Can you take another run at this? This says that to explain the relationship between tokens we will generally have recourse to something that does not itself explain the relationship. The only sense I can make of that is that objects don't talk, people do. — Srap Tasmaner

I don't know how you got that out of what I said. There are a number of approaches to explaining the type-token relationship. You can do it the way you originally proposed, by exploiting action types. You can do it Bromberger's way and exploit properties which are projectible across the type. You can try to exploit structural properties shared by the tokens and which figure in certain scientific explanations. There are a myriad of strategies, but all strategies which I know of exploit the existence of types (e.g. action types) and properties (e.g. projectible properties), and hence are incompatible with nominalism.

What would you say about the ontology of abstract objects? Why is math a valuable tool for describing the world? — frank

I'm not sure what you want me to say about the ontology of abstract objects. I don't hold any systematic views on the topic (e.g. I don't know if they are grounded on equivalence relations, as proposed by neo-Fregeans, or if they are more fundamental). I do however hold a very generous ontology of abstract objects, and I also don't think that the usual way of distinguishing them from concrete objects is all that useful---I think that some abstract objects (say, works of art and fictional characters) exist in time, for instance.

As for the unreasonable effectiveness of math, I'd say that math is effective because it carves natures at its joints. It describes types of objects and structures that are natural. These objects and structures then play (at least) a double role in describing the world: (a) some mathematical structures constrain the space of possibility, thus effectively ruling out some possibilities from happening (if you adopt a Stalnaker-like approach to inquiry, this means that part of our knowledge is won by eliminating some worlds from the space of possibility); (b) relatedly, some mathematical structures are instantiated in the physical world, so their physical instantiations inherit their mathematical properties (e.g. groups).

I'm not sure what you want me to say about the ontology of abstract objects. — Nagase

I didn't want you to say anything in particular. I was just curious about your opinion. Thanks!

Maths bit.

I strongly disagree with this statement. I actually think the opposite is true: by paying attention to the history of mathematical concepts, we see that they emerged not because we "made it just so", but were rather forced on us by the nature of the entities in question and the problems surrounding them. To my mind, mathematical entities form natural kinds, and the most fruitful mathematical definitions (such as continuity) capture the structure of those kinds.

This isn't meant as a refutation, it's an honest series of questions to see if you've got any internal distinctions between 'mathematical kinds'.

Are transfinite cardinals or ordinals natural kinds? Are categories natural kinds? What about partially ordered sets or finite fields?

I suppose I just don't see how they could be anything but man made, in response to a history of problems and the conceptualisation of new problems. I quite like the idea that 'natural kind' as a type is part of the discursive play of concepts, same with the type-token distinction. All of these are part of the self annihilating critical battery of philosophical abstractions.

From a modern perspective, mathematicians like Euler and Fourier would have gotten away with their 'intermediate value property = continuity' blunder/equivocation because continuity, differentiability and the IVP apply to most of the interesting functions these mathematicians studied. It was only after the axiomatisation of these properties that you get pathologies like the Weirstrass W function and these Darboux ones. It's tempting to read the history like that, but it's very retrojective.

I prefer to read it as the evolution of a concept whose boundaries are fuzzy - something like a composite of continuity/differentiability/IVP - becoming more demarcated when the level of mathematical precision was elevated through the emphasis on axiomatisation. I don't see what insisting that mathematical objects are real does to help someone actually doing/teaching maths (the community thereof + history is where mathematics comes from).

Now for the other bit.

If the questions is 'what makes the tokens stick together in the type' - why isn't 'they're used together with some commonalities between them' a sufficient answer? Something like 'I see red' and 'I see red', if there's an underlying redness it better also reference anger; 'red' is a lot more complicated than 'redness' in the colour. Where do you get the ontological or epistemic resources to glue tokens together relationally? Also, how's this furnished through there being an abstract object or natural kind to save us and instantiate itself?

Another aside, I'd be quite surprised if there wasn't an equivalence relation approach to tokens and types here, in terms of exemplifications. Like in the construction of fractions. 2=1+1=4/2=...(every other possible expression for 2), then the number 2 is defined as [2], that set of expressions which evaluate to 2. And arithmetic is defined in terms of operations on equivalence classes rather than on their constituent terms (this is why algebraic substitution works). Thus simultaneously every object exemplifies the type.

The same thing would apply for continuous functions; in demarcating a collection of functions from other functions there's an equivalence between partitions of this space -into discontinuous and continuous- and that property of continuousness, so 2 functions are equivalent iff they are both continuous. That gives the partition, and they all represent it as exemplifiers and generalities - representative of class and class.

The question becomes how are the representatives taken as representatives, and how are two things related to each other (this is probably related to the sortal idea).

Edited for clarity, did my usual 'leave a sentence fragment' error.

But in the example at hand, you're grounding the type-token relation on the intention of the speaker/writer to use the relevant type. — Nagase

Not the intention, the fact of it being asserted to be so (and not: 'the fact of it being asserted to be so').

