I think it's kind of the opposite, as I see it: we see imperfect triangles all the time, which makes us think of triangles (which are perfect in our minds). You could perhaps say that imperfect triangles are a kind of derivative of mental triangles.



Absolutely nothing. T'was a hit and miss.

Have you come up with anything in that respect....from scratch? — Mww

You mean something no one else has? I don't know. The odds are against it, of course. But it's more fun, for me anyway. And it means that when I reach for an argument it's because it persuades me, not because I recall that Hume said it, even if I learned it from Hume and have forgotten that I did. (When you do mathematics, it's not generally important where you got the argument, but that it works.) It also means I have the experience of reading works of philosophy and finding on the page thoughts I have already had; having already worked through something, knowing some of its ins and outs, provides a framework for seeing what another thinker does with it.

Should I actually be defending thinking for myself here? Or were you making some point about the conceptual scheme I ought to admit I'm stuck with?

I would not be surprised if there were cases of people who lacked the capacity to visualize such elementary figures — Manuel

That part is just fact, I understand, as there are people who have no visual imagination. I heard an interview with one such person who works as a professional animator.

That's a good point, but is it any use? If there's no criterion for membership, then the class you create is arbitrary, isn't it? — Srap Tasmaner

It seems that I could in principle define a part of the ball that constitutes the ball's particular red color. That part would be a subcollection in the ball, a subcollection whose structure interacts with light in such a way that it reflects certain wavelengths of light, and I could define this subcollection by enumerating its parts. My point is that a particular instance of a universal is a particular collection. According to set theory, any mathematical universal can be instantiated as a collection.

I think it's kind of the opposite, as I see it: we see imperfect triangles all the time, which makes us think of triangles (which are perfect in our minds). You could perhaps say that imperfect triangles are a kind of derivative of mental triangles. — Manuel

I don't see what "perfection" has to do with universals anyway. What would it mean for a universal tree to be "perfect"?

Should I actually be defending thinking for myself here? — Srap Tasmaner

If you’re doing philosophy, you are thinking for yourself. No need to defend it. If you’re speaking from exegesis, as I readily admit for myself, you’re merely philosophizing.....which I also have to admit.

Or were you making some point about the conceptual scheme I ought to admit I'm stuck with? — Srap Tasmaner

Truthfully, I wouldn’t have any warrant to do that; I don’t even know whether you consider yourself operating under that condition. I might suggest.......er, you know, from my own exegesis.....that every human does, but, there is no proof for it, so.....

Still, if you’re going to come up with properties “from scratch”, that sorta implies thinking for yourself, which in turn implies some sort of conceptual scheme you’d obviously be stuck with.

Just curious, that’s all.

I heard an interview with one such person who works as a professional animator. — Srap Tasmaner

:rofl:

That's extraordinary.



I think mathematical conceptions are different in nature than world phenomena. A perfect tree does not exist of course, but Plato had an interesting take on this.

Just curious, that’s all. — Mww

See, that's what threw me off.

Mww, is Mww.

He's great! :)

I don't see what "perfection" has to do with universals anyway. What would it mean for a universal tree to be "perfect"? — litewave

For a triangle perfection may be linked to ideal self-identical repetition of the pattern. For a line or angle to be perfect, it would have to conform to an iteration of an exact self-identical procedure.

Hey.....always lookin’ for a different way of lookin’.

And no, I didn’t send tickets to his favorite Vegas show to post that comment.

That's extraordinary. — Manuel

Right? I believe he said he just doesn't picture the drawing before doing it, but that working on a drawing is otherwise straightforward. Still...

It seems that I could in principle define a part of the ball that constitutes the ball's particular red color. That part would be a subcollection in the ball, a subcollection whose structure interacts with light in such a way that it reflects certain wavelengths of light, — litewave

Is there a difference in principle between a simple looking predicate like "is red" and a complicated looking predicate like "whose structure interacts with light in such a way that it reflects certain wavelengths of light"? I don't see how you allow yourself the latter if you can't allow yourself the former.

Anyway, there's no trace here of your proposed resemblance relation. You're just reducing gross properties to microstructure. You don't need resemblance to do that.

According to set theory, any mathematical universal can be instantiated as a collection. — litewave

It doesn't matter much in practice, but of course we *don't* have the axiom of comprehension because of frickin' Russell and his damned paradox.

