roughly the same models and demonstrations would be constructed. It would not be perfectly the same, line by line (there is some contingent variation in symbolic communication), but on the whole, the concepts behind these mathematical proofs would shake out. Perhaps in a particular framework, philosophy can work similarly, but other camps would negate this process. So initial creativity is there for both, but beyond that, the way it works out (the discovered-like process of math/ consensus vs. the more synthetic-like aspect of philosophical moves). But now we are getting into the epistemic differences between the two.

Edit: Granted, there are some conventions (like certain statistical constants, etc.) but this is recognized as such in the name of pragmatic reasoning.. which this field is especially amenable to. I know apo mentioned using 360 degrees being contingent, but again, the "discovered" aspect I refer to are the concepts behind them.

Neither can a point have an edge ... A point marks the limit to a line segment. — Metaphysician Undercover

So a point can be the edge to a line? Make up your mind.

It is contradictory to say that a point is a line segment which can't be cut any shorter, because a point and a line segment are fundamentally different. — Metaphysician Undercover

So if we cut away all the line to one side, it is bounded by a point on that edge. And if we then cut away all the rest of the line to the other side, what then? Is the point bounded by a point or is there just the point?

Isn't the fundamental difference that the point is the natural unit of which lines are composed? It has a locally emergent symmetry which marks the place where no more can be cut away. A point is all featureless edge?

A point has zero dimensions, while a line signifies a dimension. — Metaphysician Undercover

But doesn't the point have a location? It exists as a limit on dimension. A line represents a space of points. A point represents that space without a line.

What this indicates is that our spatial concepts, in terms of dimensions, are incorrect. The concept of dimensions of space produce an unintelligibility and therefore must be incorrect. — Metaphysician Undercover

Seems radical. But sure, throw away the concept if you can tell us about something better to replace it.

Or maybe it is your logic that lets you down. My logic expects metaphysical truth to be rooted in the fruitfulness of dichotomies. Yours is instead deeply troubled by discovering dialectical "contradiction" at the heart of things.

I think that the application of the theory of general relativity has proven this to be false, the shortest distance to connect two points is not actually a straight line. — Metaphysician Undercover

You got it exactly backwards. I was saying GR indeed shows that "straightness" is relative. It cashes out as the shortest path, the least action principle, once your geometric intuitions include some proper notion of action or energy density along with the spacetime dimensionality.

That is one of the issues with classical geometry. It all rests on spatial intuitions. It doesn't have a natural way of including energy, thus actual time and change, in the picture. It is a story of the directions but not the actions.

So GR is geometry with energy density included. It is more physically realistic as maths. And now the least action principle comes to the fore when we are thinking about "straight lines". We have generalised Euclidean geometry so that there is just universal curvature. We have removed a major constraint - the one picked out by the parallel lines axiom. And now straightness becomes defined more clearly as the shortest possible (energetic) distance between two points.

GR changed the simple definition of what counts as straight. That was the bleeding point.

I answer this question by saying that the entire conceptual structure which models space in terms of distinct dimensions is inadequate and therefore incorrect. — Metaphysician Undercover

Seems coherent - in being dichotomistic - to me. Dimensions are defined by being orthogonal to each other. Mutually exclusive and jointly exhaustive. The x axis is oriented so that no part of it - apart from a point, an origin - intersects with the world of the y axis.

You can head for infinity in the x-axis without moving an infinitesimal amount in the y-axis. And that is your strong definition of a spatial dimension. You have two disconnected or asymmetric directions that exist for motion~rest.

Remember how that distinction played out in Newtonian mechanics. Spacetime became defined by its energy conserving transformations. Masses could spin inertially on the spot or move inertially in a straight line. These were local symmetries that couldn't be broken down as they were the terminus to the very possibility of a more global symmetry breaking.

Then along comes GR, and even QM, to add the missing ingredients of time and energy back into this mathematical picture. The classical view was certainly correct, but still carried extra constraints that proved themselves to be local and particular rather than cosmically general.

The "angle" is something totally arbitrary, inserted into spatial conceptions as an attempt to alleviate the described problem of an incompatibility between linear dimensions. — Metaphysician Undercover

It is not arbitrary. What got inserted was the very notion of a dichotomy or asymmetry. Dimensions are distinct due to their orthogonality.

Ask yourself why pi = 180 degrees. Hint: a circular rotation that flips you back to a flat line having transversed its orthogonal "other".

