## Friday, November 04, 2016

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Don't disagree with the point about Ex x = a, and I think we have discussed this before, and I agreed then. The predicate calculus is incapable of expressing existence of objects via singular term statements. It can assert that Ex Fx, where F does not include a referring term to the object that satisfies it (example, 'there are cats), but the singular term itself, in order to be meaningful within the predicate calculus at all, has to refer to something in the domain. Thus Ex x = a asserts that a is self-identical.

>>Thus Ex x = a asserts that a is self-identical.<<

Right. But surely the 'property' of existence cannot be reduced to the 'property' of self-identity. It follows that existence lies beyond the Discursive Framework. Yes or no?

Do you see the structural analogy with the unity of the sentence/proposition? The unity lies beyond the DF. Yes or no?

I exploit the analogy in my existence book wherein I argue that the existence of an individual is the unity of its constituents.

My point is that the English proposition ‘there was a such a person as Moses’ does not say that Moses was self-identical. I.e. standard English can express what the predicate calculus cannot.

However, this does not commit us to the thesis that existence is a predicate. We have discussed this a few times before. As you know, I espouse singular concepts. The whole of the ‘same God’ book is about this. The thesis is (1) in a possible world where the Hebrew Bible was never written, no one could have a concept of Moses, (2) we have such a concept through through the availability of the Bible, hence of back-referential chains which refer back to that text and (3) ‘there was such a person as Moses’ states that this concept is satisfied.

But is the argument

A1. Stromboli exists. Ergo,
A2. Something exists,
in fact valid? If it were it would be so by virtue of its logical form. This is
B1. name exists. Ergo,
B2. Something exists.
But if this were a valid form then
C1. Oberfringelhorn exists. Ergo,
C2. Something exists,
would be a valid argument. I say it's not because (C1) informs us of nothing whereas (C2) informs us of something and information cannot arise from no information. So by reductio ad absurdum the (A) argument and the (B) form are invalid.

However, I think we can say that argument (A) is enthymematic for a valid argument. And when the missing steps are put back in we get an argument that can be expressed in predicate calculus language.

I don't get it, David. But thanks for the comment.

Whether we are talking about Stromboli, Todtnauberg, or Icarus, if that item exists, then something exists. Surely that is a valid move. And non-enthymematic to boot.

The fact that many people have never heard of Stromboli and do not know it is an island volcano does not invalidate the argument. And whatever Oberfringlehorn is, if it exists, then something exists.

What would the Astute Opponent say to David?

I am agreeing with the Maverick here. If Moses existed, then someone existed. This is true in both predicate logic (Fa implies Ex Fx) and ordinary English.

However I deny that 'It is not the case that Moses existed' implies 'someone was such that they did not exist', unlike in predicate logic where '~Fa' implies 'Ex ~Fx'.

I also agree that the fact that many people have never heard of Stromboli and do not know it is an island volcano does not invalidate the argument.

I have a little more trouble with statements like 'some of the characters in War and Peace are fictional, and ‘all the characters and places in The Lord of the Rings are fictional’. Clearly true, but problematic.

Hello Bill,

Astute and I have discussed this and we disagree. I have hopes of winning him round because what I'm suggesting is hugely simplifying.

In the PC there is just one way of introducing a name. This is the rule of Existential Elimination (EE). Argument (A) as it stands flouts EE. EE says that in the context of an existential claim such as ∃x.P(x) one can introduce a new name, 'c', say, and infer P(c). 'c' names one of the entities that satisfy P(). Entity c is said to 'witness' the existential. Names cannot arise in any other way. Textbooks often gloss over this point, with examples that use names without introduction. They will launch into

Man(Socrates)
rather than the more formal
∃x.Man(x)
Man(Socrates)
One can translate this into informal English as
There is a man called Socrates,
which is, of course, how every story begins!

Can I refer you back to Deducing John McCain from the Principle of Identity? Your solution (B) to this puzzle is essentially what I am saying here.

