Wednesday, October 1, 2008

Worry about abstract entities #3

Help me out. I presume that either my methodology is flawed, or my methodology is sound but my analysis lacking, or everything is fine in principle but I am failing to see something apparent.

Let us imagine I have the following sample of things:

▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫

I should be tempted to introduce a category-term for them, “shape”. So I would introduce a “shape framework” which would function as a sort of kind. Thus in my shape framework I have the following:

▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫

I guess I’m sympathetic to a distinction between fundamental and superficial existences, since I want to talk about the things in my framework that are models and the things in my framework that are commentaries. Thus the shapes *▲*, * ◯*, *◼*, etc. are models for things in the world, in this case my original sample, and my category term “shape” is in the commentary. Also in my commentary are the names of the shapes, “isosceles triangle”, “circle”, “square”, “rectangle”, “rectangle”, “right triangle”, etc. The wordy bits are in the commentary, the thingy bits are in the model. The thingy bits are ‘fundamental’ in some sense, and the wordy bits are ‘superficial’.

And since I have names for the things, I can introduce terms for the tokens, and also construct for myself token-classes. Thus, I can construct the ‘triangle kind’ which includes:

▲ ◣

The ‘black shape kind’ which includes:

▲ ◼ █ ◣ ★ ⚡ ♻ ♫

and so on. So I have given in my commentary: 1) A name of the type in question, namely shapes. 2) Names for the tokens in question, namely isosceles triangle, circle, square, etc. 3) Names for the token-classes in question, namely black shapes, white shapes, triangles, stars, etc. In my model I have the shapes.

Now I seem to be pretty content with this. I have appealed to types and token classes, but they were pragmatically introduced into my commentary. Maybe I’m just nominalist leaning here. But I imagine a Platonist saying: but you have need of Platonic entities! Don’t you see that the symbols

★ ★ ★

are each instances of the same universal? The universal in question is ★ness, which is instantiated in three locations above!

Maybe I haven’t done a very good job of explaining the Platonist’s position, since I do think that “This is a *★*” is true of the three shapes above. But I don’t see the need for an appeal of a Platonic entity. After all, the first *★* is located to the left, the second is in the middle, the third is to the right. So isn’t there three kinds of *★* in play?

Maybe every shape below is an instantiation of a distinct universal:

▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫ ♫ ♻ ⚡ ☆ ★ ◒ ◣ █ ◼ ◯ ▲

I presume there will be an appeal that the left-most shape and the right-most shape are of the same kind, namely the ‘▲-kind’. But one is left-most and one is right-most. Why not say that there is a ‘▲-left-most-kind’ and a ‘▲-right-most-kind’? This surely does seem silly. But I don’t see why we shouldn’t say this. We seem to need token-classes here.

I also wonder about shapes in general. If I have a square that is well drawn and a square that is poorly drawn, are each instances of the same universal? Or is there a poorly-drawn-squareness in the one case, and a well-drawn-squareness in the other?

If the universal doesn’t care how well or how poorly a square is drawn, why don’t rectangles count as squares? Why can’t a poorly drawn square that looks more like a trapezoid count as a square?

If the universal does care how well or how poorly a square is instantiated, then it seems we have an infinite degree of squareness. But then how to we stop a slide into every token of anything being an instance of a distinct universal?

I presume that we can bundle general shapes together. Thus, obtuse triangles, obscene triangles and scalene triangles are all triangles. Small squares, large squares and middle-sized squares are all squares. But are we not getting into a relativity to how things appear to me? If I had fuzzy vision, circles and square-like circle-impostors would look the same, and I might think that they instantiate the same universal because they strike me as being of a common and general shape. If I had sharp vision, I would notice that there are no straight lines or right angles, and that Euclidean geometry is false. Then do I have to give up on there ever having been universals for the Euclidean shapes in the first place?

And even if all this can be ignored, how can we ever figure out the fine cuts between instances of triangles of one sort or another and just near cases? How can we divide between when I pile instantiates pileness, and then when reduced instantiates something else?

Perhaps in the case of pileness is problematic in itself, but what of other shapes. I can clearly move pixels a micron this way or that. Does squareness come and go based on these little movement? I presume as well that there are no straight lines, no perfect circles, so wouldn’t we always be stuck with shades of grey?

I could go on and on. I may have gone on too long already. But this really bothers me. I think the modest and tidy framework I had up above avoids these problems. Am I wrong? Or am I right, and the framework is lacking as a result. Or is the notion of Platonism, or something near-to, lurking in the neighborhood?


Dan said...

He Wess,
You raised a number of issues here:
1) If a nominalist can tinker with semantics enough and still get truth conditions right, why go realist?
2) If there are universals, which ones are there? Does any arbitrary classification of individuals count?
3) If there are universals, how can we meaningfully talk about them, given that vagueness is rampant?

