Tag: existence

Pre-Print: Peter van Inwagen, Existence: Essays in Ontology

The following review article is scheduled to appear later this year in Studia Neoscholastica.  The editor grants me permission to reproduce it here should anyone have comments that might lead to its improvement.

REVIEW ARTICLE

William F. Vallicella

 Peter van Inwagen, Existence: Essays in Ontology, Cambridge University Press, 2014, viii + 261 pp.

This volume collects twelve of Peter van Inwagen's recent essays in ontology and meta-ontology, all of them previously published except one, “Alston on Ontological Commitment.” It also includes an introduction, “Inside and Outside the Ontology Room.” It goes without saying that anyone who works in ontology should study this collection of rigorous, brilliant, and creative articles. One route into the heart of van Inwagen's philosophical position is via the theory of fictional entities he develops in chapter 4, “Existence, ontological commitment, and fictional entities.”

 Fictional Entities

One might reasonably take it to be a datum that a purely fictional item such as Sherlock Holmes does not exist. After all, most of us know that Holmes is a purely fictional character, and it seems analytic that what is purely fictional does not exist. Van Inwagen, however, demurs:

The lesson I mean to convey by these examples is that the nonexistence of [Sherlock] Holmes is not an ontological datum; the ontological datum is that we can use the sentence 'Sherlock Holmes does not exist' to say something true. (105)

So, while many of us are inclined to say that the nonexistence of Holmes is an ontological datum in virtue of his being a purely fictional entity, one wholly made up by Sir Arthur Conan Doyle, van Inwagen maintains that Holmes exists and that his existence is consistent with his being purely fictional. One man's datum is another man's (false) theory! To sort this out, we need to understand van Inwagen's approach to ficta.

Continue reading “Pre-Print: Peter van Inwagen, Existence: Essays in Ontology“

Van Inwagen on the Univocity of ‘Exists’

In "Being, Existence, and Ontological Commitment" (in Metametaphysics: New Essays on the Foundations of Ontology, eds. Chalmers et al., Oxford 2009, pp. 472-506), Peter van Inwagen argues that 'exists' is univocal: it does not have "different meanings when applied to objects in different categories." (482)  This post will examine one of his arguments, an argument found on p. 482.  All quotations are from this page.

Van Inwagen begins by noting that number words such as 'six' or 'forty-three' do not "mean different things when they are used to count objects of different sorts."  Surely he is correct: "If you have written thirteen epics and I own thirteen cats, the number of your epics is the number of my cats."  So the first premise of the argument is the indisputable:

1. Number-words are univocal in sense: they mean the same regardless of the sorts of object they are used to count.

Van Inwagen takes his second premise straight from Frege:

2. "But existence is closely allied to number."

How so?  Well, to say that unicorns do not exist is equivalent to saying that the number of unicorns is zero, and to say that horses exist is equivalent to saying that the number of horses is one or more.  Surely that is true for both affirmative and negative general existentials.  Whether it is true for singular existentials is a further question.

Van Inwagen proceeds: "The univocacy [univocity] of number and the the intimate connection between number and existence should convince us that existence is univocal."  The conclusion of the argument, then, is:

3. Existence  is univocal.

The first thing to notice about this argument is that it is not even valid.  Trouble is caused by the fudge-phrase 'closely allied to' and van Inwagen's shift from 'exists' to existence.  But repairs are easily made, and charity demands that we make them.  Here is a valid argument that van Inwagen could have given:

1. Number-words are univocal

2*. 'Exist(s)' is a number-word

Therefore

3*. 'Exist(s)' is univocal.

The latter argument is plainly valid in point of logical form: the conclusion follows from the premises.  It is the argument van Inwagen should have given.  Unfortunately the argument is unsound.  Although (1) is indisputably true,  (2*) is false.

Consider my cat Max Black.  I joyously exclaim, 'Max exists!'  My exclamation expresses a truth.  Compare 'Cats exist.'  Now I agree with van Inwagen that the general  'Cats exist' is equivalent to 'The number of cats is one or more.'  But it is perfectly plain that the singular  'Max exists' is not equivalent to  'The number of Max is one or more.'  For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.

This question makes sense: 'How many cats are there in BV's house?'  But this question makes no sense: 'How many Max are there in BV's house?'  Why not?  Well, 'Max' is a proper name (Eigenname in Frege's terminology) not a concept-word (Begriffswort in Frege's terminology).  Of course, I could sensibly ask how many Maxes there are hereabouts, but then 'Max' is not a proper name, but a stand-in for 'person/cat named "Max" .'  The latter phrase is obviously not a proper name.