These things aren't arbitrary at all. They are logically founded. They are Platonic strength.

That is why SX is so off the mark in his OP. Maths is "unreasonably effective" because - where it is based on the metaphysics of symmetry and symmetry-breaking - it is finding ways to model the necessary structure of existence. For anything to be, it would have to have being in this self-justifying form.

I know apo mentioned using 360 degrees being contingent, but again, the "discovered" aspect I refer to are the concepts behind them. — schopenhauer1

That was MU in fact. I agree with you that the fundamental structures of mathematical thought are the inevitable rules of form or constraint that are there (so "somewhere" a bit Platonic) to be discovered.

So where does the arbitrary or the contingent come in? Two ways.

First - the Peircean point - the deep structures or constraining rules must be themselves emergent from a ground of arbitrariness. They are precisely the states of organisation that will emerge from chaotic possibility itself. Order must evolve to regulate instability. It might be a very minimal order, a very permissive order. Yet still it will be a generalised state of order.

Even statistics depends on bounded action. Randomness can have macro properties like a mean or a variance because there is some kind of global constraint bounding a system of independent variables. You get a temperature or a pressure only when your gas is confined in a flask. And any workable notion of randomness or probability depends on a duality of free local action coupled to definite boundary constraints. Otherwise there just wouldn't be any "statistics" - any macro properties to speak of.

So our very notion of the arbitrary or the contingent only makes metaphysical sense in the context of its "other" - the necessity, the regulation, to be found in some set of bounding constraints. You can't even have the one without the other. Hence there is the Platonic structure to be discovered as the necessary spine of existence. That can't not be the case ... if you do in fact believe in the matching "other" of the accidental or contingent. Each secures the reality of the other in complementary fashion. Hence why SX's orientation, as expressed in the OP, is so off-base from the start.

Then second, in discovering the deep and necessary structure of existence, we humans can gain our own local possibilities of control. We can insert ourselves as agents into the cosmic equation. If we construct mathematical models that encode the basic rules of the game - the game that is symmetry and symmetry breaking - then we can start to use them in our own "arbitrary and contingent" fashion.

We can do things that Nature doesn't seem to be thinking about or caring about. And folk of course find that a big philosophical deal. Suddenly our values and desires start to affect the metaphysical story. We are the source of meanings. We are the source of inventions. We are the source of fictions and fables and beliefs.

All this can lead to a PoMo-style rejection of metaphysical structure and meaning. Dichotomies and hierarchies become dirty words. Humans can transcend nature to become ... well, now it seems philosophy has solid grounds for its Romantic revolt against all "merely" physicalist constraints or necessities.

But this gets the metaphysics wrong. Constraints only constrain. So there is room enough in our cosmos for the very mild and attenuated constraints - the generalised thermodynamic tendencies - and then the much more complex and particular kinds of natural organisation that are reflected in evolved life and mind.

There is no basic conflict here, no real battle that the Romanticist must fight. We don't need to be like SX and fetishise the arbitrary and the plural, anathemise the Platonic and the unitary.

To get back to the 360 circle, I would note how the choice of 360 wasn't so accidental. It seemed important that we find a numbering system that made division into simple fractions easy, while also offering enough divisions to capture the differences that were of (Babylonian/astronomical) interest to us.

Again, some deeper symmetry was the reason for 360 being a choice that lasted. It was a number that offered the kind of symmetry breaking we found most convenient. Given an infinity of numbers we could have chosen, picking on 360 was not an arbitrary act from the point of view of a human having to do the calculations on a regular basis.

Mathematicians seem to think about creativity in mathematics this way; a certain 'accuracy of ideas' which doesn't immediately reduce to the accuracy of a proof. — fdrake

So inference to the best explanation - the principle of least action in practice. We jiggle the bits about until it all snaps into place with a holistic best fit.

That is, we start with a broken symmetry - some "problematic" that is a collection of disjointed parts. And then we probe for the symmetry, the global coherence, that must have originally connected them.

Proof follows because that is the formal (re)construction. It is the creation of the bottom-up deductive path that connects us securely to the top-down glimpse of the Platonic reality.

So first comes the abductive leap that allows us to see the fragments in an inductively retrospective light. We see the smashed glass across the floor, the cat innocently licking its fur on the bench. In a flash we see how the symmetry of the vase got broken.

