I am racking my brains over the question why commenter 'Ockham' cannot appreciate that standard quantificational accounts of existence presuppose rather than account for singular existence. It seems so obvious to me! Since I want to put off as long as possible the evil day when I will have to call him existence-blind, I will do my level best to try to understand what he might mean.
Consider the following renditions of a general and a singular existence statement respectively, where 'E' is the existential or particular quantifier:
1. Cats exist =df (Ex)(x is a cat)
2. Max (the cat) exists =df (Ex)(x = Max)
Objectually interpreted, what the right-hand sides of (1) and (2) say in plain English is that something is a cat and that something is (identical to) Max, respectively. Let D be the domain of quantification. Now the right-hand side (RHS) of (1) is true iff at least one member of D is a cat. And the RHS of (2) is true iff exactly one member of D = Max. Now is it not perfectly obvious that the members of D must exist if (1) and (2) are to be true? To me that is obvious since if the members of D were Meinongian nonexistent items, then (1) and (2) would be false.
Therefore, 'Something is a cat' is a truth-preserving translation of 'Cats exist' only if 'Something is a cat' is elliptical for 'Something that exists is a cat.' And similarly for 'Something is Max.' But here is where 'Ockham' balks. He sees no difference between 'something' and 'something that exists' where I do see a difference.
I am sorely tempted to call anyone who cannot understand this difference 'existence-blind' and cast him into the outer darkness along with qualia-deniers, eliminative materialists, deniers of modal distinctions, and the rest of the terminally benighted. But I will resist this temptation.
And were I to label 'Ockham' existence-blind he might return the 'compliment' by saying that I am hallucinating, or suffering from double-vision. "You've drunk so much Thomist Kool-Aid that you see a distinction where there isn't one!" But then we get a stand-off in which we sling epithets at each other. Not good for those of us who would like to believe in the power and universality of reason. It should be possible for one of us to convince the other, or failing that, to prove that the issue is rationally undecidable.
The issue that divides us may be put as follows.
BV: Because the items in the domain of quantification exist, there has to be more to existence than can be captured by the so-called 'existential' quantifier. Existence is not a merely logical topic. Pace Quine, it is not the case that "Existence is what existential quantification expresses." Existence is a 'thick' topic: there is room for a metaphysics of existence. One can legitimately ask: What is it for a concrete contingent individual to exist? and one can expect something better that the blatantly circular, 'To exist is to be identical to something.' To beat on this drum one more time, this is circular because D is a domain all of whose members exist. Therefore, 'something' is elliptical for 'something that exists.'
O: Pace BV, the items in the domain of quantification admit of no existence/nonexistence contrast. Therefore, 'Something is a cat' is indistinguishable from 'Something that exists is a cat.' There is no difference at all between 'something' and 'something that exists,' and 'something' is all we need. Now 'something' is capturable without remainder using the resources of standard first-order predicate logic with identity. 'Exist(s)' drops out completely. There is no existence and there are no existents. There are just items, and one cannot distinguish an item from its existence.
Now if that is what O means, then I undersdtand him, but only on the assumption that for individuals
3. Existence = itemhood.
For if to exist = to be an item, if existence reduces to itemhood, then there cannot be an existence/nonexistence contrast at the level of items. It is a logical truth that every item is an item, and therefore an item that is not an item would be a contradiction: 'x is an item' has no significant denial. Therefore, on the assumption that existence = itemhood, there is no difference between 'Some item is a cat' and 'Some item that exists is a cat.' And if there is no such difference, then existence is fully capturable by the quantifier apparatus.
But now there is a steep price to pay. For now we are quantifying over items and not over existents, and sentences come out true that ought not come out true. 'Dragons exist,' for example, which is false, becomes 'Some item is a dragon' which is true. To block this result, O would have to recur to a first-level understasnding of existence as contrasting with nonexistence He would have to say that every item exists, that there are no nonexisting items. But then he can no longer maintain that 'something' and 'something that exists' are indistinguishable.
I appreciate you saying that. But I still don't follow your argument. I agree that 'dragons exist' is false. That is because 'no thing [or 'item'] is a dragon' is true. I also agree that 'every thing [or item] exists' is true. That is because 'F's exist' means 'F's are things', thus 'every thing [or item] exists' means 'every thing is a thing'. Which is of course true.