Van Inwagen's argument strikes me as very bad, and I am puzzled why he is seduced by it.  (Actually, I am not puzzled: van Inwagen is in lock-step with Quine; perhaps the great prestige of the latter has the former mesmerized.)  Here is my counterargument:

4. 'Exists' sometimes functions as a first-level predicate, a predicate of specific (named) individuals.

5. Number-words never function as predicates of specific (named) individuals

Therefore

6. 'Exists' is not a number-word.

Therefore

7. The (obvious) univocity of number-words is not a good reason to think that 'exists' is univocal.

Of course, there is much more to say — in subsequent posts. For example if you deny (4), why is that denial more reasonable than the denial of (2*)?

Another Round on the Circularity of the Thin Conception of Existence

London Ed quotes me, then responds.  I counterrespond in blue.

1. ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’

Agree, of course.

2. This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.

Disagree profoundly. The equivalence, being logical, cannot depend on any contingent assumption. From the logical equivalence of (1), it follows that ‘the domain of quantification is a domain of existing individuals’ is equivalent to ‘some individuals are in the domain’. But the equivalence is true whether or not any individuals are in the domain. E.g. suppose that no islands are volcanoes. Then ‘Some volcano is an island’ is false. And so is ‘island volcanos exist’, by reason of the equivalence. But the equivalence stands, because it is a definition. Thus the move from (1) to (2) is a blatant non sequitur.

Ed says that the move from (1) to (2) is a non sequitur.  But the move cannot be a non sequitur since (2) is not a conclusion from (1); it is  a separate premise.  In any case, Ed thinks that (2) is false while I think it is true.  (2) is the bone of contention.  To mix metaphors in a manner most atrocious, (2) is the nervus probandi of my circularity objection.

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) and sentences of the same form are to hold.  Let me explain.

On the thin theory, 'exist(s)' has no extra-logical content.  It disappears into the machinery of quantification.  It is just a bit of logical syntax: it means exactly what *Some ___ is a —* means.  But quantifiers range over a domain.  In first-order logic the domain is a domain of individuals.  That is not to say that the domain cannot be empty.  It is to say that the domain, whether empty or non-empty is a domain having or lacking individuals as opposed to properties or items of some other category.

Now there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals.  So suppose we have a domain populated by nonexistent individuals only.  Supppose a golden mountain is one of these individuals.  We can then say, relative to this domain, that some mountain is golden.  But surely 'Some mountain is golden' does not entail 'A golden mountain exists.'  The second sentence entails the first, but the first does not entail the second.  Therefore, they are not logically equivalent.

To enforce equivalence you must stipulate that the domain is a domain of existing individuals only.  If 'some' ranges over existing individuals, then 'Some mountain is golden' does entail 'A golden mountain exists.'   In other words, you must stipulate that the domain be such that, if there are any individuals in it, then they be existent individuals, as opposed to (Meinongian) nonexistent individuals.  The stipulation allows for empty domains; what it rules out, however, are domains the occupants of which are nonexistent individuals in Meinong's sense.

I hope it is now clear that a necessary presupposition of the truth of equivalences like (1) is that the domain of quantification be a domain of existing individuals only.  Again, such a domain may be empty.  But if it is, it is empty of existent individuals – which is not the same as its harboring nonexistent individuals.

In other words, we can eliminate 'exist(s)' in favor of the particular quantifier 'some,' but only at a price, the price being the stipulation that quantification is over a domain of existing individuals.  But then it should be clear that the thin theory is circular.  We replace 'exist(s)' with 'some,' but then realize that the particular quantifier must range over a domain of existing individuals.  The attempt to eliminate first-level existence backfires.  For we end up presupposing the very thing that we set out to eliminate, namely, first-level existence.  The circularity is blatant.

Ed's argument against all this is incorrect.  We agree that (1), expressing as it does a logical equivalence, is necessarily true.  As such, its truth cannot be contingent upon the actual existence of any individuals.  If existence reduces to someness, then this is the case whether or not any individuals actually exist.  My point, however, was not that (1) presupposes the existence of individuals, but that it presupposes that any individuals in the the domain of quantification be existent individuals as opposed to (Meinongian) nonexistent individuals.

(1) presupposes, not that there are individuals, but that any individuals that there are be existent individuals.  If you appreciate this distinction, then you appreciate why Ed's argument fails.