But they can't deny the 'law of identity'. — Wayfarer

You have to read the whole sentence. "They're denying the reality of multiple things having an identical (in the A=A sense) property."

Nominalists are not denying the reality of similarities or resemblances. They're denying the reality of multiple things having an identical (in the A=A sense) property. — Terrapin Station

So then nominalism is now disproven by quantum mechanics? - https://en.wikipedia.org/wiki/Identical_particles

Note how at the quantum level, identicality and indeterminism go hand in hand. So nature is telling us something there.

Sure. For an excellent discussion of generality and particularity, check out the Introduction to Deleuze's Difference and Repetition. For a discussion of singularities and their relation to generality, see chapter 1 of Giorgio Agamben's The Signature of All Things, particularly §5-9. See also chapter 4 of Manuel DeLanda's Intensive Science and Virtual Philosophy. Slavoj Zizek's various reflections on universality - which subtend his work - also inform much of what I say, but check out The Parallax View and chapter 4 of The Ticklish Subject as well. There are probably other sources which feed in to all of this, but also of this is latent and ingrained from much of the various reading I do into this stuff.

I still hesitate at this description, because I am contemplating the alternative that a universal (or a general) is not one single "item" exhibited by multiple particular things, but rather a continuum. In Peirce's words, "Thus, the question of nominalism and realism has taken this shape: Are any continua real?" — aletheist

I tried just now reading through a bit of "The Logic of Relatives," which is what that quotation is from, but I'd have to spend a lot more time on it, read it a lot slower, etc.--because per the relatively speedy way I just read some of it now, I don't know what the heck Peirce is on about really (which unfortunately isn't an unusual response from me to the little I've read of Peirce in the past).

Not at all. It rather shows why (a) physics shouldn't be taken as doing philosophy, and sometimes by extension (b) physicsists shouldn't be considered to be competent philosophers (hello David Deutsch for example) simply due to expertise in another field.

I still hesitate at this description, because I am contemplating the alternative that a universal (or a general) is not one single "item" exhibited by multiple particular things, but rather a continuum — aletheist

That's why universals are best understood as constraints. (And why habits too are best understood as constraints.)

The puzzle arises because it is clear that information needs to be present to break a symmetry. If a particle is positively rather than negatively charged, something must have happened in its developmental past to make that be the case. It must have been marked in a way it remembers.

This becomes a problem if we take the nominalist approach and think about the particle as it is now - with its history locked-in by the fact the world is generally, everywhere, too cold for the particle to change its character, its properties.

But it is not a problem if we roll the history of the Cosmos back to when the particle was in such a hot and dense world that it simply existed as a fleeting fluctuation in a generic vanilla field - where effectively no identity was yet locked in.

So for a charged particle, its universality is ancestral. There really was a time it existed in a more generic form - a meaningless fluctuation in a Big Bang plasma. But now it has particularity because of a new generic universal condition - the continuity of a near Heat Death vacuum. And in good time, at the actual heat death, your charged particle will become re-assimilated to that generality. It will be de-materialised back to event horizon radiation.

So physics really does take a substantial approach to generality. The story of the Cosmos is about a phase transition from the vanilla generality of the Big Bang to the vanilla generality of the Heat Death. And more particular states of constraint or individuation - such as everything material we could be concerned about in practice as humans - are just habits of structure that arise to complicate the journey along the way.

Not at all. It rather shows why (a) physics shouldn't be taken as doing philosophy, — Terrapin Station

So you think the discovered facts of reality oughtn't inform contemporary metaphysics? You don't think the truth of things ought to act as a constraint on our speculative ignorance.

Curious.

Haha--you can't discover that identical properties obtain in different particulars. You'd have to not understand the concept of them being identical properties to even think that that would be discoverable.

