Wednesday, March 23, 2011

Two kinds of Platonism about properties

According to strong Platonism about properties, if F is a fundamental predicate, then F expresses the property Fness and the sentence "x is F" should be analyzed as saying that x instantiates Fness.

Weak Platonism makes no such analysis claim. It merely claims that to each fundamental predicate F there corresponds a property Fness such that, necessarily, x is F if and only if x instantiates Fness. Weak Platonism thus drops two claims that strong Platonism makes: (a) that the predicate expresses the property; and (b) that we should analyze predications in terms of instantiation.

Here is a problem with strong Platonism.

  1. If strong Platonism is true, then in an ideal logic—one that follows the metaphysics as closely as possible—there is one and only one (multigrade) predicate: Instantiates.
Thus, instead of saying that Romeo loves Juliet, we would say something like: Instantiates(Romeo, Juliet, love). But:
  1. In an ideal logic there would be more than one predicate.
  2. So, strong Platonism is false.
I don't think this is a very powerful argument against strong Platonism, but it does highlight something a little troubling—Platonism objectifies all predicates but one, and in effect has only one predicate.

If strong Platonism were true, then in some sense there would only be one thing one would ever be doing—instantiating (of course sometimes one would be instantiating together with others, and what property one would be instantiating would vary).

I think weak Platonism is much more attractive. An example of weak Platonism is Lewis's account of properties as cross-world sets of objects. This is merely weak Platonism. We don't want to say that "is a circle" expresses the set of all of circles. Nor do we want to say that "Socrates is a circle" holds because of Socrates' membership in the set of all circles. But Lewis does not intend it as more than a weak Platonism.

I think that on some readings, divine conceptualist views on which properties are divine ideas are a weak Platonism.


David Parker said...

Are there books you recommend to (non-math whiz) students for studying predicate calculus?

Alexander R Pruss said...

I use Barwise and Etchemendy, Language, Proof and Logic in my logic class. There are probably more basic books, too, but I've only ever taught logic from this one.

Jarrett Cooper said...

Prof. Pruss,

I looked up the book and can get it extremely cheap (less than $2.00). The things is is that it does not come with the CD. Just how crucial is the CD with regards to learning the material?

Alexander R Pruss said...

The software includes a very helpful proof checker. You want that CD.

(A note for anybody else reading it. If you want to take a class using the book, buying a used copy may not work, because the CD will have been registered to the first owner, and hence will not submit your assignments to the professor on your behalf. If you're buying for self-study, you don't need to worry about this, I think.)

Phaedrus said...

I've read and been through a logic class using Bawise and Etchemendy. I wouldn't recommend it for a beginner. I'd recommend Harry J. Gensler's "Introduction to Logic". It's the most down to earth description of symbolic logic I've found.

Alexander R Pruss said...

Could be. I have no experience at all in teaching undergraduate logic. I only teach our graduate logic class.