Maverick finally replies to my circularity objections. I agree with his broad conclusion, as it happens. I just disagree with his way of getting there. He argues (I have numbered his sentences).
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.
3. If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.
This rests on the assumption that it is a contingent matter whether the description ‘Meinongian nonexistent objects’ is satisfied. But if the equivalence is logical, i.e. if ‘some objects are in the domain’ is logically equivalent to ‘some object in the domain exists’, then by definition there cannot be Meinongian nonexistent objects, any more than there can be bachelors who are married. Maverick takes an equivalence which is purportedly true by definition, then turns it into a contingent statement. But if it is contingent, the equivalence cannot be true by definition, he argues, and the rabbit is out of the hat.
4. The attempted reduction of existence to someness is therefore circular.
Wrong. The argument is fallacious, because the move from (1) to (2) is fallacious. We cannot agree that something is true by definition, i.e. subject and predicate are logically equivalent, to making its truth a contingent matter, as in (2).
11 comments:
I'm getting better at this. I properly predicted that Vallicella would object to your second alternative as requiring haecceity properties.
I couldn't understand your first alternative, but after reading the response I think he is right that you have it backward.
Is "Prime numbers exist" logically equivalent to "Some number is prime"?
>>Is "Prime numbers exist" logically equivalent to "Some number is prime"?
yes (setting aside the subtlety of the plural).
>>I couldn't understand your first alternative, but after reading the response I think he is right that you have it backward.
Sorry, what first alternative? What have I got backwards?
Oh right, I see. Second alterntive involves haecceity properties. Both Bill and I agree on that. We disagree on whether they are possible, of course.
On the first alternative, 'getting it backwards', more later.
Is "equivalence" a well-defined operator without a domain?
>>Is "equivalence" a well-defined operator without a domain?
Semantic equivalence, yes?
I am going with my mathematical instincts; mathematical functions require a mapping and a domain, and I understand why this is so. In contrast, I do not see why logical operators would be different, and thus prima facie it requires some explanation. Keep in mind that as long as we describe algebraic functions as mapping, we need not think of math as implying computability, which is not required in logic.
Dear Ockham,
If Vallicella does say 'some' and 'exists' statements are logically equivalent--i.e. have the same logical content--it is hard for me to see how you could be wrong.
What would you have thought if Vallicella had instead chosen to say 'material equivalence' instead of 'logical equivalence'? I think Vallicella's argument about general existence presupposing the singular existence of individuals has something to be said for it; it needs to be addressed. Best.
>>f Vallicella does say 'some' and 'exists' statements are logically equivalent
He says 'Ed and I agree that ...', so he does say that.
I think his claim has a lot to it. It's just his way of getting there, i.e. his argument, that I struggle with.
"He says 'Ed and I agree that ...', so he does say that."
Well, he says that for one particular, rather simple, example.
You don't agree on what exactly that equivalence means, as evidenced by our prior "some men are not men" discussions (which, as far as I'm concerned, you still have not completely addressed).
>>"some men are not men" discussions (which, as far as I'm concerned, you still have not completely addressed).
Give me time, Anthony.
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