Then proof is the mopping up operation. All the parts get gummed together to show that the vase did exist as we imagined. We have sound reason to blame the cat as we are certain the vase wasn't just stuck in a cupboard while we weren't looking and meanwhile some random collection of glass just materialised on our floor.

@StreetlightX@schopenhauer1

Somewhat related Samzdat on Kuhn

On second thought, quite related. One quote to signal he’s not talking Kuhn in the way Kuhn’s often talked

One of the weirder results of Kuhn’s philosophy was an emphasis scientific relativism. A whole generation of philosophers brandished his book as a way to point out a certain groundlessness to the sciences, mistaking “paradigm” for something totally arbitrary, mistakenly demanding a kind of truth that comes from a different language. At the extremes, this tends to mean a total rejection of scientific fact as being “merely contextual fact.” Which is, you know, true, but equally true of everything else. This is particularly jarring because Kuhn provides something that should give you the opposite conclusion. — samzdat

Even statistics depends on bounded action. Randomness can have macro properties like a mean or a variance because there is some kind of global constraint bounding a system of independent variables. You get a temperature or a pressure only when your gas is confined in a flask. And any workable notion of randomness or probability depends on a duality of free local action coupled to definite boundary constraints. Otherwise there just wouldn't be any "statistics" - any macro properties to speak of. — apokrisis

Ugh, is it in fact true, that I actually agree with apokrisis? Yes this sounds right in the context of this topic.

So our very notion of the arbitrary or the contingent only makes metaphysical sense in the context of its "other" - the necessity, the regulation, to be found in some set of bounding constraints. You can't even have the one without the other. Hence there is the Platonic structure to be discovered as the necessary spine of existence. That can't not be the case ... if you do in fact believe in the matching "other" of the accidental or contingent. Each secures the reality of the other in complementary fashion. Hence why SX's orientation, as expressed in the OP, is so off-base from the start. — apokrisis

I agree with you here up until you said "existence". Your idea about constraints and symmetry-breaking works great in the cases of math and physics. This idea is perfectly ammenable to these topics. This is where your talk of constraints and symmetry-breaking shine and hold the most weight. However, you seem to make the illegal move to apply it to any and every subject in a totalizing fashion.. Besides killing any other angles of inquiry (which would be taking advantage of the open-endedness of philosophy I was talking about) you are quick to dismiss all else to constrain your framework, thus limiting possibilities of other frameworks. But more important than this, you apply such methods/language-games to problems such as the Mind-Body problem. This is where your theory is in deep water and breaks down. Where math is all modeling, you try to overmine the modeling language-game (constraints/symmetry breaking, etc.) to experience itself, and then when people accuse you of never penetrating beyond the models- you defensively go back to the Romantic vs. Enlightenment rhetoric to hand-wave the rebuttal. Your argument becomes a circularity back unto the modeling.

Now, I agree with you very much about your ideas as they relate to math. I have no problem with that move. Its the totalizing of its application to all areas that this becomes questionable.

I agree with you here up until you said "existence". — schopenhauer1

But the context of that is my own earlier posts in this thread.

So in terms of metaphysics, the question becomes what is the most universal goal? And one obviously sensible answer is the limitation of instability. If any kind of world is going to exist - given the primal nature of chaotic action - then it has to develop the kind of regularity that gives self-perpetuating stability. — apokrisis

So I was specific that existence = persistence in the face of instability or chaos. I am talking about Peircean process metaphysics.

However, you seem to make the illegal move to apply it to any and every subject in a totalizing fashion. — schopenhauer1

Illegal? It could be warranted or unwarranted - the evidence can decide the case. But it is illegal to hypothesise?

Besides killing any other angles of inquiry (which would be taking advantage of the open-endedness of philosophy I was talking about) you are quick to dismiss all else to constrain your framework, thus limiting possibilities of other frameworks. — schopenhauer1

Hey, do you see me trying to rule out hypotheticals by resort to rhetoric like SX? I welcome your hypotheticals. I just introduce them to the facts of reality. Nature has already chosen what is true. :)

But more important than this, you apply such methods/language-games to problems such as the Mind-Body problem. This is where your theory is in deep water and breaks down. Where math is all modeling, you try to overmine the modeling language-game (constraints/symmetry breaking, etc.) to experience itself, and then when people accuse you of never penetrating beyond the models- you defensively go back to the Romantic vs. Enlightenment rhetoric to hand-wave the rebuttal. Your argument becomes a circularity back unto the modeling. — schopenhauer1

Blah, blah, blah.

