## Tuesday, July 17, 2012

### Metaphysical circularity

Following my post on my return from sunny Greece, the Maverick now has finally conceded that the 'thin' definition of 'exists'

(1) A-B exists =df A is B

cannot be circular, at least in the strict and ordinary sense of circular. However, he insists that the following equivalence (note the omitted 'df') is still circular.

(1a) A-B exists = existing A is B

He adds: "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." That's roughly right, but let's see why I am saying that. It follows from definition (1) that "A man who is white" is equivalent to "an existing white man", and it clearly follows from this that "existing white man" is equivalent to "white man". Thus (1a) above is a mere logical consequence of the original definition.

But Maverick goes on to claim that I am confusing semantic with metaphysical circularity. He says (I modify his wording to accommodate my example):
A presupposition of (1)'s truth is that the domain of quantification -- the domain over which the variable 'A' ranges -- is a domain of existents. Therefore, if I want to know what it is for A to exist, you have not given me any insight by telling me that for A to exist is for A to be identical to something that exists. For of course the A is identical to something that exists, namely the A! 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.
I reply: the fact that the "domain of quantification", i.e. all the items which satisfy 'A is B' is not a presupposition of the definition, but rather a consequence of it, for essentially the same reason I gave above. Let's first define 'satisfy':

(2) 'A is B' is satisfied by any A that is B

And then make the following assumption:

(3) 'A man is white' is satisfied by that man over there.

Then the following statements logically follow:

(4) That man is white (2, 3)

(5) That white man exists (1, 4)

(6) 'A man is white' is satisfied by an existing white man (3, 5)

So of course the items in the domain of quantification have to be existing items, but the sense in which they 'have to be' existing is a matter of logical consequence alone. They 'have' to exist in the same sense that a bachelor 'has' to be unmarried.

He adds that his claim that the thin conception is 'ontologically' or 'metaphysically' circular is something I fail to understand. This I agree with, of course, for the reason that 'metaphysical circularity' is incoherent.