Existence and Quantification: Does London Ed Beg the Question?

In his latest installment, London Ed writes:

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[al] assumption about the meaning of the verb 'exists'.

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

[. . . ]

I suppose I need to explain why there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals.  There would be something to stop us if the notion of a nonexistent object were logically self-contradictory.  But I see no contradiction in it.  So let me put the question to Ed:  Do you think that the very idea of a nonexistent object is logically self-contradictory?  If you do think this, then I refer you to my November 2009 post, Is Meinong's Theory of Objects 'Obviously Self-Contradictory'? Van Inwagen Says 'Yes.'

There is also the issue of question-begging.  Ed needs to justify the slide from

a. 'A golden mountain exists' is logically equivalent to 'Some mountain is golden'

to

1. 'A golden mountain exists' = 'Some mountain is golden.'

Equivalence is not identity!  Not even logical equivalence is identity. Propositions p, q are logically equivalent iff there is no logically possible world in which p is true and q false, or vice versa.  Now Ed and I agree about (a).  But the inference from (a) to (1) is invalid.  Consider triangularity and trilaterality.  There is no logically possible world in which it is true that something is triangular but not true that something is trilateral.  So 'Something is triangular' and 'Something is trilateral' are logically equivalent.  But it doesn't follow that they express the same proposition or that the triangularity = trilaterality.

Likewise, it does not follow from (a) that existence = someness.  Every world in which cats exist is a world in which something is a cat.  No doubt.  But how is it supposed to follow that the 'property' of existence is identical to the syntactical 'property' expressed by *Some ___ is a ---*?

Ed begs the question against me by simply stipulating that the meaning of the verb 'exists' shall be identical to the meaning of 'Some ___ is a --.'   That is what I deny.

Comments

[Account Deleted]

(Note: While this post may not quite fit in this thread, I am unsure where to post it, so it might as well be posted here)

A) Bill’s argument against the thin-conception of existence stated in a paper discussed in the last few posts can be presented as follows (quotations are from the aforementioned paper):

1) “…the most fundamental question [regarding existence] concerns the general status of existence.” (p. 1) which in turn is a question about “what sort of item existence is.” (ibid).

2) The so-called thin-conception of existence is one of the primary theories or accounts of existence that answers the “general status” question about existence. It is the principal rival of the *thick* theory or account.

3) The thin theory maintains that (i) existence is a univocal concept; (ii) it is fully captured by the apparatus of quantification specifically by the second-order concept of *instantiation* together with the concept of number (i.e., how many?); and (iii) existence has no metaphysical content:
Bill says: “Existence is instantiation. Equivalently, existence is someness. … ‘Exist(s)’ disappears into the machinery of quantification.” (p. 3)

4. The thin theory of existence falls prey to several objections. Two of these objections are the circularity objection and the nonexistent-objects objection.

(a) The circularity objection proceeds as follows. The thin-theory explicates, explains or identifies existence with instantiation. But existence cannot be explicated, explained, or identified with instantiation because the individual in question must be already assumed to exist in order for it to instantiate a concept. Therefore, existence is in a deep sense more fundamental than instantiation.

(b) The second objection aims to show that in the case of nonexistent objects instantiation is present but existence is obviously lacking. Hence, existence and instantiation cannot be identical concepts.

Therefore,

5) The thin conception fails as a theory of existence.

B) While I agree that Bill’s arguments cast a shadow of suspicion on the adequacy of the thin conception of existence, I am not convinced that his arguments actually demonstrate that the thin conception is guilty of being inadequate. I have two reasons for my lack of conviction.

(a) Bill’s second argument (A4b) stated above is easily dismissed by the proponents of the thin conception by simply denying that it makes sense to say that there are nonexistent objects. A proponent of the thin conception need not give a general argument for this claim. Instead he could simply show case by case that any story that attempts to make sense of such claims ends up nonsense (see van Invagen’s ‘Meta-Ontology’, reprinted in his Ontology, Identity, and Modality, Cambrindge University Press, (2001)).

Note that I am not taking sides on this issue. I am merely showing that Bill’s argument from nonexistent objects is not conclusive. The matter is undecided. Hence, while the considerations Bill adduces here suffice to cast a shadow of suspicion on the thin-conception, they do not amount to a conclusive argument.

