Or put otherwise: there is no 'ultimate symmetry', the breaking of which explains individuation — StreetlightX

In case I left you confused - it does happen - I hope it is clear that symmetry-breaking is what connects a triadic system of symmetries. So the "ultimate symmetry" would be a three cornered structure, if you like.

You have the symmetry of vagueness - a state where (material) contingency and (formal) necessity are differences not making any difference. As Peirce noted, the PNC does not apply.

You have the symmetry of generality - a state where globally there is the continuity that has formally absorbed all possible differences so that they don't make a difference. As Peirce noted, the LEM does not apply.

Then you have that final symmetry of atomistic particularity. Eventually, even constraint no longer makes a difference. Locally, things arrive at the ultimate simplicity of a geometric point, a mathematical identity element, a quantum particle, an informational bit, a semiotic mark, or a fundamental entropic degree of freedom.

Or as the laws of thought would have it, the emergent entity to which the principle of indiscernibles does finally successfully apply.

So symmetry is something to be understood in a formally general fashion - hence why maths is the domain that winds up speaking about it.

But in a holistic metaphysics with a triadic structure, we are talking about three kinds of symmetry-producing limitations. If we pursue symmetry-breaking back to its source, we find it in three types of bounds - Peirce's triad of firstness, secondness and thirdness. Each is a "level" of symmetry - a terminus to a dichotomous "other".

something I'd love to see a thread on if you're interested/knowledgeable in the intersection btw Wayfarer). — fdrake

Kind of you to say so, and while it’s true I have an interest in Buddhist philosophy and also philosophy of math, I skipped undergrad Formal Logic so I don’t think I really have the chops. I will have to content myself with the occasional parenthetical comment. [By way of consolation, here is a podcast I listened to recently - an interview with Graham Priest on Buddhist Logic.]

What I want to add to this is that philosophical concepts are just like this. — StreetlightX

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.

So, Cheers!

You mean that game where the goal, the meta-rule, was to show that no particular rule could hold firm?

Yet, that’d work as prescribed. It would serve the purpose of anti-metaphysicians. ;)

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.

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.

Oh please. If mathematical physics tells us that existence is the result of broken symmetry, then who are you to disagree? Get over yourself - your Copernican belief in the worldly problematics that revolve around your Being. Good lord.

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

Did you actually contest any of the content of my posts. Must have missed it somehow. :yawn:

So maths and physics are talking about the same universal mechanism.

Maths deals with symmetries in Group theory, and those mathematical tools are used by physicists and other scientists to model reality and this or that part of reality. Does that tell us anything about reality, or does it just tell us about the way we currently model that reality?

Not convinced by the Standard Model, hey? You think it might be just a big coincidence?

Sounds legit.

But that game was too arbitrary: — StreetlightX

That was part of it's attraction for me; it describes wheels spinning without ever engaging, an aspect of much of philosophy. It's, as you set out, the use to which we put the rules that makes for one choice over another.

It would depend what you mean. The standard model has its problems and its alternatives/adaptations, and the existence of "gravitons" is contentious (some even think it is a conceptual confusion to model gravity as a force at all). So if you mean by "convinced" "convinced that the Standard Model describes reality as it is in itself independently of our means of modelling it", then no I am not convinced. What would convince me of that? Well, something that had already convinced me that metaphysical realism is true would be a pre-requisite. But perhaps you think there is a way in which one can be convinced of the Standard Model without having to be a metaphysical realist? In which case, let me know and I might have a different answer to your question.

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.

The standard model has its problems and its alternatives/adaptations, and the existence of "gravitons" is contentious — jkg20

... or gravitons aren't even part of the Standard Model yet.

So if you mean by "convinced" "convinced that the Standard Model describes reality as it is in itself independently of our means of modelling it", then no I am not convinced. — jkg20

I'm not asking you to deny that the Standard Model is "only a model". The clue on that score is probably in the name.

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

So do you think group theory is arbitrary? Are its results contingent in some fashion you can explain?

And is particle physics success in using symmetry maths to account for particle relations arbitrary? When a model fits like a glove, why would we have reason to think that was also merely contingent?

Of course, it could be a lucky accident. No one can deny Descartes his demon.

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.

Yeah. I should have said something catchier like "intra-systemic imposition that responds to no genuine, worldly problematic".