You are back to front. Peircean metaphysics begins in phenomenology. And it is not surprising that I arrived at Peircean metaphysics via a dissatisfaction with the prevalent reductionism and epiphenomenalism in mind science (and philosophy of mind).

So Peirce (like Rosen and others) made the deep structural connection that can connect epistemology and ontology.

Mind is a modelling relation. Epistemic fact.

Our model of mind is then going to be a model of this as a suitably general ontic fact. Modelling - or semiosis - is how minds arise in a natural fashion.

Then completing this philosophical trajectory, even matter may be explainable as a pansemiotic fact. Matter exists as an (attentuated or effete) form of the same essential modelling relation ... in some intellectually useful sense.

And guess what. As I keep saying. Physics has gone that way. Everything that exists is the product of informational or holographic constraints on entropic degrees of freedom.

Keep up with science and it is pan-semiotic.

Now, I agree with you very much about your ideas as they relate to math. I have no problem with that move. Its the totalizing of its application to all areas that this becomes questionable. — schopenhauer1

Questions are fine. This is the bleeding edge of metaphysical speculation. You ought to be questioning.

I'm just reminding that I've already replied many times on the same questions. And the criticisms are not penetrating.

I would also note that the reason why Peirce (and all the others I would cite) are getting it right is because they are structuralists, they are thinking in terms of fundamental mathematical basics.

Vagueness, dichotomies, hierarchies - these are all mathematical-strength concepts. They capture the architecture (the architectonics!) of Nature because they begin from first logical principles. They are what symmetry/symmetry-breaking looks like when described in general mathematics.

Now - because they are logical/holistic arguments - they are not the kind of maths you do a lot of calculation with. They are the meta-models rather than domain specific models. But there are then plenty of those kinds of models too now - all the stuff arising out of condensed matter physics, non-linear dynamics, whatever.

So maths itself is doing a better job of describing the structure of nature as it actually is.

As I said, it started out with geometry - existence in space, with time and energy left out of the equation. That was what made the Platonism objectionable - what is real about the form of a triangle?

But replace the bloodless triangle with some real life dynamical flow - like a fractally branching river - and suddenly you really are starting to talk about Nature in a way that has fundamental unifying scope. Suddenly you can see why Nature has to express fractal order so as to be able to exist - or rather, persist as a now regulated and equilibrated source of instability.

So a point can be the edge to a line? Make up your mind. — apokrisis

I never said a point is the edge of a line. Your putting words in my mouth. An edge marks the boundary of a region, a point marks the boundary of a line segment. A region is two or three dimensional, a line is one dimensional. Why are you intent on producing ambiguity?

So if we cut away all the line to one side, it is bounded by a point on that edge. And if we then cut away all the rest of the line to the other side, what then? Is the point bounded by a point or is there just the point? — apokrisis

Take away the line and there is just the point. Remember, this is conceptual, we're not talking about a line drawn on a paper or any such thing, we are discussing concepts.

Isn't the fundamental difference that the point is the natural unit of which lines are composed? — apokrisis

No, that's absolutely false, a line is not composed of points. Who taught you geometry? A point is zero dimensional, and a line is one dimensional. An infinite number of zero dimensional points could not produce a one dimensional line. This is the incompatibility between the dimensions which I referred to.

But doesn't the point have a location? — apokrisis

No again, a point doesn't have a location. It is conceptual and concepts do not have spatial location. A point represents a location, it does not have a location. When I say that there is a point which is half way between where I am and where you are, I use "point" to represent this place. It does not mean that there is literally a point existing at this location. When someone says assume a point halfway between A and B on line AB, it does not mean that there is a point existing at this location, making up part of the assumed line. "Point" is used to represent this location.

It is not arbitrary. What got inserted was the very notion of a dichotomy or asymmetry. Dimensions are distinct due to their orthogonality. — apokrisis

Again, that's not true. Geez, what are they teaching in school these days, that kids like you get so mixed up?

Two lines may cross at any random angle, and represent two distinct dimensions. "Orthogonality" is the product of choosing "the right angle" as the distinction between two dimensions. The choice of the right angle (because it had already been proven to be very practical for producing parallel lines), means that any line at a different angle from the arbitrarily chosen two perpendicular lines, is necessarily a two dimensional line. Why not choose that two dimensional line as the representation of one dimension instead? Why are those other, arbitrarily chosen perpendicular lines the privileged signifiers of the two dimensions?