A more prosaic example may be the following: x is soluble iff if x is put into water, then x dissolves (this is a very rough characterization of solubility---a more exact approach would need to use counterfactuals and ceteris paribus clauses, but bear with me for the moment). The property of being soluble is not an atomic property, but a complex one, since it is structured. My point is: Jumblese cannot capture this internal structure of the property. — Nagase

I need to respond to this in more depth in a bit, but I don't see why this would pose any problem, in principle, to a treatment in terms of metalinguistic illustration: there is a way of speaking about an x, such that, when the thing so designated an x dissolves in water, we call x soluble. And to learn this way of speaking, is to understand just that language game involving certain rule-governed correlations between linguistic and non-linguistic objects.

I've been thinking about the difference between 'atomic' properties versus 'complex' ones.

Is this an absolute difference in kind?

The complexity of solubility, in the example above, comes out in its being defined --- which is to say it comes out in explication. Another way to put it: If I make a 'move' in a language game calling some x soluble, I thereby implicitly approve of other, more complex moves about x. Explication is only possible given a previous, implicit, familiarity. You can only define or explicate something if you're already in some way familiar with it. Knowing how 'soluble' is used - knowing, through exposure to patterns of language, what things can or can't be said of x after it has been established that 'x is soluble' - this then allows one to approve or disapprove of more complex elaborations.

For instance, as @fdrake's example draws out (I think)- we've only been able to so precisely define what it means for a function to be continuous through a process of explication based on implicit familiarity. @Nagase is right, I think, that we're led to this definition by the object (?) itself, but we're only able to do so if we have a pre-explicit understanding of continuousness. In other words: For a mathematician to recognize a new formulation of 'continuousness' as valid, they have to compare what they've been tracking by the term 'continuous' with what this new formulation tracks. The scope can't be too wide or narrow. It's only because we already 'know' what it means for a function to be continuous, that we can recognize a new formulation as accurate, even illuminating. (There's a kind of meno thing going on here)


But isn't this true of any property, even the simplest ones?

The 'internal structure' isn't really 'internal' - it's laid out in patterns of usage and webs of explication.

In other words: Any property is susceptible of being indicated through a simple notation, and any property also harbors a complexity which comes out in explication and usage (I think that's the significance of the 'myth of the given' - things aren't simply 'given' because to know what something is requires having some minimal ability to explicate)

But isn't this true of any property, even the simplest ones?

The 'internal structure' isn't really 'internal' - it's laid out in patterns of usage and webs of explication. — csalisbury

As I suggested in an earlier post, all properties (predicates) are really relations, and relations may be more or less complex, of course. Seeing predicates as relations dissolves the problems with predication that Sellars is trying to address, as far as I can see. I agree with @Nagasse in that I don't believe any form of nominalism can provide an adequate solution.

The idea of predication as implicit relation is interesting. I went and looked up your earlier post

Another thought I had is substituting the idea of relation for the idea of predication. So, a red apple would be a particular relational complex comprising the apple, the light and the percipient. There would be no universal predicate redness unifying all the different red apples, but merely a set of "family resemblances" or relations.

Quick thought. When we say 'the apple is red' we don't mean 'the apple is red to me.' If Tom, god bless him, were to see the apple, he'd see red as well. But we also don't mean by 'the apple is red' 'the apple is red to tom and me'. The relation as you describe it, above, is a relationship between three 'things' (for lack of a better word). But the relation of 'is red', if it is a relation, doesn't involve any particular percipient. (Though, of course, a particular percipient is required to stand in front of a red apple in order to say, to their loved one, 'listen babe, this apple is red'. By which I mean: the meaning of the sentence and the conditions required for someone to say it are two different things)

I don't know if that really means anything significant, or is relevant to the conversation at hand, but figured I'd throw it out there. (tho it does kinda echo Sellars' short fable about colors and ties in Empiricism and the Philosophy of Mind)

I agree with @Nagasse in that I don't believe any form of nominalism can provide an adequate solution.

You both may very well be right, I'm not sure, but I don't understand the connection between this statement and predication as relation. The way you formatted the post suggests they're related, but I'm missing something. If anything, your discussion of predication-qua-relation seems anti-universals.

I've been thinking about the difference between 'atomic' properties versus 'complex' ones. — csalisbury

The 'internal structure' isn't really 'internal' - it's laid out in patterns of usage and webs of explication. — csalisbury

The funny thing about the "atomic" is that it is not the ultimately simple. It in fact represents the complexity of a dichotomy. The atomic is both maximally located - point-like in space - and also of maximal duration - unchanging until the end of time.

So the invocation of atomism is often a metaphysical sleight of hand. We ought to be talking about events, instances, accidents or fluctuations if we want to drill down to the simplest localised spatiotemporal existents. An atom already has to explain why it endures in "uncuttable" forever fashion.

If reality is indeed a web of relations, then what preserves the individual identity of some located entity? It has to be something else that is going on.

So the very idea of the atom is irreducibly complex. It binds together two extremes of being in being both spatially local yet temporally unbounded.

