Quantifying over intentional objects

I emphasised earlier that the nominalist must at all cost pre-empt the Intentionalist’s driving a wedge between ‘some thing’ and ‘some existing thing’. This appears to be just what Peter Lupu has done here. Peter agrees that the consequence ‘Tom is thinking of a mermaid, so there are mermaids’ is invalid, but (apparently) for the reason that in the antecedent sentence the term ‘mermaid’ ranges over mermaids thought-of, i.e. intentional mermaids, and so is true. In the consequent, the same term ranges over ‘ordinary objects’, and so is false, and so the consequence is invalid.

There are many reasons against this. Some I have already given. I will repeat them, together with some more.

1. If Peter’s reason is correct, then the consequent of ‘Tom is thinking of an intentional object, therefore there are intentional objects’ is false, as the term ‘intentional objects’ ranges over ordinary objects (intentional objects being weird, not ordinary). But as I argued here and here, it would not be possible for the intentionalist and the nominalist to disagree at all unless they agreed on the meaning of categorical statements like 'no A is B' or 'some A is not B'. When the nominalist says that there aren't any intentional objects, he is denying exactly what the intentionalist asserts when he asserts that there are such things. They both agree that the scope of ‘intentional objects’ includes potentially any kind of objects, queer and straight, and the nominalist is denying there are any queer ones.

2. In ‘Tom is thinking of a mermaid, but there are no such things as mermaids’, the second ‘mermaid’ clearly picks up the scope of the first. So if the first ranges over queer objects, so does the second. But the second denies there are any such things. Indeed, we could leave out the second ‘mermaids’ and just say ‘Tom is thinking of a mermaid, but there is no such thing’, where it is clear that what the second sentence denies the existence of precisely what Tom is thinking of.

3. The sentence ‘Tom wants a cigarette’ does not assert that Tom wants some weird object that ‘a cigarette’ ranges over. No: Tom wants a real cigarette, and the only reason he wants one is because none is there. Intentional cigarettes are so unsatisfying.

4. Similarly in ‘this house lacks a bathroom’, the scope of term ‘bathroom’ does not include a non-existing bathroom. The statement is merely equivalent to the negative statement ‘this house does-not-have a bathroom’.

Meaning and Meinong

David Brightly asks whether we can avoid Meinong quite so easily. Meinong draws a distinction between being and existing. Thus some things which have Being may not exist - the golden mountain which I am thinking of, perhaps?

I already engaged with this objection in my second point here. The problem for the Meinongian thesis is that "Vallicella is thinking of a non-existent thing" is perfectly consistent with "no thing is non-existent", where scope of 'no thing' covers every object whatsoever, and is therefore inconsistent with "some non-existent thing has Being". So the Meinongian solution doesn't solve anything.

I suppose the Meinongian could object that the scope of 'no thing' may fail to cover those things that have Being but which are non-existent. But (a) I can still insist that I mean nothing whatsoever, not just nothing that is not a non-existent Being. And (b) as I argued here it would not be possible for the Meinongian and the anti-realist to have an argument at all unless they agreed on the meaning of categorical statements like 'no A is B' or 'some A is not B'. When the anti-realist says that there aren't any non-existent, he is denying exactly what the Meinongian asserts when he asserts that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.

David also comments on the curious fact we can reason about apparently non-existent objects. Indeed. The Square of Opposition seems to work for fictional characters. 'All the characters in Lord of the Rings are hobbits' implies 'some of the characters in Lord of the Rings are hobbits', is the contrary of 'none of the characters in Lord of the Rings are hobbits' and is the contradictory of 'some of the characters in Lord of the Rings are not hobbits'. More is needed.

Azzouni and equivocation

There is a very fine argument in Ockham's Summa Logicae book II, chapter 4. He is objecting to the claim that the verb 'to be' is ambiguous in certain arguments. But this is completely irrational, he says " for it amounts to destroying every argument form. For whenever it pleases me, I will say that 'to be' is equivocal in the premisses, and I will ascribe at will a fallacy of equivocation to every syllogism".

Absolutely right. The verb 'is' is implicit in every proposition. If this verb is ambiguous, we can disprove any argument whatever at will, by appealing to this ambiguity or equivocation. But that is irrational, and amounts to destroying all logic. For logic is about the form of arguments, and not about what we can 'ascribe at will'. If we can challenge the validity of any argument 'at will', you destroy all logic.

This claim that Ockham objects to is precisely the claim that Jody Azzouni appears to be making when he argues against the 'triviality thesis', which is the thesis that the existential quantifier just means 'there is', and 'there is' just carries ontological commitment. Azzouni argues that the triviality thesis is wrong since there are assertions of the form 'there are Fs' that do not always carry ontological commitment.

If Azzouni is correct, it really does amount to destroying all logic. I have already argued this in my objection to William Craig's claim that there is no contradiction in 'some x's are numbers and no numbers are created' and 'all x's are created by God', by reason of equivocation on the existential quantifier. If an argument as basic as this is invalid, all argument is invalid.

Here are two more arguments for this.

1. Meinongians say there are fictional entities. Nominalists say 'there aren't'. Regardless of what is the correct position, this disagreement could not take place at all unless both sides were agreed on the meaning of 'there are' and 'there aren't'. When the nominalist says that there aren't any fictional entities, he is denying exactly what the Meinongian asserts when she says that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.

2. Azzouni might argue that (for example) 'there are hobbits in Tolkien' is true, but 'there are hobbits in Jane Austen' is false. But this is not an argument that 'there is' is equivocal. On the contrary, it means exactly the same in both cases. What is asserted is different, for in one case we say there are hobbits in Tolkien, in the other, that there are hobbits in Jane Austen. It is the qualifying 'in Austen' or 'in Tolkien' that changes the assertion. But in both cases 'there are' means the same. If it doesn't mean the same it amounts, as Ockham says, to the destruction of all logic.

Ontological dependence

My argument again. The following formally expressed statements are inconsistent.

1. (E x) number(x)
2. (x) number(x) implies not created(x)
3. (x) God created x

If (1) some x is a number, then (2) that x was not created. But (3) for all x, God created x, so God created that x. Contradiction.

Given this, it doesn't help to say that existentially quantified statements such as (1) don't really express or imply existence, or that (1) has no 'ontogical commitment'. This is irrelevant. Even if (1) is true of some x's to which we have no ontological commitment, it still logically follows that (3) is true of all x's, and so (presumably) is true of x's to which we are not ontologically committed. This is no way out.

Azzouni argues that our criterion for existence should be 'ontological independence'. If an object's properties depend wholly upon us (as in the case of fictional objects) then that entity does not exist. If our method for establishing the truth about an object is trivial (as in the case of mathematics) then it is ontologically dependent upon us. Accordingly, mathematical objects do not exist.

This does not help with the theological problem above. Even if (1) is true of ontologically dependent objects, there is still a contradiction, because there is nothing to prevent the universal quantifier ranging over such objects. If God created all things, then he made ontologically dependent things. But according to (2) some ontologically dependent things (numbers) are not created. Contradiction.

And Azzouni's suggestion creates another problem. I can meaningfully ask whether there are such things as 'ontologically dependent' objects. If yes, then why does Azzouni say that such objects do not exist? If not, in what sense is Azzouni offering any kind of solution at all? More on this later.

Azzouni on Ontological Commitment

Deflating Existential Consequence: A Case for Nominalism. Jody Azzouni, New York: Oxford University Press, 2004

I haven't got hold of a copy of this book yet, but the next best thing is a review. Three below.

Mark Colyvan
Thomas Hofweber
Joseph Melia