Did you mean something else?

Is there a difference in principle between a simple looking predicate like "is red" and a complicated looking predicate like "whose structure interacts with light in such a way that it reflects certain wavelengths of light"? — Srap Tasmaner

No, both predicates refer to the same property of redness, the second predicate just elaborates what it means to be red.

Anyway, there's no trace here of your proposed resemblance relation. — Srap Tasmaner

I just identify a universal with a resemblance relation and thus simplify the metaphysical picture: instead of (1) a universal, (2) an instantiation relation between a universal and a particular, and (3) a resemblance relation between particulars, we would have just a resemblance relation between particulars.

both predicates — litewave

That was my point. You're supposed to be grounding the use of predicates, aren't you? Or was your intention all along to ground some kinds of predicates in other kinds?

I just identify a universal with a resemblance relation and thus simplify the metaphysical picture — litewave

I know what you say you're doing. It's just not what you're doing. Unless I've missed something.

That was my point. You're supposed to be grounding the use of predicates, aren't you? Or was your intention all along to ground some kinds of predicates in other kinds? — Srap Tasmaner

But they are the same predicate, just in different words. "To be red" means "to reflect certain wavelengths of light".

Then forming your collection by using that predicate presumes you have access to a whole machinery of predicates, membership, and classes. I thought we weren't going to do that, but ground our use of predicates in the resemblance of things to each other.

Instead you're just analyzing one sort of predicate (color) in terms of others (microstructure). Nothing at all to do with resemblance.

ground our use of predicates in the resemblance of things to each other. — Srap Tasmaner

So, for example there is a resemblance relation between two red particulars in the sense that they are both red. Sure, there is a circularity or primitiveness in this account of resemblance relation, but so is in the account of universal redness and its instantiation. So I drop the universal and instantiation and just leave a primitive resemblance relation, as a simpler account of resemblance.

So you intend to keep "is red", for instance, so that we get to say A resembles B because they are both red. That just makes the resemblance relation entirely derivative of predication: predicate F of two objects, and poof they resemble each other. If I say that predication is constituted by the instantiation of universals, you have exactly the same resemblance relation, and its existence is no challenge at all to the universals account of predication. Resemblance is merely a consumer of predication, not a producer.

If I say that predication is constituted by the instantiation of universals, you have exactly the same resemblance relation, and its existence is no challenge at all to the universals account of predication. — Srap Tasmaner

Yes but then you have two additional entities (a universal object and an instantiation relation) that are primitive and purport to explain the resemblance relation: poof there is a universal and poof it is instantiated in the particulars. Those two additional entities seem redundant.

Okay, I think I get how you're thinking now. Your idea is that we start with the phenomenon of resemblance, explain that in terms of predication, then explain predication in terms of universals. You want to cut off the last step, but you keep saying it means taking resemblance as more fundamental: it means no such thing; you're still explaining resemblance using predication, you just want to take predication as primitive.

You can do that, but you need to argue for it, and you ought to quit talking about resemblance, which is apparently of no interest to you.

How many resemblance relations are there? Just the one? Or (e.g.) one for each property?

I see what you're trying to say, but you can't say "part" because parts are concrete rather than abstract exactly in the sense that they can exist independently. (That much I learned from Andrew M's explanation of hylomorphism.) And you really shouldn't be saying "collection" because that's a soft word for "class" and you precisely can't have classes without universals or predicates to define them. Clearly you're hoping to get structure — which is crucial, particulars aren't bags of properties — out of how the various collections are arranged.

Stepping back, this begins to sound like breaking down an object into its fundamental particles and then reassembling it, down the chain through chemistry to quarks and then back up again. We assume such a thing is possible in principle, I guess, but the argument for special sciences has always been that on the way back up, you have no way to know where you are and what you're building, so the particulars of interest are gone forever, leaving just an undifferentiated sea of particles. — Srap Tasmaner

Nicely put. I think this also relates to Gilbert Ryle's examples of category mistakes. The color of a ball is not reducible to the ball's machinery, so to speak, but neither is it therefore a ghost. As Ryle puts it in Thinking and Saying, this is the way by which "an Occam and a Plato skid into their opposite ditches."