Hence a good reason why logical atomism came unstuck. A logical holism - a logic of relations - is needed because the story is irreducibly complex. As I've already argued, following Peirce, a logic of relations is indeed irreducibly triadic or hierarchical.

To stabilise real atoms, they must be in causal relation with a void. Old school atomism of course treated the void as a second a-causal backdrop - not really a relational thing. But modern physics has found that it actually does require causal relations between its local excitations and its global spatiotemporal frameworks.

Again, where reality goes, logic ought to try to follow. :)

This is gonna bring things far afield, but I'm interested.

I can't say much of anything about physics, because I don't know much of anything about physics. My hunch is the research probably bears out what you're saying. I'm just gonna approach conceptually what you've thrown down conceptually, to see if you can help me untie some conceptual knots.

My feeling is that when people naively resort to atomism, the whole maximally-located, maximally-durable thing is exactly what they mean by 'simple'. I mean any term, right, has to include its opposite and differentiate itself from it. The very act of trying to locate some 'simple' necessarily takes place in non-simple discursive space (for lack of a better term). The spirit driving the search for the simple, I think, is one that sees anything less-than-maximally located or less-than-maximally-enduring as relying on things that are maximally-located, maximally-enduring. It says this (everything) comes from that.

An atom already has to explain why it endures in "uncuttable" forever fashion. — apo

'has to explain.' Does it? So, for instance, the whole Pierce triadic thing. Does it have to explain itself or not? and, if not, why not? It just is? The world is messy and complex and all sorts of weird stuff etc etc, but, if you look it it the right way, looking for the fundaments, then maybe eventually you end up with Peirce. I'm not sure. But what stops me from saying this procedure is as infected, at heart, as the atomist thing? It wants to find the base of everything - then it thought a while and said, well, not the base, but the engine. But it still is driven toward the central thing, even if the central thing is a weird triadic relationship.

"it already has to explain."

Why?

My feeling is that when people naively resort to atomism, the whole maximally-located, maximally-durable thing is exactly what they mean by 'simple'. — csalisbury

Yep, commonsense would tell you that the world is composed of substantial parts. It is a very natural starting supposition - especially for humans who specialised in constructing things.

And atomism is an especially convincing idea once you have the mathematics to show that there are such things as the simplest forms - little spheres. Or the Platonic solids.

So matter is already ultimately simple in being located generalised "stuff". And mathematical form tells you the simplest possible shapes of that stuff.

It is all so superficially attractive as an understanding of basic simplicity. And I am emphasising how logic has simply echoed that metaphysics - even to the point of winding up calling itself atomistic. A calculus of objects with properties, rather than a matrix of relations with emergent regularities.

I mean any term, right, has to include its opposite and differentiate itself from it. — csalisbury

Yes, we should expect dichotomies as soon as we start asking fundamental questions.

Matter vs form already reveals itself in atomism. It was the way to unite the two aspects of reality in some kind of ultimate simplicity. Atomism is convincing as you had the simplest matter in its simplest forms. And then the causation was divided so that atoms owned all the change, the void was an a-causal backdrop.

The spirit driving the search for the simple, I think, is one that sees anything less-than-maximally located or less-than-maximally-enduring as relying on things that are maximally-located, maximally-enduring. It says this (everything) comes from that. — csalisbury

Again yes. But is this really the simplest ontology of development?

I am contrasting the atomist conception - where for no reason, the world starts with a bunch of balls in motion in a void - with a Peircean-style ontology where there is less than nothing at the beginning. Beginnings are vague - just unbound fluctuation without a relational organisation. There are no meaningful elements to get a game going. These meaningful elements have to evolve out of the murk via bootstrapping self-organisation.

And this is the new physical view of reality. Atoms only exist because the Cosmos expanded and cooled. Protons last forever (or near enough) because the Universe eventually got too cold to melt them.

So the fact that localised matter can endure is an emergent property, not an inherent one. Physics has proved that. Even a point particle like an electron only endures until it meets its anti-particle, a positron, and the two disappear back into the radiative void in a puff of energetic symmetry-restoration.

Metaphysically, physics is showing that the localised does not endure except due to a global thermal accident. Everything would be merely an event, a fluctuation, if it weren't for the way that some of the cosmic radiative crud didn't get trapped for a while as localised atomistic matter. Wait a while and it is all going to get fizzled back the Heat Death end of the Universe. The true simplicity of smeared-out events will be restored to Nature.

So, for instance, the whole Pierce triadic thing. Does it have to explain itself or not? and, if not, why not? It just is? — csalisbury

Of course it must explain itself. And the point is that it does. It is as near to a bootstrap ontology as human metaphysics has imagined.

So pragmatically, it is the metaphysics that works. And it is a metaphysics that arose out of Peirce's foundational contributions to logic. That is what I am drawing attention to. The bootstrap Cosmos expresses a bootstrap logic.

This is not arbitrary. This is delivering on the Platonic promise that logical atomism couldn't fulfil. This is about the form or relational structure that was always inevitable and so foundational to existence.

