A Quick Proof that 'Exist(s)' is not Univocal

Suppose we acquiesce for the space of this post in QuineSpeak. 

Then 'Horses exist' says no more and no less than that 'Something is a horse.'  And 'Harry exists' says no more and no less than that 'Something is Harry.'  But the 'is' does not have the same sense in both translations.  The first is the 'is' of predication while the second is the 'is' of identity.  The difference  is reflected in the standard notation.  The propositional function in the first case is Hx.  The propositional function in the second case is x = h.  Immediate juxtaposition of predicate constant and free variable is the sign for predication.  '=' is the sign for identity.  Different signs for different concepts.  Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.

Those heir to the Fressellian position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.

So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot be upheld.  It cannot be upheld across the divide that separates general from singular existentials.

Or have I gone wrong somewhere?

Comments

[Leo Carton Mollica]

Pardon me if I'm wrong, but doesn't Quine actually advocate assimilating English proper names to general terms? That, presumably, would give "Something is Harry" the translation "(Ex)(Hx)".

[Bill Vallicella]

Hi Leo,

I see you are up late. Me, I'm up early.

In "Existence and Quanitification" in Ontol. Rel. Quine explicates 'a exists' as '(Ex)(x = a).' (pp. 94-95)

'a' is an individual constant not a predicate connstant.

Of course. one could argue that there is a property expressed by '= a,' the haecceity-property identity-with-a. But this is a metaphysical monstrosity as I have repeatedly argued. There is no such property as the property of being identical to Harry.

However, if there were such properties, then one could assimilate identity to predication and uphold univocity.

To put it in a slogan: the price of univocity is haecceity. But the price is more unpayable than the U. S. debt.

Thanks for the comment.

[Bill Vallicella]

Here is one of my posts against haecceities: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/06/my-difficulty-with-haecceity-properties.html

[Alex Leibowitz]

I'm not sure how coherent this is, but could you analyze the two as follows?

1. Harry is.
2. Something is a horse and it is.

(There's an implicit predication in the second sentence but not in the first, and "is" in the sense of "exists" is univocal throughout.)

[Edward Ockham]

>>the price of univocity is haecceity

As you know, I agree entirely with you here.

[David Brightly]

Bill,

I put forward the following as counterexample to the claim that we cannot have univocity of 'exists' without the monstrosity of haecceities.

Consider the cubic polynomial p(x)=x**3-7x+6 over the real numbers. p(3)=12 and p(-4)=-30 so by the intermediate value theorem p has a real root: ∃x.p(x)=0. Denote this root by 'a'. Now 'a exists' is surely true. But this, despite the proper name 'a', has to be understood as a general existential claim---the concept 'real root of p' is instantiated---since this is all we know about a. So we have univocity of 'exists'. Yet we don't pay the price of a haecceity property that uniquely captures a-ness. There can be no such haecceity because a could be any of -3, 1, or 2.

[Bill Vallicella]

David,

What I don't understand is why you think 'a' is a proper name if it refers to -3, 1, or 2.

[David Brightly]

Bill,

Perhaps by analogy with the following dialogue.

A: I met one of the Beverley Sisters last night.
B: Really! Which one?
A: I forget. Let's call her 'Bev'.
B: OK.
A: Bev said she was born in 1927.
B: Ah. Bev must have been Teddie or Babs.

The logical constant 'a' seems to play the same role as 'Bev' in the dialogue as argument to predicate functions/subject of predicates. And though we never find out exactly which Sister A met, it's clear that 'Bev' is essentially singular. A met only one woman that night.

[Spencer]

Hey Bill,

I have a professor whose pet peeve is the claim that there is an 'is' of identity and an 'is' of predication. I don't know his arguments for thinking so, but his view is that 'is' is univocal and what differs is the content of the copula. If he's right, that would be a problem for you here. Do you know more about this position than I do?