Is there any difference between a universal and a resemblance relation?
A universal is supposed to be a general property that is somehow instantiated/exemplified in particular objects (instances/examples) that have this property, which coincides with a particular resemblance relation among these particular objects. For example, redness as a universal is instantiated in particular red objects, which coincides with a particular resemblance relation among all red objects: they all resemble each other in the sense that they are all red.
But is there any reason why not identify the universal with the resemblance relation itself? What would be the difference between a universal and a multi-place (potentially infinite-place) resemblance relation? Note that I am not suggesting that a particular redness (an instance of general redness) is a relation; rather I would say that a particular redness is a quality (a non-relation), but that the general redness (a universal) is a relation.
But is there any reason why not identify the universal with the resemblance relation itself? What would be the difference between a universal and a multi-place (potentially infinite-place) resemblance relation? Note that I am not suggesting that a particular redness (an instance of general redness) is a relation; rather I would say that a particular redness is a quality (a non-relation), but that the general redness (a universal) is a relation.
Comments (83)
I'm not quite following.
Is the idea to drop the idea of instantiation?
But what are you going to do with universals if not instantiate them?
If that model has issues you want to avoid, then you just go for predicates (which you're already keeping) and their extensions.
The idea of *starting* from resemblance and building everything from that might be worth pursuing. (@bongo fury has some ideas about how to police the borders.)
But then you won't start out talking about universals.
Yes, the idea is to drop instantiation and replace a universal with a resemblance relation.
So the question is (1) whether resemblance, or similarity in some respect, or something like that, gets us everything we want from universals, and (2) whether such an account is coherent, non-circular, doesn't need to smuggle in universals somewhere to work.
Yes?
Right. And I assume we're talking about this logically, not psychologically. An account of, I guess, properties, rather than how we come to learn them, or think them up, and so on.
A theory of universals presumably has something to offer, is supposed to explain how something works or what something means. I haven't thought about universals in a long time (having gotten accustomed to predicates and such) but it would appear to be in the neighborhood of where you started, two numerically distinct objects both being red, for example.
We have to first see how this is a problem, right? The objects are distinct. Anything you pick out to describe a concrete object is a bit of that object, is that object minus almost everything about it except some particular aspect you've chosen. (Passing over how we do that, for the moment anyway.) At least, that's how I presume abstraction works.
So you take a ball and you imaginatively delete its location, its mass, the texture of its surface, everything but the light it radiates and you call that its color. (This is no good, of course, since it needs to be a propensity or a disposition, but we don't know whether we need to bother yet.) We do the same thing with some other object, maybe a car. If this is how we 'create', as it were, colors of things, by taking a particular and leaving out everything else, we still end up with just a partial particular.
What you get is still two numerically distinct abstract objects rather than concrete ones, yes? No matter how similar the abstract objects are, they are distinct. What could possibly entitle us to say that they are in any sense the same thing?
Now we might think identity of indiscernibles to the rescue! And now that we come to it, how did we imagine the sort of partial particular I described being a numerically distinct entity? It's not, after all; it's only an aspect of a 'genuine' concrete entity. Not even a part of it, but something that, obviously it seems, cannot exist on its own, but only as an aspect of something concrete.
No problem; we knew that as soon as we said we were creating an abstract object (the red of this ball) from a concrete object (this ball). But if it's no real objection that these things can't exist on their own, then we can't rely on their individual existence to underwrite their being numerically distinct. Maybe abstract objects can be numerically distinct, but if they can it's not the way regular concrete objects are.
Which leaves us where? We want to head toward saying these two abstract objects are the same or similar, but now it's not even clear in what sense they are objects at all, or whether they can be distinguished in order to be compared or identified. If these are objects, it's not clear what use they can be to us. We're in a muddle.
Abstraction looked so straightforward, but it seems to leave us nowhere.
So what do you think? We want an account of properties of objects, and we expect to be able to say that two objects have the same property, or that they have properties that are similar but not identical. But how do we fix our account of properties? Was my account of abstraction all wrong? Or are we in a better position than it seems?
Quoting litewave
I would say that the resemblance relation is dependent on the instances of a given general property - if there is no or if there is a single instance of such property, for example, there would not be a resemblance relation. The universal, on the other hand, I think, is independent of there being any instances of it. In the case of instances of red, for example, these instances are not found everywhere in space, and in addition their distribution in space changes; that is, the resemblance relation, although invariant relative to the total instances of red* is not invariant relative to instances of other properties, meaning that it cannot be potentially infinite-place (if I understand what you mean by this, correctly) since it is possible that in a given moment in time a point in space will not be red, excluding any chance of it being red**. In the case of redness, it is the fact that any point in space (or that there are points in space that) has/have the potential to be red. Thus, the resemblance relation requires that there are points in space that are red, and since their number and distribution is limited (not all points in space are red), the resemblance relation is also limited; on the contrary, redness requires that there are points in space that have the capacity to be red, independent of there being any red points.