Instead of taking the commonsense approach - believing in uncuttable matter and wondering what would be the simplest form it could take - this is instead going direct to the principles of symmetry and symmetry-breaking themselves.

A sphere is as simple as it gets as a form. But why is that exactly? What context, what unbounded set of possible relations, makes that so?

From there, it is a simple flip to see the endurance of spherical atoms as instead the universal confinement of excitations by thermal symmetry-breaking. Electrons persist as local features because they can no longer self-annihilate back to a vaguer radiative state.

And they are not spheres but point particles. Or rather, they are no longer any kind of located material being at all but simply chiral twists in the vacuum fabric of reality. They are trapped knots of broken symmetry that can't untwist any more.

So physics has gone right through the mirror and reflected through to the other side. It has gone from hard material spheres, through point particles with no external material presence at all, all the way to purely formal strings or loops which are representations of mathematical symmetries, not material things at all.

Analytic metaphysics is catching up on this shift with its Ontic Structural Realism. It is what has happened. Reality is being explained by the inevitability of mathematical structure, not by the mystery of material substance. Symmetry-breaking principles tell us why the primal state of things - an unbounded sea of fluctuations - would evolve a stabilising structure of final habits.

But what stops me from saying this procedure is as infected, at heart, as the atomist thing? — csalisbury

Well, it works better. So at worst, it is the least infected metaphysics.

I mean atomism works - for us at our very cold and large classical state of being. We are only a couple of degrees above absolute zero and so near enough to a Heat Death.

But physics is about seeing the bigger picture. And atomism melts away as you return towards the initial conditions of the Big Bang. It will even radiate away when the Cosmos does finally reach its Heat Death, with even protons and electrons being fizzled to cosmic background radiation by dying super-massive blackholes. So atomism is, at best, a passing phase of complexity in the great journey from one form of maximum simplicity to - reciprocally! - its other form of maximum simplicity.

(You can't say that physics ain't completely precise about these things. :) )

It wants to find the base of everything - then it thought a while and said, well, not the base, but the engine. — csalisbury

It is a fair point that this cosmology/logic needs still some kind of base of initial conditions. The argument on that is the Peircean view - which is built on a Vagueness, a Firstness, an Apeiron, as the least imaginable kind of starting point. A Vagueness is literally less than nothing - nothingness simply being a void, and a void being ... a hole, a concrete absence, in some thing.

So yes, the focus is on the engine of structure creation - a triadic relation. But the problem of a starting condition is not denied. The claim is that it becomes the least concrete kind of starting point that could be imagined. The achievement of a Peircean approach is to do the most to minimise this aspect of the Cosmic mystery ... while also managing to shed the most light on the engine of structure creation that explains everything the Cosmos has then become.

When we say 'the apple is red' we don't mean 'the apple is red to me.' If Tom, god bless him, were to see the apple, he'd see red as well. But we also don't mean by 'the apple is red' 'the apple is red to tom and me'. — csalisbury

Hmmm. You seem to be working your way up to "The apple is red to speakers of English," which is not only not an unreasonable thing to say, but just the sort of thing people say when teaching a language.

Hmmm. You seem to me working your way up to "The apple is red to speakers of English,"... — Srap Tasmaner

Not if you just assert that the apple is red to speakers with a shared neurology. No need to take things to the Whorfian extreme on colour perception.

[ All of what you've said, in terms of physics/cosmology, strikes me as unimpeachable (or at least unimpeachable by me.)

The thing I really wanted to focus on was the "has to explain" part. As in "An atom already has to explain why it endures in "uncuttable" forever fashion."

So we can easily trip up the atomists by saying that their search for an explanation failed by their own lights - they stopped too soon, and without realizing that they were being false to their own, implicit, ontological/methodological directives.

What is an explanation? would be another way of going about this. How does something explain something else? And why do we think what we talk about when we talk about explanation is baked into the structure of everything?

When you talk about Peirce, it seems like you're talking about the terminal state of a certain way of looking at things. It seems quite refined, and finished. But why should I think this represents a core metaphysical truth rather than a completed way of thinking about the world? The final formalization of 'explanation' maybe.

The achievement of a Peircean approach is to do the most to minimise this aspect of the Cosmic mystery — apo

That's a sad achievement though, isn't it? Why would that minimisation be an 'achievement'? What's left, after that achievement? But to trumpet the achievement? louder at first, then softer. But trumpeting nonetheless. because there's nothing left anymore, but to....

Not if you just assert that the apple is red to speakers with a shared neurology. No need to take things to the Whorfian extreme on colour perception. — apokrisis

I just can't get on board with the Whorf-Sapir thing. I know there's still controversy, but I like to think of it as refuted for color perception.

I think LW had a bit about "Because I speak English" being a perfectly good answer to "How do you know that's red?" A little like Austin answering "How do you know that tree is real?" with "Well, it's not fake."