My view is that 'Moses existed' can be seen as a reiteration of the general existential statement under which the name 'Moses' was (must have been) introduced. And that general existential would have said that someone existed.

Likewise the denial 'It is not the case that Moses existed' does not have the form ~Fa which would have the unfortunate implication Astute supplies. Instead we take it as a denial of the general existential (which I'm saying has to be present for the argument to be valid) under which the name 'Moses' was introduced. In informal English we can say 'There never was such a man as this so-called 'Moses''.

Astute writes,

>>The thesis is (1) in a possible world where the Hebrew Bible was never written, no one could have a concept of Moses, (2) we have such a concept through through the availability of the Bible, hence of back-referential chains which refer back to that text and (3) ‘there was such a person as Moses’ states that this concept is satisfied.<<

So concepts for you are not objective like Frege's Begriffe, but subjective in the sense of being dependent on minds like ours. My objection is that the existence of Moses cannot be identified with the instantiation of the singular concept in question because there are possible worlds in which Moses exists but that concept does not exist.

>>So concepts for you are not objective like Frege's Begriffe,

No they are just as objective as Frege's Begriffe. They exist in some worlds, not in others.

Can there be possible worlds in which dolphins do not exist? Surely. Does that prove that being a dolphin is a subjective property? Surely not.

I devote a whole chapter of the book to this question.

David has this emotional attachment to the predicate calculus, which I do not share.

You're not getting my point. The existence of the Moon cannot be identified with the instantiation of a concept that came into being in the heads of humans long after the Moon came into existence.

>>You're not getting my point. The existence of the Moon cannot be identified with the instantiation of a concept that came into being in the heads of humans long after the Moon came into existence.<<

Ah my mistake. Yes, the singular concept corresponding to Moses does exist in every possible world. However people in that possible world will not have access to it unless the Hebrew Bible exists in that world. Good point.

I also question whether there are singular concepts at all. A singular concept is one that 'captures' the very haecceity of the individual whose singular concept it is. It is not merely a concept that has a single instance, but one that has the same single instance in every possible world in which is has an instance.

In addition, the singular concept of Moses, say, exists in every possible world including those worlds in which Moses does not exist.

I have argued more than once that all these conditions cannot be jointly satisfied.

One of the problems for you is that you are committed to saying that, before Moses came to be, there was a singular concept of that very individual.

Whereas my view is that the very haecceity of Moses first comes to be only with Moses.

Now here is one hairy metaphysical question: Does existence enter into the very individuation of an individual as I maintain? Or not, as you are committed to maintain?

This also bears on the nature of divine creation. You must hold that creation is the causing of the instantiation of singular concepts. So God creates out of a stockpile of singular concepts, not out of nothing.

>> A singular concept is one that 'captures' the very haecceity of the individual whose singular concept it is.

The proper name ‘Moses’ has a meaning. This, unlike ‘man’, does not correspond to any property or characteristic of Moses. So I deny ‘haecceities’.

>>It is not merely a concept that has a single instance, but one that has the same single instance in every possible world in which is has an instance.

According to the narrative theory of reference, in the modal proposition ‘It might have been the case that there was no such person as Moses’, the name ‘Moses’ has the same meaning as the non modal ‘There was such a person as Moses’. Remember that nominalists don’t buy ‘possible worlds’. There are merely modal propositions.

>>In addition, the singular concept of Moses, say, exists in every possible world including those worlds in which Moses does not exist.

There can be singular concepts, say the meaning of ‘Frodo Baggins’, without any corresponding individual, yes.

>>One of the problems for you is that you are committed to saying that, before Moses came to be, there was a singular concept of that very individual.

I don’t think that’s true, except in the sense that your expression ‘before Moses came to be’ has the name ‘Moses’, which is meaningful, yes? Remember that nominalists are suspicious of ‘previous times’ just as they are suspicious of possible worlds.

That said, these are interesting objections and deserve further thought.

Yours in 'interesting times' in London. My wife woke me up at 5am London time to tell me the result.

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