A foreigner watching his first game of cricket learns what are the functions of the bowlers, the batsmen, the fielders, the umpires and the scorers. He then says ‘But there is no one left on the field to contribute the famous element of team-spirit. I see who does the bowling, the batting and the wicket-keeping; but I do not see whose role it is to exercise esprit de corps.’ Once more, it would have to be explained that he was looking for the wrong type of thing. Team-spirit is not another cricketing-operation supplementary to all of the other special tasks. It is, roughly, the keenness with which each of the special tasks is performed, and performing a task keenly is not performing two tasks. Certainly exhibiting team-spirit is not the same thing as bowling or catching, but nor is it a third thing such that we can say that the bowler first bowls and then exhibits team-spirit or that a fielder is at a given moment either catching or displaying esprit de corps. — Concept of Mind - Gilbert Ryle

Abstract, "pure mathematics" shows that we dream up universal principles (axioms) first, from the imagination, or they come to us intuitively, then we try to force the particulars of specific circumstances to be consistent with the universals. — Metaphysician Undercover

That's at least in the neighborhood of Sellars's argument and the impasse I expected to reach, that empiricism from a blank slate can't actually get started. — Srap Tasmaner

MU makes a good point regarding some highly abstract mathematics. I'll tell the story again of a PhD student writing a fine looking thesis about a certain class of functions, but when asked to illustrate the class by a specific example discovered the class was the empty set.

Your idea is that we start with the phenomenon of resemblance, explain that in terms of predication, then explain predication in terms of universals. You want to cut off the last step, but you keep saying it means taking resemblance as more fundamental: it means no such thing; you're still explaining resemblance using predication, you just want to take predication as primitive. — Srap Tasmaner

Ok, how about this:

The predicate "is red" refers to the resemblance to an arbitrary red particular, instead of referring to the instantiation of the red universal. The resemblance relation among red particulars could then be defined as mappings among parts of the structures of the red particulars.

Ok, but I am saying that these "universal principles" are just resemblance relations between particulars rather than additional entities (universals) that instantiate in the particulars. — litewave

But in saying that, you are already assuming the existence of particulars. And by taking the existence of particulars for granted, you do not consider the process whereby we individuate particulars from the universe, in your representation, and this skews your perspective.

If you step back and take a better look, you'll see that the real problem is the question of individuation, by what principle do we say that this is a separate entity from that, as a particular, or individual. If you do this, then you'll see what was evident to the ancients whom I mentioned, that the universal is necessarily prior to the particular. Therefore your whole question, or starting point, as the issue of how we produce universals from particulars is based in a complete misunderstanding of reality.

How? — litewave

You don't see how this produces an infinite regress? If a concrete particular is a collection of concrete particulars, then each concrete particular in that collection is itself a collection of concrete particulars, and each concrete particular in that collection is itself a collection of concrete particulars, ad infinitum.

t seems that I could in principle define a part of the ball that constitutes the ball's particular red color. — litewave

See, look what you are doing here. You are individuating, separating out "a part of the ball", and passing judgement, to make it into a particular thing which you can refer to. But at the same time, you want to take it for granted that particulars have already been individuated, and we proceed from those particulars to produce universals.

Once you accept that a particular is produced from this sort of individuation, then you must see that the way that a human being produces universals is completely dependent on the way that one produces individuals. So we cannot proceed toward understanding how one produces universals, unless we first produce an understanding of how one produces individuals. If we take the existence of individuals for granted we cannot get anywhere.

So, for example there is a resemblance relation between two red particulars in the sense that they are both red. — litewave

So, let me explain, using this example. If the two supposed "particulars" are both the same in the sense of red, then why would you say that they are two, and not one instance of "red". If they are different shades of red, or something like that, then there is nothing to support saying that they are both the same colour, red. If they appear to be the exact same colour, then whatever it is which separates them as two distinct particulars, must be something other than colour. But how could it be that two exactly the same instances of colour could come to exist under completely distinct circumstance? Wouldn't they have been originally one thing which got divided? Any way you look at it, we would have to conclude that there is something "the same" about the circumstances, something underlying, which is truly the same, which could produce the exact same colour in two completely different situations. And if we say that the colour is not really exactly the same, it is only similar, then we have no reason to say that they are both the same colour, "red". Therefore we must conclude an underlying sameness as the reason why they are both red, or else saying that they are both the same colour, "red", is completely unjustified.