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. — StreetlightX

Really? Because it sounds remarkably like you want to defend your favourite kind of philosophy against charges of obfuscatory meaninglessness but reserve your right to dismiss any philosophical positions you don't like on exactly the same grounds.

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

Group theory itself not arbitrary: given the Group axioms and classical laws of inference, all sorts of theorems follow of logical necessity - I used to be able to prove a few of them myself at one time. So no, Group theory is not arbitrary. As for the axioms of the theory and the status of the rules of inference - that might be a different issue.
How do we account for the usefulness of pure mathematics in describing and predicting reality? That's a different question, but I'm certainly not convinced that the answer to it requires either mathematical realism or physical realism.

How do we account for the usefulness of pure mathematics in describing and predicting reality? That's a different question, but I'm certainly not convinced that the answer to it requires either mathematical realism or physical realism. — jkg20

Sure. If you read my posts, you will see I am a pragmatist. You’re talking about bread and butter epistemic issues.

But again, do you want to claim that the connection is arbitrary? Do you have reason to believe that nature plays by different structural rules despite the evidence to the contrary?

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 '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. — StreetlightX

You're mistaking the boundaries set within schools by the restriction of their premises with the boundaries set within entire disciplines on the "schools" that can be contained therein. It's not that, once a commitment is made, philosophy is still less contained than maths, it's that commitments of almost any sort can be made (and followed) and still constitute 'philosophy'. This is not the case with maths, where commitments of the sort you describe are still made and followed, but the range of possible commitments is severely constrained by the nature of the broader investigation (the whole of maths, sensu lato)

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.

I haven't said maths doesn't have a variety of commitments, some of which are "less well-travelled", in fact I said the opposite. The point I'm making is that it is not sufficient to support your argument simply by stating that maths has a variety of commitments whose properties then constrain further investigation, and so does philosophy, so they're basically the same.

What differentiates them, I would argue, are the types of constraints that are placed on those commitments, the breadth of the field. It is easy to describe what isn't maths by reference to the activity alone. I think it's considerably harder to describe what isn't philosophy, without reference to other subjects. Even harder to describe what never will be philosophy and hope to have any certainty that you'll be correct.

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.

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.

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*

In math, there are at least some moves that are universally considered invalid. — schopenhauer1

My claim is that all those moves which in math are universally considered to be invalid, are based in ontological principles. The principles of addition and subtraction, just like the principle of non-contradiction, is based in ontology. So consensus on these mathematical principles requires consensus on ontology.

All that needs to occur is that a higher amount of constraints that needs to take place math than in philosophy. — schopenhauer1

I don't think you've properly elucidated the pertinent parameters. You've defined consensus in terms of constraint. However, consensus is properly defined in terms of agreement. And there are two principle parameters to agreement, one is the scope of the content of the agreement (narrow or broad), and the other is the scope of the formal aspect (the number of individual human beings engaged in the agreement). So your designation of "a higher amount of constraints' is really quite vague because it doesn't directly take into account either of these parameters. Saying that there is a high number of constraints in place doesn't say anything about the number of people engaged in each of these constraints, nor does it say anything about the scope of application of each of these constraints. For example, whether 100 instances of 20 people agreeing to some specific constraint constitutes a "higher degree of consensus" than a million people agreeing to some broad principle is highly doubtful. You cannot judge "degree of consensus" by "amount of constraints".

I could not solve a mathematical problem with a treatise on "being" for example. However, a metaphysical argument might be framed as a problem of "being", a problems of propositions/linguistics, problems of a priori synthetic knowledge, problems of empirical data gathering, etc. etc. It is framed too broadly for even a consensus on what a valid answer looks like (unless you fall within a camp with another philosopher who shares that point of view, but that doesn't negate that philosophy itself is much broader outside this compartmentalization). Thus I said earlier: — schopenhauer1

In order to even count something intelligibly, a consensus on what constitutes a unit is required. If "a unit" is understood as an individual being, then a treatise on being, and consensus on "being" is required before we can have an accurate count. This extends to all forms of measurement, consensus on the unit of measure is required. This is exposed by Wittgenstein when he claims that a metre stick is both a metre, and not a metre.