(b) Bill assumes (premise A2) that the thin-conception is a *theory* or an *account* of existence. But a proponent of the thin-conception is well advised to reject this assumption. A proponent of the thin-conception can deny this assumption by saying that the concept of *existence* is just not the sort of concept about which we can devise a theory or give an account like we can in the case of a theory of water or even a theory of justice.

While Bill construes the thin-conception as maintaining that the apparatus of quantification (instantiation and all) offers an account or theory of existence, I suggest that the proponent of the thin-conception should not view matters in this light. The proponent of the thin-conception can maintain instead that because a theory of existence is not possible, all we can do is translate or paraphrase existential claims into the language of quantification with the aim of making explicit inferential relations involving existential statements.

Thus, according to the present construal of the thin-conception, the *thinness* of existence is precisely that a theory of existence is not possible. Hence, all that is left for us to do, all we can do, is to paraphrase or translation existence statements into quantification form, thereby, preserving inferential structure.

Such an approach undercuts Bills circularity argument. For the circularity argument has a bite only if one takes the thin-conception to be a *theory of existence* which includes the claim that the nature of existence is captured by instantiation. But I am suggesting that the thin-conception makes no such a claim. According to the present proposal, the apparatus of quantification does not give the nature of existence, for according to the thin-conception there is no such nature to give. Instead the apparatus of quantification offers a convenient way of translating or paraphrasing common English existence statements so as to unveil their inferential structure. There is no circularity in such a project.

C) I wish to emphasize that I have not endorsed above the thin-conception. I merely pointed out that proponents of the thin-conception need not buy Bill’s construal of their view as a theory or account of existence. If they take this view, then Bill’s circularity objection no longer applies. It is now up to Bill to show that this way out is not viable.

[Alfredo]

Dr. Vallicella, I wonder if some misunderstanding has occurred because the two of you are using the term 'logical equivalence' differently? I suspect that Ockham will not be happy with your definition of logical equivalence in terms of possible world. Maybe we should just wait and see.

[Alfredo]

Nevermind, he has already replied, accusing you of dealing in continental philosophy: http://ocham.blogspot.com/2012/05/analytic-vs-european.html Yikes!

[Account Deleted]

I am not clear about some points that are debated by Bill and Ed.

1) For instance, in first-order classical quantification theory the domain of quantification must contain at least one individual (i.e., cannot be empty). Without this assumption the theory will not work. On the other hand, there is Free-Logic in which this assumption is not required.

2) Is the notion of *nonexistent object* self contradictory?
In his November 2009 post Bill shows that such a conclusion is not inevitable at least on the surface. But Bill's argument requires a more in depth scrutiny. For instance, at crucial point in his argument against van Invagen, Bill employs the notion of an 'item'. (Incidentally, the very same notion appears in his draft article which I quoted in my previous post on this tread (premise A1)). But what is an *item* in the context of the present discussion?

3) As for the dispute (if there is one?) about equivalences such as (a) above:

(a) 'A golden mountain exists' is logically equivalent to 'Some mountain is golden'

On the one hand, Bill is right in maintaining that in general logical equivalence does not amount to identity and for the reasons he gives above. On the other hand, Ed (I think) views logical equivalences such as (a) as being "definitional", in the sense that the notion of *exist* in ordinary discourse (LHS of (a)) is *defined* in some other terms; in this case in terms of the quantificational vernacular of 'some' etc. Thus Ed's use of '='.

My question, however, is this: What does this dispute have to do with the issues about the thin-conception of existence?

As stated in my post above, the thin-conception need not maintain any of the following theses: the relevant apparatus of quantification provides a *theory of existence* (in any useful sense of theory); we can define the *concept* of existence in terms of *someness*; the *property* picked out by the notion of existence is identical to the second-order property of instantiation; the apparatus of quantification gives us the *nature* of existence; etc.

In fact, according to the above proposal, the thin-conception has no use for equivalences such as (a). Instead, the thin-conception need only say that statements such as the ones on the LHS of (a) are paraphrased (roughly) in ways that appear on the RHS of (a). Such paraphrases do not give the meaning of the concept of *exist* nor do they state identity of properties or...etc. They simply preserve inferential structure in some logical system, period!