Yes, that is the (singular) actuality. But then that still leaves the question of how best to deal with the two aspects that are required to produce such a history. And you did seem to be collapsing them in talking about this confusing thing of a "singular generality". Your choice of jargon seems unhelpful here. — apokrisis

Yes, but then, I'm elaborating in 'enemy territory' as it were, and if I could give up the use of generality altogether, I would. In any case what I'm getting at with the singular is more akin to what Aristotle understood as the 'example' or the paradigm, which more or less explodes the general-particular matrix altogether. Consider the following passage by Agamben (which should have you thinking along the lines of Pierce's 'abduction'): "The locus classicus of the epistemology of the example is in Aristotle's Prior Analytics. There, Aristotle distinguishes the procedure by way of paradigms from induction and deduction. "It is clear,” he writes, "that the paradigm does not function as a part with respect to the whole (hos meros pros holon), nor as a whole with respect to the part (hos holon pros meros), but as a part with respect to the part (hos meros pros meros), if both are under the same but one is better known than the other." That is to say, while induction proceeds from the particular to the universal and deduction from the universal to the particular, the paradigm is defined by a third and paradoxical type of movement, which goes from the particular to the particular. The example constitutes a peculiar form of knowledge that does not proceed by articulating together the universal and the particular, but seems to dwell on the plane of the latter.

Aristotle's treatment of the paradigm does not move beyond these brief observations, and the status of knowledge resting within the particular is not examined any further. … The epistemological status of the paradigm becomes clear only if we understand - making Aristotle's thesis more radical - that it calls into question the dichotomous opposition between the particular and the universal which we are used to seeing as inseparable from procedures of knowing, and presents instead a singularity irreducible to any of the dichotomy's two terms. … A paradigm implies the total abandonment of the particular-general couple as the model of logical inference. The rule (if it is still possible to speak of rules here) is not a generality preexisting the singular cases and applicable to them, nor is it something resulting from the exhaustive enumeration of specific cases. Instead, it is the exhibition alone of the paradigmatic case that constitutes a rule, which as such cannot be applied or stated… A paradigm entails a movement that goes from singularity to singularity and, without ever leaving singularity, transforms every singular case into an exemplar of a general rule that can never be stated a priori." (The Signature of All Things - this is for @aletheist too).

Those familiar with Wittgenstein might recognise here the discussion in the PI regarding the meter rule in Paris which is neither a meter nor not a meter long, but simply an exemplar of a meter. Anyway, the point is that I don't align singularity with what you refer to as actuality: while actuality is indeed singular, what the above is meant to convey is that singularity runs diagonal or transversally to the general-particular couple, and that it is not confined to 'actually exiting things'. It applies no less to a (general) meta-stable system than crystalization of particularities engendered from it. So while I understand where you're coming from, I'm after something different. The stakes are ultimately ethical and political (and ontological, when it comes to thinking in terms of novelty and the new), but I'll not go into that here.

But quantum mechanics says that "discoverable" is now the issue.

On a short or hot enough scale of "discovery", or measurement, everything could be anything. Which rather screws with classical notions of the principle of identity for a start, don't it?

On a short or hot enough scale of "discovery" — apokrisis

You're getting loopy already. What does a "short (enough)" or "hot enough" "scale of 'discovery'" refer to?

I was looking at the Armstrong book I mentioned to you. It's been ages since I read it, so I forgot most of it--I especially forgot that he starts by mentioning Peirce!--surely you'd enjoy that. Anyway, so re the "THE" example and Armstrong mentioning Peirce, he sayd that Peirce would say that there are two tokens of one type. One type is the same as one universal per my earlier comments. And the issue is whether that type is something real, something that's identically instantiated in the two "tokens."

That is to say, while induction proceeds from the particular to the universal and deduction from the universal to the particular, the paradigm is defined by a third and paradoxical type of movement, which goes from the particular to the particular. — StreetlightX

I don't see that as abduction. I would agree that Peirce failed to be completely satisfactory in accounting for abduction. But it is not that type of movement.

Instead, it is a retroductive leap. It is being able to see - vaguely - the deductive structure that would explain the particular situation in question.

So at a glance, we can suddenly see the hierarchy of informational constraints which would produce some phenomenon as its most likely outcome. But that retroductive insight is only "paradoxical" in that we know it to be right, in pattern matching fashion, before we have fully fleshed out its detail in our minds.

So in usual triadic fashion, we have the three things here of the general, the particular and - now - the vague. Instead of crisp possibility, we have vague possibility. We have the inkling of the right hypothesis accompanied by a neurobiological feeling of certitude - an emotional aha! of recognition. And the job then - as Peirce says - is to flesh out the hypothesis to make it a crisp and testable deductive statement. That is then followed by the inductive confirmation.

So yes, in human thought and also (more controversially) in metaphysical development generally, there are the three things of deduction from generals, induction from particulars, and abductive leaps - or the symmetry breaking of vagueness itself.