In one sense this is just annoying, a sort of pretended obtuseness. So my reasonable sentence above ("This is red to speakers of English") turns out to be an explanation of how the word "red" is used, not an explanation of how perception works.

But I have some residual affection for this move, and I think it might be because it is sort of anti-Whorfian. There's a presumption that whoever you are and wherever you're from, you can't really be struggling with the concept of [red], so you must need help with the word "red". (There's something else here but I can't quite put my finger on it. Will mull ...)

There's a simpler way to put this: The world was rich and full of excitement and texture when I was young. Recasting all of that in Peircian terms seems possible, but then, having done so, I feel like something is lost. I can say that I only lost my youthful illusions and now am acquainted with the truth. But then what did I lose? How did the Perician engine at the heart of everything generate something that is lost when you recognize the peircian engine? This is romanticism, sure, but do you see what I mean? Something eludes it, the Peirce thing, and you can only bring it back by quashing it. You have to kill it to touch it. In other words: The whole peirce thing still relies on an outside itself. do you see what I mean?

My hunch is that the peircian engine only explains itself, and casts the whole world in a way that makes it fit. It's supple that way. Even that which exceeds it, gets brought back in the fold. But why does it have to keep demonstrating itself, as if compelled to?

tldr: if you have a peircian hammer, everything looks like a peircian nail


and if youre smart to boot, really perfect that hammer

then

The thing I really wanted to focus on was the "has to explain" part. As in "An atom already has to explain why it endures in "uncuttable" forever fashion." — csalisbury

Well, the argument is that metaphysical reasoning says it is one thing or the other. Either the stability the material parts is fundamental, or instead it is their dynamism that is fundamental. So we have two competing hypotheses. And we would ask which delivers the more complete ontology we are seeking?

So both views have something they must explain. A foundational assumption of stasis has to then account for the possibility of flux. An assumption of foundational dynamism has to then account for the emergence of stability.

I was saying no more than that.

Except that atomism also has to explain how the void could arise, how its localised form would endure, etc. It is already a complex ontology. And as I say, in particular, folk take the unwarranted view that to endure forever unchanged is something natural and not in need of explanation.

So we can easily trip up the atomists by saying that their search for an explanation failed by their own lights - they stopped too soon, and without realizing that they were being false to their own, implicit, ontological/methodological directives. — csalisbury

But I also say that the world - at the very cold and expanded scale that supports our own being in the Cosmos - is fairly accurately described by atomism. As an ontology, it really works for us.

It is only because we can no go deeper in terms of the observable that we might want to reconsider - get back to the kind of holistic ontologies we have been ignoring since Anaximander.

When you talk about Peirce, it seems like you're talking about the terminal state of a certain way of looking at things. It seems quite refined, and finished. But why should I think this represents a core metaphysical truth rather than a completed way of thinking about the world? The final formalization of 'explanation' maybe. — csalisbury

Isn't terminal the new foundational here? And the reason I see Peirce as metaphysically complete is the ontology is the epistemology. He started with the logic, the reasoning method, that makes the world intelligible to us. And then realised that the same logic was what made the Cosmos intelligible to itself - the way it developed its own rational state of being.

So it is an epistemology that works as that is how the ontology itself works. And we "know" that because modelling the reality that way is what works.

Neither our minds, nor the Universe itself, could escape the essential simplicity of the symmetries of a sphere. Neither epistemology, nor ontology, gets a choice about what we discover to be the mathematical or rational strength essentials of existence.

Now many folk don't like that kind of totalising talk. But let's see their counter-argument against the structural facts.

That's a sad achievement though, isn't it? Why would that minimisation be an 'achievement'? What's left, after that achievement? But to trumpet the achievement? louder at first, then softer. But trumpeting nonetheless. because there's nothing left anymore, but to.... — csalisbury

Huh? So now you want to play the unsatisfied totaliser?

If I say - as part of my univocal metaphysics - that certainty only asymptotically approaches its limits - then you say, well, that ain't good enough for you. The glass that is 99.999...% full is, gulp, sad.

Maybe you prefer complete mystery or radical uncertainty to my story of things only ever being "almost sure". Takes all sorts.

So my reasonable sentence above ("This is red to speakers of English") turns out to be an explanation of how the word "red" is used, not an explanation of how perception works. — Srap Tasmaner

But you added here the constraint of a particular language. And there is no warrant for it's addition - given you agree about the evidence from anthropology.

So if we say speakers of a shared language with a shared neurology, that would cover off both the cultural and biological factors involved here. We wouldn't get hung up on either distinction by becoming overly specific and thus nonsensical.

But Whorfianism does still apply. Redecorating our house, I discovered the infinite number of shades of white. I learnt a language that did anchor the memories that allows me to make more reliable hue discriminations.

So that was a controversy presented as a black and white story (by Whorf, not Sapir). Either social constructionism was the case, or biological determinism. And the actual story is that both levels of semiosis are constraints on our habits of interpretance. Quite a different psychological model - like a Vygotskian sociocultural one - is needed to capture the connection between nature and nurture.

tldr: if you have a peircian hammer, everything looks like a perician nail — csalisbury

Your view. My view was formed by encountering the fundamental problems of neurocognition and philosophy of mind, then finding Peirce sorted out the epistemology/ontology for life and mind in general. And for 20 years, biosemiosis has been roaring away.

