Monday, September 21, 2015

Platonism and Ockham's razor

One of the main objections against Platonism is that it offends against Ockham's razor by positing a large number of fundamental entities. But the Platonist can give the following response: By positing these fundamental entities, I can reduce the number of fundamental predicates to one, namely instantiation. I don't need fundamental predicates like "... is charged" or "... loves ...". All I need is a single multigrade fundamental predicate "... instantiate(s) ...", and I can just reduce the claim that Jones is charged to the claim that Jones instantiates charge, and the Juliet loves Romeo to the claim that Julie and Romeo instantiates loving. In other words, the Platonist's offenses against Ockham's razor in respect of ontology are largely compensated for by a corresponding reduction of ideology.

Largely, but so far not entirely. For the Platonist does need to introduce the "... instantiate(s) ..." predicate which the nominalist has no need for. On pain of a Bradley-type regress, the Platonist cannot handle that predicate using her general schema.

(But maybe Platonist can go one step further. She can eliminate single quantifiers from her ideology, too, using the Fregean move of replacing, say, ∃xF(x) with Instantiates(Fness, instantiatedness). Extending this to nested quantifiers is hard, but perhaps not impossible. If that task can be completed, then it seems that our Platonist has gained a decisive advantage over the nominalist: she has only one fundamental predicate and no quantifiers other than names (if names count as quantifiers). Not so, though! For this move needs to be able to handle complex predicates F, and the property Fness corresponding to such a complex predicate will probably have to stand in various structural relations to other properties, and we have complication.)


Heath White said...

The difficulty is that this defense of Platonism risks making it a notation rather than a theory. For the latter, you would need the "instantiates" predicate or the Forms to do some theoretical work that mere regular objects and predicates could not do. Plato thought the Forms did do such work--they were objects of knowledge that was otherwise inarticulate, they explained approximations, and so on. But something of that kind would be needed.

Jeremy Pierce said...

I would have thought Plato's main response to this sort of argument would simply be that Ockham's Razor is an illegitimate argument against a theoretical entity that is needed to explain something that isn't explained by the alternative theory, and he would say that Platonism is needed to explain what things have in common with each other when there isn't a trait that they have in common other than the category they belong to (e.g. beauty isn't something had by each item that's beautiful because nothing is comnmon to them other than that they're all beautiful). Nominalism leaves something without explanation, so it doesn't matter if it's simpler.