*No matter the number or distribution of red instances, they will resemble each other in the fact that they are red.
**A potentially infinite-place resemblance relation, as I understand it, would mean that any point in space at any given time would have the potential to become red and part of the resemblance relation, which I do not think is the case since it is possible that any point in space at any given time is not red or will not be red - if a point in space is not red at a given time it is because at some previous time it was potentially not red. So, that a point in space has the potential to be red is not equivalent to a point in space having the potential to be part of the resemblance relation of red. A point has the potential to be red and never be red and thus never be part of the resemblance relation.
Actually, I would say that the partial particular, for example the particular redness of this ball, is a concrete part of the concrete whole (this ball). A concrete object is a collection of other concrete objects and there are various overlapping collections inside this collection. In the case of this ball, one of those overlapping collections is a particular red color because the structure of that collection is such that it reflects certain wavelengths of incoming light. Other collections inside the ball constitute the texture of the ball, the mass of the ball (the structure that interacts with other objects via gravitational force), and the ball as a whole (regardless of its internal structure) is a collection that is a sphere (a particular roundness). So I would say that the particular properties of a concrete object are overlapping parts (collections) of that object; their existences are mutually dependent on each other and the existence of the object as a whole is dependent on its parts. Perhaps even the object's location could be argued to be a particular property that is identical to the whole of the object (including its complete internal structure), because the whole constitutes the object's unique identity and thus determines its place in reality - all of the object's relations to all other objects. (And all relations between objects are resemblance relations determined by the objects' parts/particular properties.)
Just curious. Where did you get the idea for doing this?
I think that a general property without particular instances is an oxymoron because it is inherent in the meaning of "general" property that it is instantiated in "particular" instances. Also, a general property with only one particular instance seems to be an oxymoron because if such a property is instantiated in only one particular instance, why call this property "general" and not simply identify it with the particular instance?
Quoting Daniel
The resemblance relation I am talking about holds timelessly, among all similar objects that exist, have ever existed and will ever exist. (Actually, I would say that reality itself is timeless, in the sense that time is a special kind of space, as described by theory of relativity.) Also, I don't think that a non-red point of spacetime has a "capacity" or "potential" to be red; if such a point were red, it would change the definition of the spacetime that contains this point and so it would be a different spacetime, a different world, and the red point in this other world would be a different point than the non-red point in the former world. So it is not logically possible (consistent) for a non-red point of a particular spacetime to be red. We can say that a point in space can "change" in time, for example from non-red to red, but the non-red point of spacetime is non-red forever and the red point of spacetime is red forever. So, like the resemblance relation, the instantiation of a universal exists timelessly too, in all similar objects that exist, have ever existed and will ever exist.
By the way, when I said that the resemblance relation is "potentially" infinite-place, I just meant that maybe it has infinitely many relata.
Quoting litewave
The problem with litewave's representation here is that the existence of the particular "concrete whole" is taken for granted. Srap demonstrates how this is not an acceptable starting place. The idea that we build universals through observation and abstraction from particulars, is just not consistent with what we really do. 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. If we cannot produce such consistency, the universals get rejected and replaced. What is neglected, or left out from litewave's representation, is that whenever we proceed toward comparing particulars, we do so with a preconceived standard, or rule, for comparison. A comparison without such a standard is impossible, therefore the standard must be prior to the comparison and cannot be properly represented as being produced from it.
This is the problem which Plato faced with Pythagorean Idealism, the question of how the reality of the particular individual, the "concrete object" is supported, justified, or substantiated. Litewave's suggestion, that a concrete particular is a collection of concrete particulars had already been demonstrated to be faulty because it was known to produce an infinite regress. The Idealists proposed that the existence of the particular is supported by the universal, the Idea, and this was seen to be necessary from the reality of the concept of "generation". When a particular being comes into existence, it is necessarily the type of being which it is, therefore the universal, or Idea, must precede in time, as a cause of existence of the particular. The universal must precede in time, the particular, in order for the particular to be caused to be the type of thing which it is.