So if we must do battle by cheap metaphor, why not say Peirce is the key that unlocks every door, or the language that expresses every thought? Who said rhetoric was dead.

And the actual story is that both levels of semiosis are constraints on our habits of interpretance. — apokrisis

That's the lines I was thinking along, but it's hard to say "When you talk about concepts you're also talking about how we use words" (details to be filled in) without it coming off as "When you talk about concepts you're only talking about how we use words." (And to top it off: when you talk about things, you're only talking about "our" concepts of things. Yuck.)

This tangent is strangely on-topic.

So if we say speakers of a shared language with a shared neurology — apokrisis

Should have addressed that. The full version is: "If you don't know that's red, either you don't speak English or there's something wrong with you."

Isn't terminal the new foundational here? And the reason I see Peirce as metaphysically complete is the ontology is the epistemology. He started with the logic, the reasoning method, that makes the world intelligible to us. And then realised that the same logic was what made the Cosmos intelligible to itself - the way it developed its own rational state of being.

So it is an epistemology that works as that is how the ontology itself works. And we "know" that because modelling the reality that way is what works.

There's a difference, though, between works-because-it-establishes-some-relation-with-the-outside and works-because-it-totally-captures-the-outside.

Think of it - logic-genius (which I'm sure he was) tussles with logic for a long time. Then he realizes this logic he's been tussling with is part of the fabric of the universe itself. A strange and beautiful revelation. How does he see the world now, the parts of it he allows himself to confront? Through what lens does he view it.? Does he or does he not edge the fragments of the world he experiences toward this or that aspect of his solitude-won system?

Isn't terminal the new foundational here?

Yes, exactly.

If I say - as part of my univocal metaphysics - that certainty only asymptotically approaches its limits - then you say, well, that ain't good enough for you. The glass that is 99.999...% full is, gulp, sad.

My metaphor wasn't about the fullness of the glass. It was more like: its sad to drink alone, at the end of the world.

Your view. My view was formed by encountering the fundamental problems of neurocognition and philosophy of mind, then finding Peirce sorted out the epistemology/ontology for life and mind in general. And for 20 years, biosemiosis has been roaring away.

So if we must do battle by cheap metaphor, why not say Peirce is the key that unlocks every door, or the language that expresses every thought? Who said rhetoric was dead.

No, I'm sure you're smarter than me, and I mean that.

But

"The language that expresses every thought" is....

"The key that unlocks every door"

I don't want to drag you into tawdry battles you'd normally avoid, but these kinds of metaphors....How do we fold peirce upon himself, in order to talk about unlocking everything or expressing everything through reference to one thing?

The full version is: "If you don't know that's red, either you don't speak English or there's something wrong with you." — Srap Tasmaner

Being pedantic, is that the fullest version? It could be the case that you both don't speak English and you are also not neurotypical.

So I prefer my: "If you know that's red, you both speak English and there's nothing wrong with you in the neurotypical sense."

That better reflects the holism of what I mean - the fact that this is semiosis doubled up.

There's a difference, though, between works-because-it-establishes-some-relation-with-the-outside and works-because-it-totally-captures-the-outside. — csalisbury

Well doesn't regular logic depend on the commitments of an object-oriented ontology? Don't the laws of thought seem to work because they get something unarguably right - if you believe in the counterfactual definiteness of individuated objects that possess sets of properties?

Reductionism believes it describes a reductionist reality.

And remember that Pragmatism accepts upfront that it is only telling stories about the world. That is why I said it can only then minimise our uncertainty about our models of reality. It is totalising only in Pragmatism's usual falsification-seeking fashion. We are setting things up so that we could know that we were wrong.

Does he or does he not edge the fragments of the world he experiences toward this or that aspect of his solitude-won system? — csalisbury

Yes. But experimentally verified.

After all, Peirce said reality is propensity-based, for instance. Chance is fundamental. And then shortly after, along came quantum mechanics.

He also proposed experiments to see if space was curved before general relativity came along. He wasn't just some armchair metaphysician. He had a day job with the US Coast and Geodetic Survey working on the actual basics of scientific measurement, like defining the standard metre.

It was more like: its sad to drink alone, at the end of the world. — csalisbury

It's true of Peirce that he was very much drinking alone. Most of his writings were never published. Although CI Lewis sat in a pile of them and Peirce's influence seeped through Ramsey to Wittgenstein and others in ways only recently reconstructed.

I don't want to drag you into tawdry battles you'd normally avoid, but these kinds of metaphors....How do we fold peirce upon himself, in order to talk about unlocking everything or expressing everything through reference to one thing? — csalisbury

My point was that metaphors do nothing here. I am happy just to stick to actual arguments.