And it is this third thing - the abductive leap - that is the most inscrutable of all. As well as being the most important in being the genesis of all existence - either of our world of ideas or the actual Cosmos which had to guess itself into being in analogical fashion.

But talk of a movement from the particular to the particular is not the same thing as this kind of spontaneous symmetry breaking.

A paradigm entails a movement that goes from singularity to singularity and, without ever leaving singularity, transforms every singular case into an exemplar of a general rule that can never be stated a priori. — StreetlightX

Thanks for the quote but isn't it just nominalism redux? I can't see any trace of Peircean sophistication here.

A Peircean "paradigm" is a triadic whole that includes the missing element of firstness or vagueness, along with the generality of habits and particularity of dyadic reactions.

So Peirce argues for an irreducible complexity that can't be simplified to nominalistic particulars in this fashion.

The Planck scale. Don't you know the first thing about quantum physics?

Only have time for a quick schematic reply but the singular <> the particular. It's not nominalism. The singular exemplifies a universality: the particular stands for nothing but itself. The para-digmatic, is what 'stands beside itself' (qua the Greek prefix, para), unable to be subsumed under general rule and thus not a particular. Will try and reply in full later. Christmas shopping to be done!

You have to read the whole sentence. "They're denying the reality of multiple things having an identical (in the A=A sense) property." — Terrapin Station

I did read it. And to deny that multiple things have the same property, is to deny that A=A. You only have 'that instance of A over there', and 'another instance of A here' - but they're not identical. So how can you even retain 'the law of identity' at all?

The singular exemplifies a universality: the particular stands for nothing but itself. — StreetlightX

That's fine. It is obvious that processes seem separable. So they can be both wholes, in being some particular species of a process, and yet develop in isolation.

Indeed that is what gets designed in by biological information. That's how genetics works. Socrates can be Socrates and not some other bloke due to the particular DNA he carries around in every new cell he ever produces.

Well, of course, for bacteria, genetic material respects no such boundaries. It is hard to talk separably even of species let alone individuals.

And then if we are talking about physical dissipative systems and not complex biological ones, then processes - like plate tectonics - do seem far more actually universal. We can tell the difference between a mountain and a molehill (as we can feel the difference in terms of energy costs in climbing them, or building them), but the metaphysical issue is does nature care? Fractal geometry suggests not. Dissipation looks the same over all (classical) scales.

So the particularity of universals is evidence that complexity develops hierarchically via the having of some kind of memory (the essential thesis of pansemiosis). But a high degree of separability - such that we can talk about the wonderful variety of forms contained within Platonia, including cats, cups and triangles - is not the fundamental condition. The particularity of universals is itself a particular kind of late stage development, not something that is physically fundamental.

Again, this is why Peirce had to introduce the notion of vagueness into his logic and metaphysics. Before there can be particular universals, there must be vague universality. A quantum state, in fact.

The para-digmatic, is what 'stands beside itself' (qua the Greek prefix, para), unable to be subsumed under general rule and thus not a particular. — StreetlightX

Yes, I'm fine with the definition. My point is that the Peircean paradigm resolves the "paradox" of the dichotomy by going triadic and hierarchical. He includes vagueness so that symmetry-breaking or individuation becomes something that is actually possible due to a self-organising developmental machinery.

Deleuze sometimes seems to be climbing the same tree with his repetition and difference, his generative plane of immanence. But it seems much less worked out than Peirce. And given modern advances in science, that would make it doubly obsolete.

Thanks, but that seems like a lot of material to digest. I am looking for a relatively concise and neutral summary of how the various terms are typically defined and distinguished, preferably online.

You only have 'that instance of A over there', and 'another instance of A here' - but they're not identical. So how can you even retain 'the law of identity' at all? — Wayfarer

The quantum quandry is that you can neither ultimately tell if one thing is the same with itself, or if two things are indeed different. Both identity and separability go by the by as you wind existence back to its Planck scale origins.

When things are hot and small, they all dissolve back into a vanilla mush where the classical notions encoded by the laws of thought cease to apply with any counterfactuality.

... I don't know what the heck Peirce is on about really ... — Terrapin Station

I have been reading stuff by and about Peirce for two solid years, and only recently started to feel like I was finally really getting it. I was warned beforehand that this is how it would go, and for me it has been worth the effort, but it has definitely been a slog at times.

That's why universals are best understood as constraints. — apokrisis

Yes, this brings to mind Peirce's use of "determination" in the sense of constraint.

