Wednesday, September 23, 2015

An argument against heavy-weight Platonism

Heavy-weight Platonism explains (or grounds) something's being green by its instantiating greenness. Light-weight Platonism refrains form making such an explanatory claim, restricting itself to saying that something is green if and only if it instantiates greenness. Let's think about a suggestive argument against heavy-weight Platonism.

It would be ad hoc to hold the explanatory thesis for properties but not for relations. The unrestricted heavy-weight Platonist will thus hold that for all n>0:

  1. For any any n-ary predicate F, if x1,...,xn are F, this is because x1,...,xn instantiate Fness.
(One might want to build in an ad hoc exception for the predicate "instantiates" to avoid regress.) But just as it was unlikely that the initial n=1 case would hold without the relation cases, i.e., the n>1 cases, so too:
  1. If (1) holds for each n>0, then it also holds for n=0.
What is the n=0 case? Well, a 0-ary predicate is just a sentence, a 0-ary property is a proposition, the "-ness" operator when applied to a sentence yields the proposition expressed by the sentence, and instantiation in the 0-ary case is just truth. Thus:
  1. If (1) holds for each n>0, then for any sentence s, if s, then this is because because of the truth of the proposition that s.
(The quantification is substitutional.) For any sentence s, let <s> be the proposition that s. The following is very plausible:
  1. For any sentence s, if s, then <s> is true because s.
But (4) conflicts with (3) (assuming some sentence is true). In fact, to generate a problem for (3), we don't even need (4) for all s just for some, and surely the proposition <The sky is blue> is true because the sky is blue, rather than the other way around: the facts about the physical world explain the relevant truth facts about propositions. Thus:
  1. It is false that (1) holds for each n>0.

The above argument is compatible, however, with a restricted heavy-weight Platonism on which sometimes instantiation facts explain the possession of attributes. Perhaps, for instance, if "is green" is a fundamental predicate, then Sam is green because Sam instantiates greenness, but this is not so for non-fundamental predicates. And maybe there are no fundamental sentences (a fundamental sentence would perhaps need to be grammatically unstructured in a language that cuts nature at the joints, and maybe a language that cuts nature at the joints will require all sentences to include predication or quantification or both, and hence not to be unstructured). If so, that would give a non-arbitrary distinction between the n>0 cases and the n=0 case. There is some independent reason, after all, to think that (1) fails for complex predicates. For instance, it doesn't seem right to say that Sam is green-and-round because he instantiates greenandroundness. Rather, Sam is green-and-round because Sam is green and Sam is round.


entirelyuseless said...

The problem with this is that it doesn't recognize that there are different kinds of causes, and therefore different kinds of explanation. Form is the formal cause of the composite, and in that way explains it. But it is also in a certain way the formal cause of the matter, and in that way explains it. But the material cause is also the cause of the composite and of the form, and in that way explain them.

In other words by choosing two different kinds of causality and explanation, you can have the two things mutually explain each other, in different ways. There is no contradiction.

Mike Almeida said...

*If (1) holds for each n>0, then for any sentence s, if s, then this is because because of the truth of the proposition that s.*

Hard to see how propositions s might explain or ground the truth of sentences, since (for one thing) propositions are not instantiated. It's rather states of affairs that explain or ground the truth of sentences (and propositions). Just as properties are instantiated, so states of affairs are actualized. It's the actualization of an SOA s that does the explaining or grounding for the sentence or proposition s.

Alexander R Pruss said...


Propositions are just 0-ary properties.
Sentences are 0-ary predicates.
"Instantiates" is a multigrade predicate: "x1,...,xn instantiate y" in the arity (n+1)-case.
The unary case of it is just the truth predicate (as applied to propositions).

Do we agree so far?

Mike Almeida said...


Yes, I think that's the metaphysics from logic textbooks, however odd it sounds to say that a proposition is a property. You can take my suggestion then, as identifying propositions and SOA's, (in the manner of Chisholm) since it is the SOA's that are doing the explaining. There is some interesting sense in which SOA's are instantiated; there's just a very stretched sense in which a proposition is instantiated. So, let's say that a proposition's being truth-ed is just an SOA being actualized.