And yes, my argument is that a triadic relational logic is a universal mechanism. It unfolds every complexity into its greatest possible simplicity ... which is still always complex in being relational and hence triadic.

You seem to think we can get somewhere discussing the sadness or brilliance of Peirce rather than the validity of semiotic structuralism. I am always happy to discuss his character. But also, it is irrelevant to the argument. I wasn't arguing from authority, just citing my sources.

Are transfinite cardinals or ordinals natural kinds? Are categories natural kinds? What about partially ordered sets or finite fields? — fdrake

I'd say that yes, those are examples of natural kinds. As Frege would say, they have all passed the "acid test" of concepts, namely their fruitfulness.

I prefer to read it as the evolution of a concept whose boundaries are fuzzy - something like a composite of continuity/differentiability/IVP - becoming more demarcated when the level of mathematical precision was elevated through the emphasis on axiomatisation. I don't see what insisting that mathematical objects are real does to help someone actually doing/teaching maths (the community thereof + history is where mathematics comes from). — fdrake

I have the opposite idea. I think the semantics of mathematical kind terms is very similar to the semantics Kripke-Putnam sketched for scientific natural kind terms, in the sense that mathematical kind terms are (primarily) non-descriptive, i.e. their semantic value is their reference. That is why we can say that Euler and Cauchy were mistaken in (e.g.) treating convergence as uniform convergence (yes, I'm aware that the historical debate here is controversial). So, according to my story, it's not that we started with fuzzy, open-texture concepts and proceeded to precisify them; rather, we started with a collection of examples and proceeded to unveil their structure. Of course, this story needs to fleshed out, and fleshing it out is one of the projects on which I'm currently working.

I don't know if this narrative would have pedagogical value, though, it seems to me, it's almost the standard narrative that you will find in typical history books (say, Stillwell's famous one), just not articulated like this. Be that as it may, I think there's a real philosophical gain here, since, in my opinion, it does better justice to the mathematical practice of starting from examples and then generalizing (as we can see with the history of continuity, algebraic integers, group theory, etc.).

If the questions is 'what makes the tokens stick together in the type' - why isn't 'they're used together with some commonalities between them' a sufficient answer? Something like 'I see red' and 'I see red', if there's an underlying redness it better also reference anger; 'red' is a lot more complicated than 'redness' in the colour. Where do you get the ontological or epistemic resources to glue tokens together relationally? Also, how's this furnished through there being an abstract object or natural kind to save us and instantiate itself? — fdrake

In some cases, I do think there may be enough structural commonalities to ground the existence of the type, but in general these commonalities won't be acceptable to a nominalist-about-properties. And in some cases there may be superficial commonalities that are acceptable to a nominalist-about-properties but which don't correspond to anything structural, and hence don't form a natural kind (say, the case of jade, which is not a natural kind). So the ontological resources come from accepting both structures and properties as bona fide entities. Types come in with that.

As for the epistemic resources, the story is more complicated, because we need (as per Kripke) to distinguish epistemic possibility from metaphysical possibility. To give Kripke's example, given that tigers are mammals, they are (metaphysically) necessarily so. On the other hand we might discover in the future that tigers are really well-crafted robots, made by an alien space to test us in some way. This is an epistemic possibility, i.e. for all we know we could be wrong about tigers. Of course, if we are not wrong, then this epistemic possibility doesn't correspond to any real (metaphysical) possibility.

Another aside, I'd be quite surprised if there wasn't an equivalence relation approach to tokens and types here, in terms of exemplifications. Like in the construction of fractions. 2=1+1=4/2=...(every other possible expression for 2), then the number 2 is defined as [2], that set of expressions which evaluate to 2. And arithmetic is defined in terms of operations on equivalence classes rather than on their constituent terms (this is why algebraic substitution works). Thus simultaneously every object exemplifies the type. — fdrake

There are many things to discuss here. Roughly speaking, when abstracting from equivalence relations, there are three possibilities: (i) either you take a canonical representative the class to be your "abstracted" object (if memory serves me correctly, that's Kronecker's approach to quadratic forms, because you can use the canonical representative as a calculation tool); (ii) you take the equivalence class itself as the "abstracted" object (in some cases, such as when dealing with quotients, this may be the only sensible option); (iii) or you introduce a new object corresponding to the abstraction (that's what Dedekind opted for when he introduced his cuts; he explicitly rejected Weber's suggestion of simply identifying the real numbers with cuts, preferring instead to say that each real number corresponded to a cut; this is also the neo-Fregean way).

Generally, option (iii) gives a cleaner theory, in the sense that you don't end up with "junk" theorems such as "2 is an element of pi" or whatever (Dedekind mentioned this as one of his reasons for preferring (iii)). I myself was attracted to some kind of abstractionism that introduced abstract objects via equivalence relations. Unfortunately, there is a catch here: if you allow for too many abstraction principles, you end up with an inflated ontology (this is a real problem: Kit Fine has shown that the resulting theory may be inconsistent---cf. his very interesting The Limits ob Abstraction). So you need some way to select which equivalence relations give rise to abstracta and which doesn't. The most appealing way of doing this is to appeal to natural equivalence relations. But then you need to explain what it is for an equivalence relation to be natural (or you could take Lewis's route and consider "naturalness" a primitive, but I don't think that's very satisfactory). And I think that when you do so, it may open the door to use naturalness itself as a ground for the existence of abstract objects, bypassing the appeal to equivalence relations.