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 (unless your philosophy is to put certain constraints on, but then the argument about what constraints to put on would still be contested and so on). There is a certain consensus in the math community about what counts as even in the realm of what is valid for an answer. — schopenhauer1

I think that this is exactly right, but you misconstrue the implications, the conclusions to be drawn from this situation. Philosophy is less constrained than mathematics, as you say, but the constraints of mathematics are really derived from philosophical constraints. So when the philosophers produce consensus on ontological principles, mathematical constraints are derived from this. The overriding constraint, "what is valid", is a philosophical principle, not a mathematical principle. So there cannot be any consensus on particular mathematical principles without consensus on "what is valid".

But this is because the very nature of philosophy is how unconstrained it tends to be. — schopenhauer1

But philosophical constraints exist. And if they are not produced, or created by philosophy, where do they come from? You cannot accurately say that philosophy is unconstrained, then look at something like the law of non-contradiction, and dismiss this as non-evidential of constraint. Furthermore, what you do not seem to apprehend, is that these philosophical constraints are what bear upon the world of mathematics, as the foundation for mathematical constraints.

Remember that in maths, a unit is defined by the identity element - a local symmetry that can't be broken by whatever operation broke the global symmetry. — apokrisis

No, no, this definition of "unit" must be rejected as circular, or an infinite regress, and therefore not a definition at all. If a symmetry is a unit, and we refer to a prior symmetry-breaking to define that unit, then we have defined that specific unit, by allowing that there was another unit, and referring to this other unit, which is prior to that unit. You have defined "unit" by referring to the unit which birthed it. Therefore there is no definition of "unit" here, just a circle a circle, defining unit with unit, which if pursued would lead to an infinite regress of units. Such a definition is inherently contradictory, because the unit is referred to as a symmetry, but you move to define it by referring to a symmetry-breaking. Therefore what is defined is not the unit, (the symmetry) but the annihilation of the unit (symmetry-breaking).

So geometry begins with the fundamental thing of a zero-d point. Dimensionality cannot be constrained any more rigorously than a dot, a minimal dimensional mark. Having found the stable atom, the concrete unit, the construction of dimensional geometry can begin. — apokrisis

As I said, mathematics could be based in "zero", but this entails a negation of the concept of "unit". When the unit is eliminated, annihilated by symmetry-breaking as you suggest, to base the mathematics in zero, then we need a clear and precise definition of what "zero" refers to. We nave no more "units" to base this mathematics in, only the assumption of "zero". Without a clearly defined "zero", all this mathematics employs completely arbitrary zeroes (concepts of zero), and is just random nonsense.

So in the mathematical realm where 1 is the identity element - the unit that is unchanged by the kind of change that more generally prevails - it is both part of that world and separate from it. It has that incompatibility which you point out. And that is because it is a re-emerging symmetry.

Globally, a symmetry got broke by the very notion of a division algebra. Division, as an operation, could fracture the unity of the global unity that is our generalised idea of a continuous wholeness - some undifferentiated potential. But then divisibility itself gets halted by reaching a local limit. Eventually it winds up spinning on the spot, changing nothing. A second limiting state of symmetry emerges ... when our original notion of unity as a continuous wholeness finally meets its dichotomous "other" in the form of an utterly broken discreteness. — apokrisis

Your global mathematics here is based in "zero", symmetry-breaking, the annihilation of the unit. You also refer to a local mathematics based in units. Instead of attempting to work out this incompatibility, by establishing a properly defined relationship between zero and the unit, you simply introduce contradiction into these two with the necessary implication that symmetry breaking, annihilation of the unit, is derived from symmetry, the unit, and the constraints which constitute local unit are somehow derived from local freedom, lack of constraints.

If mathematical physics tells us that existence is the result of broken symmetry, then who are you to disagree? — apokrisis

It is not mathematical physics which tells us this, it is a simple ontological assumption. As I explained to Schop1 above, the mathematics follows from the assumptions. There is no inherent need to describe existence in terms of broken symmetry, that's a choice.

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. — StreetlightX

Well, I am a layman when it comes to maths and have never yet failed to identify it, and I've been in a room full of philosophy professors who couldn't even agree whether a work was 'philosophy' or not, so it's not entirely imaginative scenario posing. But I'm guessing from the hand-waiving that we've reached our usual limit to the extent you care to peruse these kinds of arguments and so further exposition would perhaps be pointless.