The problem which Plato exposed is that the Pythagoreans supported their Idealism with the theory of participation, and this could not account for a causal relationship between the universal and the particular. A particular concrete entity is supposed to be the type of thing which it is, through the means of participating in the Idea. So Plato showed how, in this representation, the Idea is passive, while the particular thing is active, by actually participating in the Idea, and this cannot account for causation. Then, in "The Timaeus" he proposed an alternative whereby the Idea is actual, and acts to cause the reality of a particular concrete entity being the type of thing which it is, therefore the Idea acts to cause the existence of the particular thing.
Quoting litewave
Again, this is an example of your misrepresentation. We can and do imagine many general properties without any particular instances. That's obvious in mathematics.
Are you (and others) referring to Carnap's Logical Structure of the World ?
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. 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.
The psychology is messy. In many cases it seems that we imagine a concrete particular example, perhaps a typical or paradigmatic example, and call it a "universal". We can't visualize a universal circle, we always visualize a particular circle, but we can later write down the mathematical relationship among spatial points that defines a universal circle. But I don't rule out cases where our mind comes up first with a universal principle and then sees that it fits with the particular examples.
Quoting Metaphysician Undercover
How?
Quoting Metaphysician Undercover
All general mathematical properties have examples in particular sets (collections). That's why set theory is regarded as a foundation of mathematics.
I haven't read Carnap's book "The Logical Structure of the World".
It's sort of the way empiricists like Hume talk. (@Manuel reads the early moderns a lot, so he could point out what a travesty of empiricism this is.)
It is also literally how I treat generating equivalence classes in everyday cases, choosing what to ignore, but there I've got a predicate machinery I don't intend to question.
It was intended as a simple, bone-headed account of abstraction, just to have a starting point. I assumed the main issue would be that you have to individuate properties in order to bracket them, which means you have to have universals to create a universal. (And now it sounds like Sellars's argument in EPM.) Never even got that far.
Quoting Metaphysician Undercover
If you say so. (Thanks for the notes on the ancients, btw.)
I don't think I demonstrated anything. I suspect the argument I gave is junk, but it had, for me, the desired effect of showing that the problem is not so simple as we might pre-theoretically think. Ask a non-philosopher friend and they'll probably sound like empiricists: concepts come from us "noticing patterns", "seeing what's in common", all this sort of thing. Maybe a "thank you, Darwin."
Quoting 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.
Not perfectly clear to me what the status of that argument is though. I was promising to look at logic not psychology, and while this isn't empirical psychology, there's something unavoidably psychological here. I have thought it might be a matter of being unable to state the empiricist position coherently, so again a matter of logic, but now it looks like the logic at stake is somewhat transcendental. Well, no big surprise since Sellars was profoundly Kantian, but I didn't intend to drag that in. I'd rather there was a clear way to avoid this whole line of argumentation...
Quoting litewave
Quoting litewave
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.
No travesty at all. Hume has a ridiculous amount of quotable sentences, paragraphs and even pages. Good on you for trying that style of writing out, it's fantastic.
I used to have a pet theory, also somewhere between logical and psychological, that generality is not a matter of classification but a type of procedure. Example: you want to talk about triangles in general, what you imagine or what you draw on the whiteboard are going to be approximate actual triangles, the edges and angles having particular values; you can treat that as a concrete triangle such that you might just measure to determine these values, or you can treat the object as general, or abstract, meaning that in your reasoning you are careful *not* to rely on these particular values. You carefully ignore them. And so in doing geometry we get to just stipulate (and indicate with those little hash marks) that these edges or those angles are equal, without giving a thought to the actual values the representation, being a concrete object, has.
Ok, thanks.
FYI....in case you didnt already know, and not that it matters....doctrines other than British Enlightenment empiricism start from that very same thought experiment for the development of purely rational theories. Its just that Ive never seen it presented by someone other than The Old Guys.
C'est moi.
HA!! I feel ya. Were still breathing, so we dont qualify as OLD guys.
It could be a bit of both, but the example you give was used by Descartes, if I don't misremember. And Cudworth too, though his examples were more varied.
In the empirical world, we don't see triangles, nor rectangles nor any other geometrical figure, for exactly the reason you point out: they are imperfect, sometimes severely so. The interesting thing is that unless it is completely unrecognizable, we see three distorted lines and judge it to be a triangle, same with other such figures. If this is not innate, then nothing is.
Hume, though not Locke (as far as I can tell), did not think this to be true, he thought we had no notion of straight line not derived from experience, but then we simply don't have such a notion. Because the experience won't yield what we take to be a straight line.