Not the intention, the fact of it being asserted to be so (and not: 'the fact of it being asserted to be so'). — StreetlightX

So if you didn't assert it, it wouldn't be so? And what is a fact?

I need to respond to this in more depth in a bit, but I don't see why this would pose any problem, in principle, to a treatment in terms of metalinguistic illustration: there is a way of speaking about an x, such that, when the thing so designated an x dissolves in water, we call x soluble. And to learn this way of speaking, is to understand just that language game involving certain rule-governed correlations between linguistic and non-linguistic objects. — StreetlightX

That may be so (though note that we have an appeal to types of rules here...), yet to learn this way of speaking is not to learn Jumblese.

In other words: Any property is susceptible of being indicated through a simple notation, and any property also harbors a complexity which comes out in explication and usage (I think that's the significance of the 'myth of the given' - things aren't simply 'given' because to know what something is requires having some minimal ability to explicate) — csalisbury

I definitely agree with this, in that I'd hold that most properties that appear simple aren't really simple (I was just agreeing that, even if redness or triangularity are simple, there are other properties that aren't obviously simple). Of course, they can't all be complex, since any theory must have its primitives. So there is a distinction here to be made.

My only disagreement is that I don't think (Carnapian?) explication is what is doing the work here---rather, I think just plain explanation is. We are not explicating a usage, we're explaining the structure of the world.

I'd say that yes, those are examples of natural kinds. As Frege would say, they have all passed the "acid test" of concepts, namely their fruitfulness.

It's strange to me that whether something is natural, rather than reflects what is natural, depends on their role in discourse. I can make sense of this if 'is a natural kind' is interpreted like 'is a useful model', but abstract objects like categories and transfinite cardinals are not, currently, a model of anything physical but themselves as interpreted as discursive formations.

Physicists think about things quite differently from mathematicians. The former should principally be dealing with mathematical objects that reflect nature or simplify previously established theories of nature. The latter deal with mathematical objects simpliciter. Like physicists taking the real part of imaginary quantities because real quantities aren't imaginary - pedagogically this is the mantra 'take the real part to find out what's real'. Or looking at bouncing as a geometric series - the mathematician would say 'infinite bounces are required to stop bouncing', the physicist says 'that isn't physical, it will stop at some point despite the model'. This 'despite the model' is a big difference between mathematical quantities qua physics and mathematical quantities qua mathematics. In mathematics it's only the model and the properties - with some imaginative background which is reflected to make it a model. In physical uses of mathematics the imaginative background mirrors, represents, tracks, call it what you will, the world.

I have the opposite idea. I think the semantics of mathematical kind terms is very similar to the semantics Kripke-Putnam sketched for scientific natural kind terms, in the sense that mathematical kind terms are (primarily) non-descriptive, i.e. their semantic value is their reference. That is why we can say that Euler and Cauchy were mistaken in (e.g.) treating convergence as uniform convergence (yes, I'm aware that the historical debate here is controversial). So, according to my story, it's not that we started with fuzzy, open-texture concepts and proceeded to precisify them; rather, we started with a collection of examples and proceeded to unveil their structure. Of course, this story needs to fleshed out, and fleshing it out is one of the projects on which I'm currently working

Regarding the history - it's really a methodological distinction. Do you prefer to read the history retrospectively from the current heights of modern insight, or do you prefer to try to look at it as it developed? I'm quite sure that there's a reading either way in terms of non/nominalism that furnishes it with some historical weight. The former looks to me like a history of mistakes, the latter looks to me like a history of expressive writing. Prefer the latter, it makes the mistakes interesting.

I don't agree that mathematical terms are primarily non-descriptive, mathematics concerns itself with the relationships of abstractions and sometimes abstractions to real world. To me this seems like saying 'logic doesn't describe anything because its elements are just a universe of discourse'. Put another way in a series of examples, the interesting things about a group aren't the underlying set - hence group theory. The interesting things about topologies aren't the underlying set - hence topology. The interesting things about their intersection isn't the underlying set - it's algebraic topology, all those loops and holes and shit. A group just is something which satisfies its axioms - something which functions in the specified way.

Mathematical abstractions, in terms just of their reference, are usually 'part of the background' when studying or producing new maths. Expertise allows you to adjoin some of their description to their reference - hence 'trivial' and that mathematical papers usually aren't written as logically valid arguments -. This scoping context reflects the use of the abstractions, and which things may be considered constitutive of them will depend on the context of the math. This is also part of what makes it so hard for people in different sub-(sub-sub-sub-...-sub)fields to communicate, and interdisciplinary work so insane (and interesting).