Monday, May 28, 2012

Existence and quantification

Maverick argues:
Ed thinks that the assumption that the domain of quantification is a domain of existing individuals is a contingent assumption. But I didn't say that, and it is not. It is a necessary assumption if (1) [namely that ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’] and sentences of the same form are to hold. [My emphasis]
But he then says that there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals, which I don't follow at all. We start with the initial logical or definition assumption about the meaning of the verb 'exists'.

(1) 'A golden mountain exists' = 'Some mountain is golden'

If we accept that, we also have to accept the equivalence where the right hand side does not explicitly contain the copula 'is', but has a verb which is logically equivalent to a copula plus participle. That is a standard assumption, namely that 'John runs' is logically equivalent to 'John is running'. Thus

(2a) 'John owns a house' = 'some house is owned by John

and thus, given (1), and given that John owns a house, it follows that:

(2b) John's house exists

A brief qualification here. The equivalence in (2a) only holds when the verb is what I call 'logically transitive. I explain this idea here. Clearly, if John wants a beautiful wife, it does not follow that some beautiful wife is wanted by John.  Given that, it is plain that our Brentano equivalence applies to the following quantifier type sentences:

(3) 'The domain contains islands' = 'some individuals in the domain are islands' = 'there exist individuals in the domain which are islands'

(4) 'The term 'volcano' ranges over volcanos' = 'ranged-over volcanos exist'

and so on. Hence there clearly is something 'in the nature of logic' which prevents us quantifying over non-existent individuals, namely the same thing as what prevents us owning non-existent houses, given the definition of 'exists' above. I can't believe that Bill does not grasp this. I think what he fails to see is that 'logical' verb phrases like 'ranges over', 'contains', 'quantifies over' are subject to the same logical rules as 'owns', 'lives next door to', 'loves' and so on. That any domain contains existing individuals is therefore a logical truth.


David Brightly said...

Ed, do you not think this over-states things? Compare

'The term 'volcano' ranges over volcanos' = 'ranged-over volcanos exist'


'The term hobbit ranges over hobbits' = 'ranged-over hobbits exist'

Bill seems to go too far in the opposite direction. We are all agreed, I thought, that there are no 'non-existent individuals' and cannot be---the term is oxymoronic----so in what sense can Bill think we can be said to 'quantify over' them? I see two possible answers: first, we can imagine our sentences spoken of alternate possible worlds or fictional worlds, or different times in this world which could be said to contain individuals non-existent in our own world, giving rise to different truth values for our sentences. Second, Bill is an extreme 'ontological liberal', thinking that any linguistic distinction is prima facie evidence for a real distinction. His method appears to be to try to carry this superabundance forward. Chaos ensues. Example: we have singular and general existential statements. So he allows himself to talk in terms of 'singular existence' and 'general existence', which none of us can make sense of, including Bill himself (I don't recall him defining these terms) and which the rest of us avoid like the plague. He claims that the thin position is to 'eliminate first-level existence'. This is absurd. No one is saying there are no things. There have to be things in order that concepts be instantiated. My kind of thin, perhaps not yours, just wants to eliminate singular existential statements. They are at best redundant and at worst misleading. More.

Bit surprised to find you seduced into 'domain talk'.

Anthony said...

What of sentences about, say, medieval philosophers? Are you saying medieval philosophers exist, or are you saying these sentences don't quantify over medieval philosophers?

Ditto substituting "fictional characters" for "medieval philosophers".

Edward Ockham said...

>>'The term hobbit ranges over hobbits' = 'ranged-over hobbits exist'

yes but on the thin conception, we cannot range over hobbits. The point is that if you agree with the Brentano equivalence - which I accept only with qualifications - then verb phrases like 'quantifying over' and 'ranges over' must take real, existing objects. What puzzles me is how Bill appears to agree with the equivalence.

>>Bit surprised to find you seduced into 'domain talk'.

Only for sake of argument.

Edward Ockham said...

>>Ditto substituting "fictional characters" for "medieval philosophers".

I'm accepting Bill's argument as a straw man.

Edward Ockham said...

>> So he allows himself to talk in terms of 'singular existence' and 'general existence', which none of us can make sense of, including Bill himself

Smiley face.

Anthony said...

"yes but on the thin conception, we cannot range over hobbits"

Okay, but what about medieval philosophers?