So, I wouldn't give up on your pet theory.
I suppose I should add, I wasn't just presenting empiricism in disguise; I was really just trying to see how I could come up with properties "from scratch". Looking back, what I did strikes me as an empiricist move, but it wouldn't surprise me to find it elsewhere. If it's one of the obvious ways to go, people have gone that way.
I like actually doing philosophy more than I like exegesis.
Over in the thread about causation, I found myself talking about approximations, and noting that we begin with noisy data and idealize it as a mathematical formula that we call an approximation; and if we can do that, we can go the other way and see the data as approximating the function.
How do we learn to do such things? If you draw a line on a chalkboard and say, "Imagine this is a straight line," what do you do if your audience asks, "What do you mean?" Once we know the trick, once we have the knack of idealizing, we can do this sort of thing all day long. But what if that trick is still opaque to you? I wonder if there are brain lesion studies on people who are unable to abstract in this way, or if there is a cognitive disorder that impedes this ability. It seems like you would get the sort of conversation you get with someone hyper-literal.
Yeah, but after 3000-odd years, the corpus of philosophy texts is so vast, its really hard to do philosophy that hasnt already been done.
Quoting Srap Tasmaner
Have you come up with anything in that respect....from scratch?
Hmmm. I would not be surprised if there were cases of people who lacked the capacity to visualize such elementary figures. But the vast majority of people call a "rectangle" or a "triangle" something which does not exist in the world.
I think that in the instance you are mentioning in your thought experiment, unless they do lack these basic capacities, I'd think you'd be arguing about the meaning of words and not the concept.
Plato goes over some of this (example of having knowledge you did not know you had) in his Meno, which I have to read. This shouldn't be too shocking; we very likely had the capacity to do math for thousands of years before we realized it could be used for things beyond very basic counting.
Pfffft.
May I invite you good Sir, to read Lacan and Derrida?
:joke:
I can also define a collection by enumerating its members, rather than by specifying a universal that is shared only by the members (or a resemblance relation that holds only among the members).
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?
But we see at least imperfect triangles and they resemble each other in a particular way. You can postulate "imperfect triangle" as a universal, with some range of deviations from the perfect triangle.
Knowing my denkweise as you do, what do they offer that might interest me? Or....what about them interests you?
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.
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?
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.
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 don't see what "perfection" has to do with universals anyway. What would it mean for a universal tree to be "perfect"?
If youre doing philosophy, you are thinking for yourself. No need to defend it. If youre speaking from exegesis, as I readily admit for myself, youre merely philosophizing.....which I also have to admit.
Quoting Srap Tasmaner
Truthfully, I wouldnt have any warrant to do that; I dont 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 youre going to come up with properties from scratch, that sorta implies thinking for yourself, which in turn implies some sort of conceptual scheme youd obviously be stuck with.
Just curious, thats all.
: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.
See, that's what threw me off.
Mww, is Mww.
He's great! :)
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 didnt send tickets to his favorite Vegas show to post that comment.
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...
Quoting 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.
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?
No, both predicates refer to the same property of redness, the second predicate just elaborates what it means to be red.
Quoting 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.
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?
Quoting litewave
I know what you say you're doing. It's just not what you're doing. Unless I've missed something.
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.
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.
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.
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."
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.
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.
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.
Quoting 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.
Quoting 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.
Quoting 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.
Quoting Srap Tasmaner
I appreciate someone who is receptive to different perspectives. I think that's what philosophy is made of.
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.
Quoting 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.
Quoting 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.
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.
Quoting 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.
Quoting 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.
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.
Quoting 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.
Quoting 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.
Quoting 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.
Quoting 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.
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.
Quoting 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...
Quoting 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".
Quoting 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.
Quoting 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.
Quoting 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.
An empty collection is a collection of no parts. A non-composite object.
Quoting Metaphysician Undercover
What? They are particulars located in space and time. Why would they not be concrete entities?
Quoting Metaphysician Undercover
Such a relation, if it can even be regarded as a relation since it is between one thing (?), is usually called identity, as far as I know.
Quoting Metaphysician Undercover
Resemblance comes in various degrees and you can understand sameness as maximum or exact resemblance. So the meaning of resemblance also covers sameness.
Quoting Metaphysician Undercover
Because the recipe describes relations between particular circles, like translation, rotation, scaling. These are mappings between parts of one particular circle and parts of another particular circle. They specify how particular circles are similar.
The title of my OP is asking whether there is such a distinction.