This does not imply that 'something' and 'something that exists' are distinguishable in any important sense. For 'something that exists' is interchangeable (according to thins) with 'something that is a thing'. Just as 'some man' = 'some man that is a man'.
To appreciate my line of argument, you have to suppose I speak a language which does not contain the word 'exist' or any of its derivatives, but which does have the word 'thing'. Thus I translate every sentence of yours into a 'thing' sentence, and find that every sentence of yours where you try to assert something meaningful with the word 'exists', I translate into a 'thing' sentence which is merely true in a banal way.
To settle these argument, we could agree that the word 'exists' for you has a different meaning than the one I take it to have, which is translateable into a 'thing' sentence, and that I will forever be unable to grasp this meaning.
But that seems unphilosophical. If 'exists' does have a meaning that is untranslateable into 'thing' language you need to explain clearly what you mean by 'exist', rather than using it in a way that presumes a meaning.
What is it? Is it right? Is it wrong? What is the upshot either way?
The purpose of this post is to examine in depth Bill’s circularity objection (BCO, in short). Naturally, it will be once again a somewhat lengthy affair. In advance I apologize for that.
(I) A brief outline of BCO:
Bill has argued repeatedly that a thin theory of singular existence (thin-TSE) is subject to a vicious circularity objection. What is his argument? Let us consider three version of a thin-TSE that have been circulating (I hope not viciously) in our discussions on this site:
(A) Quine’s Version: “to be is to be a value of a (bound) variable.”
(i) Restatement of Quine’s Version:
(QV) to exist is the same thing as to be an object that can serve as the value of a (bound) variable.
(ii) But, now, what are we to make of the bolded phrase ‘the same thing as’? Can we interpret this phrase so that what is on the right hand side (RHS) of it fully explicates the phrase ‘to exist’ on the left-hand-side (LHS)? Bill claims that we cannot! Why? Because a full explication, one that completely explains a given concept, cannot itself presuppose the very concept it is set out to explicate. But, so Bill argues, the RHS of (QV) presupposes the concept ‘to exist’ on the LHS. How? Well, the RHS of (QV) purports to explicate the phrase ‘to exist’ on the LHS by appealing to certain objects that serve as values of variables. But, which objects serve as values of variables? Well, those objects that are members of the domain of the quantifiers. But, which objects are members of the domain of the quantifiers? Or to put this point in a different way: What is the criterion of selecting objects that are to be reckoned as members of the domain of the quantifiers? Well, those, and only those, objects that exist. But we are now presupposing the concept ‘exists’ in the process of selecting those and only those objects that are included in the domain of the quantifiers. Yet the domain of the quantifiers was supposed to be part of a full explication of the concept ‘exists’. Therefore, the bolded phrase ‘the same thing as’ cannot be understood as a full explication of ‘to exist’.
(iii) The correct interpretation of the bolded phrase, the phrase ‘the same thing as’ in (QV), is extensional equivalence. It can only mean ‘if and only if’. But even if (QV) is true interpreted as extensional equivalence, it cannot be taken to fully explicate the concept of existence for extensional equivalence is insufficient as a means to explicate anything.
(B) My Version: “to be is to be a member of a set that can serve as the domain of the quantifiers.”
(i) Restatement of my version:
(PV) to exist is the same thing as to be a member of a set that can serve as the domain of the quantifiers.
(ii) Bill, of course, would raise a very similar objection against (PV) as he did against (QV). The bolded phrase in (PV) cannot mean full explication of ‘exists’ because the RHS of (PV) presupposes existence. How? Well, which objects are members of the set that can satisfy the condition ‘a set that can serve as the domain of the quantifiers’? Of course, only those objects that exists. So in selecting the set in question we must know how to apply the concept ‘exists’ to things. Therefore, our selection procedure of the correct set is conceptually prior to our concept of a set and its members. QED.
(C) O’s Version (as I understand it): to exist is to be the referent of a referring expression (such as a name, definite description, indexical expression; e.g., ‘this’).
