Can Existence Be Quantified Away?

I’ve been following some interesting stuff by Bill Vallicella about the “thickness” or otherwise of existence. I think the general debate is this: if you can use logical quantifiers to define “Socrates exists” in a sort of Quinean way then you remove at a stroke Heideggerean concerns about the import of “exists”. Thick theorists such as Mr Vallicella believe such reductionism to be misconceived. I think the idea is that the quantifiers import what they aim to omit and if they don’t they leave out other issues that are at leat as important etc….

Anyway there is no point in getting on board with this stuff without going back to primary texts so I opened Graham Priest’s texbook on non-classical logic to find that “A set X, is a collection of objects….”

OK: so how does the reductionism get off the floor then if set theory at its most anodyne uses a concept such as “object” which is, shall we say, metaphysically neutral?

(I realise that there’s an apples and oranges issue there but the point obtains doesn’t it? If you’re attemtpting to avoid ontological promiscuity via logical austerity had’t you be careful what you’re notation commits you to?)

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