Litewave, a collection is not an object. Therefore an empty collection is not a non-composite object.
Quoting litewave
They have no location, that's the issue with quantum uncertainty.
Quoting litewave
No, the recipe for making a circle, which you produced, does not describe relations between particular circles.
Quoting litewave
Exact resemblance is incoherent, for the reasons you described. If there is supposed to be no difference between two things, they cannot be assumed to be two things, they must be one and the same thing.
A particular apple is a collection of its parts. Is the apple not an object? What is an object then?
Quoting Metaphysician Undercover
Still the elementary particles are particulars and not universals, no? And I am saying that any particular is a collection.
An object is much more than a collection of parts. Each different object has its parts ordered in a particular way. It is the order of the parts which creates the unity which you seem to want to call a collection. A collection with no parts (if this could be in some way coherent) has no order, therefore cannot be an object.
Does my comment not address your question adequately? If no, why?
In set theory, ordered sets/collections (which have members arranged in a particular order) can be defined out of unordered sets. For example an ordered set (a, b) is a set with members a and b which are ordered in such a way that a comes first and b comes second, and it can be defined as an unordered set of sets { a } and { a, b }:
(a, b) = { { a }, { a, b } }
A set with the opposite order can be defined as follows:
(b, a) = { { b }, { a, b } }
https://en.wikipedia.org/wiki/Ordered_pair#Kuratowski's_definition
You can define any order, any mathematical structure in set theory.
Your comment said that my OP wishes to make a distinction between a universal and a resemblance relation when I in fact question that such a distinction exists.
But mathematics doesn't give us a true representation of what an object is. Math is composed of axioms which are produced from the imagination. That's what I told you earlier, why the relation between two things, described by a universal, need not be a "resemblance" relation, if universals are constructed by the mind. The relation might be completely arbitrary, as demonstrated by set theory, which allows an ordered set to be constructed from an unordered set. This means arbitrary relations can be assigned to a group of things with no relations.
An "unordered set", a group of things which have no order, is really an incoherent fiction, an impossible situation, because things must have position. So mathematics clearly does not give us a true representation of the reality of objects.
Objects in a topological space can have a position in such a space. But a topological space is just a special kind of collection and there are many other collections that are not topological spaces. So an object doesn't necessarily have to have a position in a topological space.
As I said, that's a fictional, imaginary, representation of what an object is. And if you look back at where I first engaged you in this thread, you'll see that my principal objection to your proposal is that you take the existence of particulars for granted. Then you claim that people construct universals from these particulars which are taken for granted. So the problem here, is that what you have taken for granted is a fiction, and this undermines your entire proposal as completely unsound.
In reality, you have shown that you construct a representation of a particular, an object, from some preconceived universals, set theory, but then you've tried to claim that universals are derived from particulars. However, you have just demonstrated the opposite of what you claim. The notion of "an object" or a particular, is actually derived from preconceived universals, so the conception of universals is prior to the apprehension of particulars.
No, I am saying that particular collections are made up of particular collections, not constructed from universals. I take particular collections as granted because I see them all around me and because for any particulars there necesarily seems to be a collection of them, and universals don't seem necessary to explain the existence of particulars.
But there are very good reasons people think it goes the other way.
For most people, for most concepts, acquaintance with instances of the concept precede, in time, the possession of the concept, and exposure to those particulars is instrumental in acquiring the universal they fall under. That's the argument from ontogeny: you are acquainted with moving, barking, licking particulars before you know that they are dogs. And there is a related argument from phylogeny: modern humans have a great many concepts that they were taught, often through the use of exemplars, but it stands to reason that not every human being was taught: there must have been at least one person who passed from not having to having a concept unaided. In essence, we imagine that person somehow teaching themselves a concept through the use of exemplars, and we imagine that process proceeding as we do when analyzing a population of objects, looking for commonalities.
In thinking about this thread, I was reminded of the Sesame Street approach to teaching about classes, an approach presumably backed by research, probably the most famous educational bit in Sesame Street:
(The irony of this song, "One of these things is not like the others. One of these things doesn't belong," in a show teaching inclusion and tolerance, was not lost on the makers of the show, and the bit was largely retired in favor of "three of these things go together," which is not much of an improvement.)
What's of interest here is that resemblance is not only relative, but comparative: resemblance is a three-way relation, a given object resembles another more, or less, than it resembles a third.