Theoretically, we could assume an infinite number of rays around a point, and assign to each ray a dimension, such that there would be an infinite number of dimensions. That classical "dimensions" are produced by right angles, and are therefore orthogonal is completely arbitrary.

Ask yourself why pi = 180 degrees. Hint: a circular rotation that flips you back to a flat line having transversed its orthogonal "other". — apokrisis

Utter nonsense apokrisis. Pi is the relation of the circumference of a circle to its diameter, as a measurement, length. That a straight line which marks the diameter is designated as 180 degrees, is irrelevant to the value of pi.

An edge marks the boundary of a region, a point marks the boundary of a line segment. A region is two or three dimensional, a line is one dimensional. Why are you intent on producing ambiguity? — Metaphysician Undercover

For pity's sake. Can't you see you are just saying what I said?

A line is a 1D edge to a 2D plane. A point is a 0D bound to a 1D line. So you are simply choosing to pretend to be confused by the fact that we use terms that speak to the specifics of some act of constraint.

Yes, a line is an edge to a plane. And a point is only an "edge" to a line. But if you can't see that in the context of my account that the similarity of the nature of the constraint, the form of the symmetry breaking, is exactly the same, then I've no idea how to talk about interesting ideas with you.

Again, that's not true. Geez, what are they teaching in school these days, that kids like you get so mixed up? — Metaphysician Undercover

You're taking the piss now? Or maybe you are 90+. Seems possible.

Two lines may cross at any random angle, and represent two distinct dimensions. — Metaphysician Undercover

And those two distinct dimensions would be distinct because ....?

[Clue: it rhymes with "morthogonal".]

Theoretically, we could assume an infinite number of rays around a point, and assign to each ray a dimension, such that there would be an infinite number of dimensions. That classical "dimensions" are produced by right angles, and are therefore orthogonal is completely arbitrary. — Metaphysician Undercover

I don't know what they taught you at high school Granddad but you are just imagining any number of rays in a spherical co-ordinate space - a description that is dual or dichotomous to the usual Cartesian one. https://en.wikipedia.org/wiki/Spherical_coordinate_system

If you did go to big school any time in the last century or two, you would have learnt that higher dimensional geometry doesn't work like that. You could indeed have an infinity of spatial dimensions, but they would all have to be orthogonal to each other as that is the critical thing making them a distinct dimension of the one connected space.

Why do 3D knots come undone in 4D? Trying working that one out.

Big D decisions are aligned with stuff already mattering a lot or stuff coming to matter a lot. First's a perturbation in stance on stuff in general; like a personality or value system, it's an island of sense demarcating what's nonsense. So it looks intrinsic, and is intrinsic to a frame for most intents and purposes. The first one is also usually accompanied by some combination of volition, permission and dedication; I choose to quit smoking as a frame (big D) every time I refuse a fag (little d). Another way of putting it is it's the conditions that naturally accompany the frame. Big D decisions in the context of little e events.

I like this, if I follow you (& I'm not 100% sure I do.) I especially appreciate the example, because I've been trying to quit smoking for a while now. This gives me some solid ground to work from.

[was gonna dig into your post by way of my own attempt to quit smoking] but actually now that I've read through that posts a few times

Clarifying question first:

the usual way people occupy frames constrains variation in their own frame changes by a delimitation of how the other frames are embedded perspectivally into each other. Most don't matter, some matter a lot, sometimes we're surprised by something that didn't matter becoming something (or already was something) that matters a lot. — fdrake

I was puzzling over the first sentence for a while. Just clicked now though, as of writing the last sentence. Is "frame changes" "frame-changes"?

If so, is the gist of the first sentence something like: each of the frames a person occupies tends to somehow refer to - or take into account - the other frames they occupy? So even a frame you're not currently 'in' is, in some way, supported by the one you are in?

I have in mind the image of a group of good friends. The experience ( frame) of hanging out will be different depending on which particular set of friends are present. But no matter what particular set, and no matter how much the experiences of the different sets vary - they still all kind of refer to each other, to the group of friends (frames) itself. You might experience radically different things and think about things in different ways hanging out with a certain person, or group of people, from within that group. But there's always (provided everyone's on good terms) a kind of unspoken awareness of how this experience can connect back to other experiences with the larger group, or different subsets from within that group. (though of course there's griping and shitting-on too.) This is why, when friends hang out, there's some fun in swapping stories about different escapades, which involve different groupings of friends.

