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?