That's an irrational, infinite regress, which we already discussed when you said that an object is a collection of objects. The problem is that you've created a vicious circle by saying that a collection is made of collections, and you have no indication of what a particular is. A "collection" is a universal, a group of many. Now you want to deny that a collection is a universal, and claim that is a particular.
You claim to see collections existing as particulars all around you. Please explain to me how you think that you are seeing a collection as a particular when you haven't even said what a particular is. Perhaps an example or two?
Quoting Srap Tasmaner
Yes, this is the effect of teaching, learning. From the perspective of learning, we see the particular as essential to learning the universal, because this is the process which taught us. However, the particular is a tool of the teacher, who already understands the universal to be taught. So from the learner's perspective, the particular appears to be essential to the learning process, as necessary for it, but it is really a weak sense of "necessary", as what has been determined by the teacher as needed, required for the process. It is not a true logical necessity because it might be possible that the student could learn the universal in another way.
This is what Plato looked at in The Meno, with what is referred to as the theory of recollection. The student is induced to produce the universal without the use of a demonstration with particulars, and the observers conclude that the student must have already somehow had the universal in his mind. So they propose, as a solution, that the student must have somehow had the universal in his mind, from a past life, and recollected it. You can see that the proposed solution is inadequate, but it gives us a good representation of the problem. Aristotle gave a better solution, by saying that the student has within the mind, the potential for the universal, prior to actually formulating it.
But use of the particular, as a teaching tool necessitates in a stronger way, that the existence of the universal to be taught preexists the use of the particular through the concept of causation. And if the potential for the universal, which precedes the actual existence of it in the mind, does not necessarily require particulars for its actualization, then what does constitute the actual existence of the universal?
Quoting Srap Tasmaner
I agree, there always must be a third in this form of comparison, because two will always be other than each other. But this only demonstrates that "resemblance" is not the true principle by which we categorize. In reality, we produce the category, like "dog" in your example, and judge the thing directly as to whether it fits the category, without comparing it to others within our minds So you see an animal and call it a dog, without performing mental comparisons. And learning the category is a matter of developing the capacity to do this, not a matter of learning how to compare. That's why learning the category is the important aspect, and it consists of seeing examples, not of comparing three things.
The material of the Sesame Street skit is only used to demonstrate that the category has been learned. That's why it gets sort of controversial, because to demonstrate that one knows the group, a person is asked to say what is not part of the group, as a simple form of confirmation. In reality an act of exclusion is not necessary if one has learned the category. We simply need to judge and include members as a part of the group without indicating what is not a member. This is like determining what pleases you without any reference to what displeases. And the commonly touted principle, that one must know "what X is not", in order to know "what X is" is a false principle. It seems to be based in the faulty idea that one must demonstrate one's knowledge, to have it.
A particular is an object that is not a property of any object. As opposed to a universal, which is a property of some object. A general collection or collection "in general" is a universal that is a property of every particular collection. A particular apple is not a property of anything, but general apple is a property of every particular apple.
I thought I did clarify my views on that score. The two concepts - universal & resemblance - are, how shall I put it?, not mutually exclusive. In fact the former seems to arise from the latter in a most exotic manner.
Too theoretical and insubstantial. Please give examples.
For example, what is a universal circle? It doesn't look like a particular circle because every particular circle is continuous in space and around a particular point in space but a universal circle is not supposed to be located in any continuous area of space. A universal circle looks like certain deviations from any particular circle and thus more like a resemblance relation among particular circles.
A universal triangle is simply the resemblance of any particular triangle to any other triangle. The resemblance consists of a set of properties common to all objects of a given kind/type i.e. in what way, for instance, is one specific circle like any other circle. In short, as I said before, resemblance and universal are the same thing.
Well, that's nice and inspiring, yet it is still too theoretical. I mean, not quite tanglible. I, personally, cannot even imagine how it would look like.
Anyway, it's OK.
Ok then.
I have the desire to drag in "fractals" to explain my views on this interesting topic. What is a fractal but something that at large scale (universal) is also exemplified in its smaller units (particular objects). There is a clear relationship between all things from top to bottom and back via the magnitude of the fractal. "as above so below".
Many believe if the universe has a clearly defined set of rules from which all things emerge, evolve or are created then the universe is a fractal. Qualities of the entire thing reflected in individual things, systems of things and people - creativity, destruction, rationality and irrationality, attraction and repulsion, etc. And people would also be built of the same processes from the ground up, structures, cycles and regulations (hormones) , hierarchies of cells and tissues.
"made in its image" as it were. When one takes psychedelic consciousness altering drugs they often report seeing fractals. Perhaps this is why.