The answer to (1) is that getting truth conditions for the sentences uttered is not enough for a semantic theory, let alone a metaphysics. There are lots of ways of arbitrarily getting the truth conditions of sentences right (I can deliver arguments if need be).
On the common sense corresondence theory of truth, a sentence must be true in virtue of it accurately representing the world. Suppose there are no universals, but you use the prescribed selarsian method of determining the truth of "These are triangles" (pointing to triangles). That sentence is "true", but has been robbed of the meaning intended of it. It meant to say something real about the way the world is, but ended up just a move in a language game.
If in fact universals don't exist, I personally would be more comfortable biting the bullet and saying "these are triangles" is literally false but pragmatically useful, rather than re-interpret english.
The motivation for thinking that "these are triangles" is literally true is because it points out a particular genuine similarity between the things refered to. This similarity is not linguistic or pragmatic, and would still be around if we weren't. It's precisely in virtue of this similarity that language hooks up to the instances in this way, and we treat them pragmatically like we do. If there weren't a genuine similarity, how could we distinguish them so easily?
Treating universals as similarities between individuals is a useful model. I think I'll stick with that for now. It's an easy answer to (2). Any genuine similarity is a universal. So traingularity is a universal because it denotes a real similarity. Rough triangularity is another universal. Same goes for nearly all the border-cases you mentioned. I don't mean for this to be definitive (we're just talking here) but consider the following characterization of a universal:
(U) A similarity relation is a universal iff there are criterion (other than identity) for individuals being related.
This is open to counter examples, but I think it gives an intuitive idea of what I'm after.
You mentioned vagueness (implicitly). Vagueness is a problem for pretty much everybody, and philosophers seem to have a general understanding with one another not to bring vagueness objections against each other without good reason. That said, I have no idea how to handle it myself.

Wes McPherson said...

Hi Dann,

Thanks for the response.

I don't mind so much the idea of there being universals. I think they are in the commentary, though. I may just be bewitched by this manner of looking at things I admit.

I don't mind saying that univerals denote similarities, but I think that different perceivers may see different similarities. If 'ultimate reality' is supposed to be perspectiveless, I wonder what we are to make of that.

If our TEs are posited as the ultimate reality, they seem to sort of fall outside of this similarity / dissimilarity talk, it seems to me. (If quanta are the ultimate beings, would we only need the universals 'quantaness'?)

And we don't want to have to say that universals are similar, and thus are instances of other universals, and that those are instances of other universals, do we? Or does is this regress not bothersome?

Thanks again for the post. I certainly have something more to think about.

Wes McPherson said...


I thought of this last night: On the view presented where universals denote similarities, how is it that we come to know universals? Do I simply look at my hands and notice the handness, 'abstracting' it out of the individuals?

Adam said...

Hi Wes:
A comment that might help out (though of course, it might not).
I’m not sure exactly what’s going on with the distinction between ‘fundamental’ and ‘superficial’ existence. You introduce it as a way of distinguishing the entities in your model- shapes- and the tokens of word types that we use to refer to these shapes. Calling the former ‘fundamental’ and the latter ‘superficial’ with respect to existence seems misleading, since it suggests that the linguistic items in the commentary don’t exist as robustly, or are somehow ‘less real’, then the things that exist in the model. But I’m assuming we don’t think this (I guess because it seems clear that the items in the commentary are just as real as the items in the model).
But maybe you’re suggesting something different. Maybe you’re suggesting that it is a contingent fact that the linguistic item ‘triangle’ refers to one of the entities in the model. This seems true. It certainly seems possible that a different linguistic item could have referred to that particular entity in the model. It also seems like the existence of minds plays a pretty big role in determining whether ‘triangle’ refers at all. If this is what you mean by ‘superficial’ existence, then I think I get it (although I think the terminology connotes something stronger).
At any rate, the question is this: how does this distinction help the nominalist? Given that commentary items denote items in the model, and given that items in the model exhibit objective similarity and difference with respect to other entities in the model, it seems like you’ve already got a view up and running according to which linguistic items denote universals. That it’s a contingent matter which entities in the commentary do the denoting doesn’t seem to support the nominalist much.

Wes McPherson said...

Hi Adam,

I guess I like the fundamental / superficial distinction because it helps with a distinction between 'first in the order of being' and 'first in the order of knowing'. So I might look at a table. But I know that really there are just quanta and stuffies, so the table is slotted lowly in the order of being, but highly in the order of knowing.

I don't know if that helps. Or does any work other than bringing me some comfort...

I guess some of what the commentary does is give meaning or draw attention to things in the model. Thus,

► ◀

might have the next-to relation modeled by virtue of the shapes but stand in need of 'reporting'. Or I might use the same model for multiple 'ostensive definitions' of relations or objects.

A traditional nominalist may not like this. A Sellarsean nominalist just wants to show that a language is presupposed for our knowledge of AEs. So he's cool with this. (Rationalists have the right idea in the end, we just need to kill the idea of a Given.)

But maybe a nominalist can still say that universals are mind-dependent (not what the Sellarsean says) because they are primarily in the commentary. How can I model redness? Well, I can draw out or gather up red things and say: "I call all these here thing-a-ma-bobs red!" That little sentence serves as a commentary.

I guess then the commentary would denote things in the model; I guess there would not be a transcendental commentary which moves through models.

But I suppose I am not clear on:

A) If the commentary has to denote things in the model and cannot denote things not in the model.

B) That we couldn't just make some sort of 'counter-part' model of abstract entities which could supplement the other models.

In the case of (A), I presume that we can denote other things, so long as they are modeled somewhere else. Thus, I might use physical terms in a commentary for a biological model.

In the case of (B), I presume we could model anything that is, including AEs. Even if we use structures or functions as AEs, we could just model those.

I guess one who was so inclined might frump on about the essential role of the commentary here, and the need AEs have of the commentary.