Existence, Circularity, and Metaphysical Grounding

London Ed must have known by some paranormal means  that I was talking about him over Sunday breakfast with Peter Lupu.  For his post upon return from sunny Greece is about the alleged circularity of the thin conception of existence.  Peter and I were discussing Peter van Inwagen's  "Being, Existence, and Ontological Commitment" (in Metametaphysics: New Essays on the Foundations of Ontology, eds. Chalmers et al., Oxford 2009, pp. 472-506.)  Van Inwagen is a Quinean about existence and perhaps the most prominent and formidable of the contemporary thin theorists.  Me, I'm a thick-head: existence is not (identical to) what so-called 'existential' quantification  expresses, and existence comes in modes.  The negations of these convictions I reject as two dogmas of analysis (from the title of a forthcoming paper).

I was lamenting to Peter that I couldn't get London Ed to see my point about circularity.  I now think I understand why Ed doesn't accept it.  It has to do with his not accepting a different notion, that of metaphysical grounding.

Let's start with a Quinean explication of a sentence such as 'Peter exists.'  It goes like this:

1. Peter exists =_df for some x, x = Peter.

What does (1) accomplish?  Well, it shows how one can get rid of 'exists' as a first-level predicate, and with it a reason for thinking that existence is a property of individuals.  For it is clear (assuming that there are no nonexistent objects) that the sentences flanking '=df' are equivalent, indeed logically equivalent: there is no possible situation in which  one is true (false) and the other false (true).

Now in one sense of 'circular' I want to concede to Ed that (1) is not circular:  the definiens -- the RHS of (1) -- does not contain 'exists.'  In other words, (1) is not circular in the way the following are circular:

X is a human being =_df x has human parents.
Knowledge is the state one is in when one knows something.
Knowledge is cognition.
A book of pornography is one that contains pornographic material.

The following, whether correct or incorrect,  are not circular definitions in the above sense:

Knowledge is justified true belief.
Justice is whatever is advantageous to the stronger.
A circle is a locus a points in the same plane equidistant to some common point.

(1) is clearly not circular in the manner of the above examples: the definiendum is not repeated in the definiens.  So in what sense is (1) circular? (1) is true iff the following is true

1a. Peter exists =_df for some existing x, x = Peter.

(1a), however, is plainly circular.  After all, (1) is  not equivalent to

1b. Peter exists =_df for some x, whether existent or nonexistent, x = Peter.

For if (1) were equivalent to (1b), then (1) would be false.

One response I anticipate Ed making is to say that there is no difference between 'x' and 'existing x': whatever is a value of the one is a value of the other, and vice versa.  If so, then perhaps (1a) collapses into (1) and there is no circularity in the sense in which the examples above are circular.

I would insist, however, that (1) is circular in a different and deeper  sense.  A presupposition of (1)'s truth is that the domain of quantification -- the domain over which the variable 'x' ranges -- is a domain of existents.  Therefore, if I want  to know what it is for x to exist, you have not given me any insight by telling me that for x to exist is for x to be identical to something that exists.  For of course x is identical to something that exists, namely x!

Suppose we distinguish between semantic and metaphysical circularity.  I am willing to concede that (1) is not semantically circular.  But I do maintain that (1) is metaphysically circular: its truth presupposes that the domain of quantification is a domain of existing items.  To put it another way, the truth of (1) has an ontological or metaphysical ground, namely the existence of the items over which we quantify.

Consider a domain consisting of just three items: Peter, Paul, and Mary. Peter exists iff one of these items is identical to Peter.  Paul exists iff one of these items is identical to Paul.  Mary exists iff one of these items is identical to Mary.  Perfectly true and perfectly trivial.  Although we learn something necessarily true about Peter, about Paul, and about Mary, we do not learn what it is for Peter or Paul or Mary to exist in the first place. 

I want to know that is is for Peter (who stands in here for any individual) to exist. You tell me that for Peter to exist is for Peter to be identical to something.  But in giving this true but trivial answer you have helped yourself to the existence of the thing to which Peter is identical.  You have evaded my question by assuming that we are just given existing individuals.

What form could an answer take?  One answer is that the existence of the items in the domain of quantification is a brute fact and thus inexplicable.  To exist is just to be there inexplicably.  That would at least be an honest answer as opposed to the silly triviality that to exist is to be identical to something.  A radically different answer is to say that for a concrete contingent ndividual to exist is for it to be a divine creation.  Both the brute fact answer and the theistic answer are consistent with Quine's triviality.

Getting back to London Ed, why doesn't he accept my circularity objection to the thin theory?  He doesn't accept it because he is operating with an exclusively semantic notion of circularity which remains at the level of sentences and does not descend to the level of the truth-makers (ontological grounds) of sentences.  (In earlier discussions it became clear that Ed has no clue as to what a truth-maker is supposed to be.) The thin theory, as expressed in (1), however, is not obviously semantically circular: 'exists' is not found on the RHS. All one finds there is a quantifier, a variable bound by the quantifier, the identity sign, and a name that functions in this context as an arbitrary constant.  My claim, however, is that (1) is metaphysically or ontologically circular.  This notion is one that Ed does not understand.

Metaphysical grounding, one of whose forms is truth-making, is for Ed a wholly unintelligible notion.  For Peter and me, however, it is an intelligible notion .  Here I think we can locate the ultimate root of our disagreement.

What say you, gentlemen?

Comments

[Hrodberht]

I don't see why the domain of quantification has to be restricted to things that exist. Certainly there are logics that allow you to quantify over more.

[Bill Vallicella]

It doesn't have to be, but it is for van I. For him there are no nonexistent objects. London Ed and I agree with him about this.

[Edward Ockham]

I commented yesterday re part of your argument. But it is deeper than that. I think you are correct that the real source of disagreement is about the 'truthmaker' part of it, which I did not have time to think about.

The notion of 'metaphysical circularity' is obscure and problematic. Are you drawing on any established sources? By contrast, The notion of 'semantic circularity' is very clearly defined and is what is ordinarily meant by 'circularity' simpliciter.

[Edward Ockham]

>>London Ed must have known by some paranormal means

No, because I opted not to have any Internet access for the whole of my break, which lasted effectively until the time of your conversation with Peter. I had been thinking about the circularity problem for the entire holiday, as I gazed on views like this. (Mt Olympus is on the right, just hiding behind the headland)*. As soon as I got back, I wrote up my thoughts. Since my flight times were determined many months in advance, there can be no question of paranormal activity. Unless of course it was on the Phoenix side.

*Here, as ever, I disagree with you on the 'indifference of places'.

[Bill Vallicella]

Ed,

If you know something via the Internet, do you know it by paranormal means?

I suppose I should be flattered that my postings on the circularity topic occupied your thoughts while you were on Greek holiday. The quasi-circularity of no Grecian derrieres distracted you?

I will concede to you that beautiful places like Greece and Arizona -- places where, unlike Boston and London, there is a SKY -- do put a bit of a dent in the Senecan/Emersonian claim about the "indifference of places."