(Thanks for the notes on the ancients, btw.) — Srap Tasmaner

I appreciate someone who is receptive to different perspectives. I think that's what philosophy is made of.

You don't see how this produces an infinite regress? If a concrete particular is a collection of concrete particulars, then each concrete particular in that collection is itself a collection of concrete particulars, and each concrete particular in that collection is itself a collection of concrete particulars, ad infinitum. — Metaphysician Undercover

Yes, that's how I think each particular is constructed. Except that there may be empty collections (non-composite particulars) at the bottom instead of infinite regress. But even if there was infinite regress I am not sure that would be a problem, as long as the whole (infinite) structure was logically consistent.

If they appear to be the exact same colour, then whatever it is which separates them as two distinct particulars, must be something other than colour. — Metaphysician Undercover

Yes, they have a different location and thus different relations to the rest of reality, which makes them two different particulars which however resemble in the sense that they are red. In a special case they could also have exactly the same internal structure (from empty sets upward), but that is not necessary since particulars with different structures can be red as long as their structures are such that they reflect light of the same wavelength.

Any way you look at it, we would have to conclude that there is something "the same" about the circumstances, something underlying, which is truly the same, which could produce the exact same colour in two completely different situations. — Metaphysician Undercover

There is an underlying sameness but I am not sure that there would need to be a single object (universal) to "produce" the resembling particulars. The particulars could resemble each other because their structures resemble each other. For example, two empty collections could resemble each other because they have no structure and not because there is a universal empty collection that produces particular empty collections.

Yes, that's how I think each particular is constructed. Except that there may be empty collections (non-composite particulars) at the bottom instead of infinite regress. But even if there was infinite regress I am not sure that would be a problem, as long as the whole (infinite) structure was logically consistent. — litewave

How could there be a concrete entity which is an empty collection of parts? That makes no sense logically, an infinite number of zeros does not make one. The issue with infinite regress, is not that it is not logically consistent, because maintaining logical consistency with unsound premises is what produces infinite regress. So the appearance of infinite regress is an indication of unsound premises. This is because the result of infinite regress is that it renders the thing described by the unsound premises as unintelligible due to the infinite regress. Therefore such premises must be considered irrational because they presuppose that the thing to be understood cannot be understood because an infinite regress (therefore unintelligibility) is accepted as the truth, instead.

Yes, they have a different location and thus different relations to the rest of reality, which makes them two different particulars which however resemble in the sense that they are red. — litewave

That they are both the same, with the same name "red" is an unjustified conclusion under this description. As you yourself say the instance of colour here is a distinct particular from the instance of colour over there. So the proper logical conclusion is that it is incorrect to say that they are both the same colour, you have stipulated that they are different. The idea that there is a resemblance relation between them just comes about from your refusal to accept the true conclusion that they are completely distinct. You deny the reality of the logic, that if they are not the same, they must be different, and so you propose some sort of compromised sameness "resemblance" instead. But this principle is not supported by empirical evidence, nor logic, it's just a product of your denial, a sort of rationalizing, which is really irrational.

There is an underlying sameness but I am not sure that there would need to be a single object (universal) to "produce" the resembling particulars. — litewave

I think you need to respect the meaning of "same" as described by the law of identity. "Same" means one and the same, "a single object". "Similar" has a completely different meaning, as it implies distinct things, rather than one thing, as "same" does. So if there is an "underlying sameness", this means that there is one and the same thing which underlies the two distinct instances, such that they are multiple occurrences of the same thing, just like two distinct occurrences of "now" could be said to have the same underlying thing, time. But two similar things do not require any underlying sameness, just a judgement of "similar", which could be based in any sort of assumption. If we say that two instances of "now" are similar, rather than having an underlying "time" which makes them two instances of the same thing, then we might employ any arbitrary principle whereby we would say that they are "similar". But this judgement of "similar" is completely arbitrary.

How could there be a concrete entity which is an empty collection of parts? — Metaphysician Undercover

It would be a concrete entity without parts. Some people may think that elementary physical particles are such entities but I suppose that they do have parts/structures that give them their different properties.

So the appearance of infinite regress is an indication of unsound premises. — Metaphysician Undercover

Mathematics is full of infinities and it doesn't mean that it is unsound although infinities can be pretty mind-boggling. Then there is also Godel's second incompleteness theorem which I don't know exactly what it means but it says something in the sense that if a consistent system is complex enough to include arithmetic and thus involve infinities it is impossible to prove that it is consistent. So we may never know whether arithmetic is consistent.