So you have a quasi-encompassing frame knit from smaller frames (though that phrasing is off too.) I think you're saying something similar about a single personality, and the variations that personality goes through?


Does that make any sense? The friend thing was really really abstract, I could probably flesh it out with illustrations

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.

It's great how you've laid out what you see as a 'problemscape' in maths, that has been helpful, but (and I feel bad I didn’t think to specify this at first) 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.

Notwithstanding the above, I'll have a stab at explaining the problem-solving algorithm using the example you've given and highlight how it might be different if I was working on a philosophical problem within a prescribed framework, and different again if I was working on a philosophical problem somewhere like a public discussion.

My first step in both types of philosophical problem would be to understand why it's a problem in the first place, I'd first want to know why it needed solving at all, what place they have in the wider problem hierarchy? Already, I'm not sure whether this step is even necessary in your maths problem. Do we need to know why integrals even need solving to approach a solution? I could certainly solve y=x+4 (much more my level) without needing to know why we might need to know X in terms of y, but I wouldn't dream of approaching a philosophical problem without such background.

The second step would be to determine what would constitute a solution, what marks the solution I might come up with as being a good one. Again, with framework-prescribed philosophy, the solution would have constraints set by the framework, with public philosophy (I'm thinking mostly of ethics committees here, but I think it applies to this forum too) a 'solution' is a completely different thing, it's more about a perfect mixture of inter-translatable direction, and explanation mixed into one. With maths/science it very different again, the definition of a solution is all about repeatability, can others using your language do what you did and get the same result.

I mean, this is an oversimplification of course, but it might go some way to explaining why I'm not on board with this "maths is like philosophy" paradigm. I think it's like saying cars are like washing machines in that they're both designed to do a task. True, but vacuously true, it doesn't tell us anything about how to design better cars, or how to critique washing machines, for that we need to know what those objects are used for.

A line is a 1D edge to a 2D plane. A point is a 0D bound to a 1D line. So you are simply choosing to pretend to be confused by the fact that we use terms that speak to the specifics of some act of constraint. — apokrisis

Good, you recognize your mistake then, when you said that a point is an edge to a line. That's a start.

Yes, a line is an edge to a plane. And a point is only an "edge" to a line. — apokrisis

What? Why contradict yourself? That's the end of that start.

But if you can't see that in the context of my account that the similarity of the nature of the constraint, the form of the symmetry breaking, is exactly the same, then I've no idea how to talk about interesting ideas with you. — apokrisis

I think that's why your account is unintelligible to me. Things which are different, you claim are the same. You'll insist that it's a difference which doesn't make a difference, but that's nothing more than contradiction. And your whole account of symmetry breaking is based in contradiction.

And those two distinct dimensions would be distinct because ....? — apokrisis

The dimensions are distinct because they are designated as such. That designation is based in the assumption that there is an angle which distinguishes them one from another. The assumption of an angle is completely fictitious. So any distinction which separates one dimension from another by employing a specified angle is a fictitious distinction and is therefore completely arbitrary.

I don't know what they taught you at high school Granddad but you are just imagining any number of rays in a spherical co-ordinate space - a description that is dual or dichotomous to the usual Cartesian one. — apokrisis

Right, and the point being that there is an infinite number of possible ways to construct "dimensions" which lie between the orthogonal way that you imagine it, and the way that I just imagined it. My argument is that each of them will end up with the very same problem of incompatibility (irrational numbers) between one dimension and another, because each utilizes the same falsity, the angle. Until we get rid of this antiquated way of modeling spatial existence, with dimensions and angles, we have no hope of producing a proper understanding.

If you did go to big school any time in the last century or two, you would have learnt that higher dimensional geometry doesn't work like that. You could indeed have an infinity of spatial dimensions, but they would all have to be orthogonal to each other as that is the critical thing making them a distinct dimension of the one connected space. — apokrisis

That spatial dimensions must be orthogonal is just a convention. You break the conventions, saying that a point is an edge, so why can't I break the conventions? Furthermore, your breaks in convention result in contradiction, because you're careless, mine do not result in contradiction, because I'm careful to analyze what I am doing.

:ok:

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."