Friday, April 15, 2011

One-Category Abundant Platonism

Standard Abundant Platonism (SAP) holds that to every predicate there corresponds a property, and items satisfy the predicate if and only if they exemplify the property.  Moreover, it holds that exemplifiers are not explanatorily prior to what they exemplify.  Normally, we think of SAP as a two-category theory: individuals and properties.

But here is a suspicion I have.  Little if any explanatory work is being done by the distinction between individuals and properties.  The serious explanatory work is all being done by the relation of exemplification.  Here are two examples.

1. Standard Platonists say that x and y are exactly alike in some respect if and only if there is some property P such that x exemplifies P and y exemplifies P.  But drop the word "property" from the previous sentence, and we have an account of exact alikeness that is even better: x and y are exactly alike in some respect if and only if there is a z such that x exemplifies z and y exemplifies z.  This is extensionally just as good, but simpler. (One can do more complex stuff about determinates and determinables to get resemblance in some specific respect, but again that doesn't need the concept of property, just the relation of being a determinable of.)

2. Standard Platonists say that to each predicate F there corresponds a property Fness, and that x is F if and only if, and if so because, x exemplifies Fness (we should probably have an exception to the "because" clause when Fness is exemplification).  But change "there corresponds a property Fness" to "there corresponds an entity Fness", and this works just as well as an account of predication.

Besides, the concepts of "individual" and "property" are foggy.  (We might try to say: "x is an individual if and only if x cannot be exemplified."  But that doesn't work for abundant Platonism, as abundant Platonism will have properties like being a square circle.)

So, if you're going to be a Platonist, why be a two-category abundant Platonist?  Why not be a one-category abundant Platonist instead?  

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