But it is not a problem if we roll the history of the Cosmos back to when the particle was in such a hot and dense world that it simply existed as a fleeting fluctuation in a generic vanilla field - where effectively no identity was yet locked in. — apokrisis

And this is reminiscent of his cosmogony, which begins with a continuum of vague potentiality that eventually actualizes our existing universe.

Peirce would say that there are two tokens of one type. One type is the same as one universal per my earlier comments. — Terrapin Station

Indeed, "the" was an illustrative example that Peirce employed more than once in his writings. Before coming up with type/token, he used legisign/replica for the same basic distinction.

And the issue is whether that type is something real, something that's identically instantiated in the two "tokens." — Terrapin Station

I am not convinced that "identically" is necessary here. It seems like two tokens of the same type could be different actual points on the same continuum of potential points. But I am still reading and thinking about all of this.

The quantum quandry is that you can neither ultimately tell if one thing is the same with itself, or if two things are indeed different. Both identity and separability go by the by as you wind existence back to its Planck scale origins. — apokrisis

That's because they're on the borderline between potentiality and actuality, as noted prevoiusly, in relation to Heisenberg's comment on same.

"Dust particles in the right atmospheric conditions resulting in snowflakes" with their variations on an invariant pattern just is an expression of universality. You are making the mistake of putting the cart before the horse.

Yes, this brings to mind Peirce's use of "determination" in the sense of constraint — aletheist

Peirce did not use the word, but he clearly employed the concept. In talking about the token~type distinction, for instance, he said:

Each instance is an instantiation of a type that: "itself has no existence although it has a real being, consisting in the fact that existents will conform to it." (1961, 2:292)

So it is all about causality as the concrete limitation on possibility. And constraints - having that concreteness - are real (if not to be confused to that which they produce via their action - ie: the substantial actuality of in-formed materiality).

And this is reminiscent of his cosmogony, which begins with a continuum of vague potentiality that eventually actualizes our existing universe. — aletheist

Hopefully it is more than reminiscent. Peirce was already on to it. :)

So it is all about causality as the concrete limitation on possibility. — apokrisis

Something like 'the form something must take in order to exist', right?

@Terrapin Station - a snippet from the wikipedia entry on Universals:

C.S. Peirce...developed his own views on the problem of universals in the course of a review of an edition of the writings of George Berkeley. Peirce begins with the observation that "Berkeley's metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop". He includes among these paradoxical doctrines Berkeley's denial of "the possibility of forming the simplest general conception". He wrote that if there is some mental fact that works in practice the way that a universal would, that fact is a universal.

Something like 'the form something must take in order to exist', right? — Wayfarer

Yep. Materiality is free possibility. And it becomes concrete stuff by "fitting in".

The point in relation the OP is that most folk want the world to be constructed of materials which already have inherent form. The essence of nominalism is the belief that has to be the case logically. Substance gets the ball rolling by bringing inherent properties to the table.

But talk about universals is recognition that shape comes from without. Properties are the result of some process of moulding to fit. So wind back the creation far enough and at some point you must have just pure form as "the first moulding action". And you must also then have some kind of ur-material that is both a stuff receptive to such moulding, and yet not yet having any characteristics at all.

Plato called it the chora. Even he had to have something that was not actual matter, yet still could play the matching role of being the receptacle of his forms.

Why are we able to be confident that you will not turn into a pineapple in 3.5 minutes? Because that is not a real possibility, any more than a triangle turning into a rectangle while remaining within the infinite continuum of real triangles. — aletheist

If you want to speak of INFINITE possibilities then that is a real possibility. Perhaps in 3.5 minutes an alien species comes down to earth with pineapple guns that turns everyone in to pineapples, such a circumstance must be included in all possibilities if we are speaking of INFINITE possibilities. Or where you using a misplaced hyperbole?

All universal theorists are arguing for is the existence of an entity that somehow exists in multiple places at the same time. The red of that firetruck is similar to the red of that fire hydrant in virtue of the fact that both objects instantiate the universal "red-ness".

It can be helpful to think of properties as ways objects are. Universal theorists think that these "ways" are repeatable entities. Those with the same property are literally instantiating the same universal. — darthbarracuda

I would of thought that when we discovered that red is a certain wavelength of the EM spectrum that is exuded by the type of material light is reflected from it would've meant that we did away with thinking "redness" is something instantiated universally by objects, that it is a thing in itself rather than just a physical occurrence. ??