As you yourself say the instance of colour here is a distinct particular from the instance of colour over there. So the proper logical conclusion is that it is incorrect to say that they are both the same colour, you have stipulated that they are different. — Metaphysician Undercover

They are two different particulars that are the same in the way that they are red. When two objects are the same it means that they are also different in some way because if they were the same in every way then they would be one object and not two.

I think you need to respect the meaning of "same" as described by the law of identity. "Same" means one and the same, "a single object". — Metaphysician Undercover

The word "same" is also used to refer to two or more different objects that are the same in every relevant way but not in every way (for example not in their location in reality). So that's how I used it when I said that two red particulars are the same in that they are red.

So if there is an "underlying sameness", this means that there is one and the same thing which underlies the two distinct instances, such that they are multiple occurrences of the same thing — Metaphysician Undercover

Ok but for example, what is the underlying thing that underlies all circles? One thing is clear: it does not look like a circle at all because if it looked like a circle it would be a particular circle and not a universal one. A particular circle is continuous in space but a universal circle would not be because it is not supposed to be located in some continuous area of space. A universal circle looks more like a recipe how to create all possible circles from an arbitrary particular circle: first define a particular circle by specifying all points on a plane that are the same particular distance from a particular point and then create additional objects by translating, rotating or scaling (enlarging/shrinking without deformation) this particular circle and you can call all those additional objects "circle" too. And they all resemble each other in the way of being a circle because any of them can be mapped onto any other via the relation of translation, rotation or scaling, and no other object can.

It would be a concrete entity without parts. — litewave

No, it would not. It would be a collection of parts without any parts. That's what your statement was, "empty collections". Your assumption that this could constitute a concrete entity is unfounded, because concrete entities as we know them actually have parts. The appeal to fundamental particles does not help you because they are obviously not known as concrete entities.

Mathematics is full of infinities and it doesn't mean that it is unsound although infinities can be pretty mind-boggling. — litewave

I've argued in numerous places on this forum that such mathematics actually is unsound. Soundness consists of truthfulness, and pure mathematics has no respect for truthfulness. So...

They are two different particulars that are the same in the way that they are red. — litewave

But "same" is the relationship which a thing has with itself. So if two distinct things are "the same" with respect to being red, then the concept of "red" cannot be a resemblance relation, which is a relationship of similarity, it would be that the two things both partake in one and the same thing, the concept "red".

When two objects are the same it means that they are also different in some way because if they were the same in every way then they would be one object and not two. — litewave

You are not respecting the law of identity. Two distinct things cannot be said to be the same, as you suppose here. If they are said to be "the same", then they are said to be one object not two. "Same" is reserved for the relationship a thing has with itself. So you are talking about being the same, in one specific way.

They are two different particulars that are the same in the way that they are red. — litewave

As I explained above, if they are the same with respect to being red, then being red means the very same thing for each of them, and this cannot be construed as a resemblance relation, which would imply that they are similar with respect to being red, not the same. If they are the same with respect to being red, then we might say that they both partake in one and the same thing, the concept red.

Ok but for example, what is the underlying thing that underlies all circles? One thing is clear: it does not look like a circle at all because if it looked like a circle it would be a particular circle and not a universal one. A particular circle is continuous in space but a universal circle would not be because it is not supposed to be located in some continuous area of space. A universal circle looks more like a recipe how to create all possible circles from an arbitrary particular circle: first define a particular circle by specifying all points on a plane that are the same particular distance from a particular point and then create additional objects by translating, rotating or scaling (enlarging/shrinking without deformation) this particular circle and you can call all those additional objects "circle" too. And they all resemble each other in the way of being a circle because any of them can be mapped onto any other via the relation of translation, rotation or scaling, and no other object can. — litewave

If it is the case, that "A universal circle looks more like a recipe how to create all possible circles", then I do not see why you want to describe this as a resemblance relation. A recipe, blueprint, or whatever you want to call it, in no way states a resemblance relation. And even if the blueprint, or production instructions end up producing similar things, this does not imply that the production instructions state a resemblance relation. The instructions make one set of statements, which if followed in action numerous times, will produce a number of similar things.