(i) Restatement of O’s version:
(OV) to exist is the same thing as to be the referent of a referring expression.
(ii) I am sure that by now everyone should see what Bill would say about (OV). Once again the bolded expression cannot be a full explication of the concept of existence. Why? Well, which objects are suitable referents of a referring expression? Why, of course, only those objects that exist. So in selecting a referent for a putatively referring expression such as ‘Socrates’ for instance we must use the concept of exist. The bolded expression in (OV) must be construed at best as extensional equivalence. But by so interpreting this phrase we are not justified to think of (OV) as a full explication of the concept of existence. QED.
(II) What exactly is going on here? It is easiest to see the strategy employed by Bill’s argument by examining it in the cases of (QV) and (OV).
(i) Consider the argument in the case of (OV). Suppose that ‘Socrates’ is a term in some language L. Consider the following:
(a) ‘Socrates’ refers to Socrates.
(ii) Strictly speaking, (a) is not a statement in L; it is rather a statement in the so-called meta-language of L; i.e., M(L). So in M(L) we are presupposing the concept of existence in order to formulate (a) for L. What is going on here is that if we are trying to explicate the concept of existence for L (OV) appeals to a meta-language of L and formulates statements such as (a). Thus, the objects that exist with respect to L, according to (OV), are exactly those objects that serve as referents for the terms in L. And in order to characterize the referents of the expressions of L we need to make statements such as (a) in M(L); and indeed we presuppose the concept of existence in M(L).
(iii) The same situation occurs when we examine (QV). The formulation of the quantification structure of L is strictly speaking stated in M(L). So the selection of the domain of quantification for a language L is done in M(L). And clearly such a selection presupposes the concept of existence in M(L).
(iv) In both cases, (QV) and (OV), we are dealing with formal semantics. A semantic theory, Tarski has thought us, requires a meta-language. And the resources of the meta-language must include the concept of existence in order to give a semantic interpretation for a given language. BCO exploits this fact and turns it into an objection against any thin-TSE that attempts to give an account of existence in terms of the resources of a rich semantic theory that include the concept of reference and the existential quantifier. The objection appeals to the fact that no thin-TSE that proceeds to explicate existence in terms of the resources of a semantic theory can fully explicate the concept of existence because the structure of such semantic theories requires a distinction between a language and a meta-language and it must presuppose the concept of existence in the meta-language.
(v) The same situation obtains in the case of (PV), except it is somewhat muted. The first thing we need to note is that set theory features an existential axiom to the effect that some sets exist. In general, this axiom is satisfied in an empty world because even in such a world the null set exists. The rest of the sets can be generated recursively from the existence of the null set. But a “null-set” set theory is useless in order to explicate the concept of existence as it applies to contingently existing individuals. So (PV) must be viewed in the context of so-called grounded set theory: i.e., the theory begins with the assumption that at least some individual objects exist. Moreover, in order for such a set theory to be capable of serving as the domain of quantification theory, the set of objects of such a grounded-set-theory must be, guess what: the domain of all and only existing objects in the actual world. So, here we go again: in order to specify a suitable set theory as an explication of existence according to (PV), we need to appeal to a grounded-set-theory. But the later cannot be a full explication of existence because it already presupposes it by the very nature of what a grounded set-theory is.
(III) What follows?
(i) So, as we can see, BCO works by identifying the underlying presuppositions behind (QV), (OV), PV), and find that they all must take for granted the concept of existence. In the case of (QV) and (OV) the existential assumption appears in the meta-language. In the case of PV), the existential assumption appears in the very notion of a grounded-set-theory which is the one we must appeal to for (PV).
(ii) Bill’s Conclusion: Hence, Bill concludes, all of these thin-TSEs fail to offer a full-explication of existence because no such an explication is entitled to presuppose this concept.
(iii) But I submit that Bill’s conclusion follows only if
(A) There can be a theory that offers a full-explication of existence without anywhere presupposing in any way the concept of existence;
and
(B) There is no form of full-explication of a concept (such as existence) that is legitimate even if it presupposes the concept to be explicated.
(iv) I do not think that Bill has adequately shown that (A) and (B) are true. As for me, I shall in time pursue these questions in other posts.
To Be Continued…
peter
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