Monday, May 14, 2012

Something exists

An excellent post by the Phoenician Maverick on the difficulty of translating 'something exists' into Frege-Russell logic, as defended by Londonista David Brightly.

I don't agree with  David 's approach, which is to invent the predicate 'Object(x)', a predicate which is satisfied by everything, and which fails to be satisfied by nothing.  This translates 'something exists' into 'for some x, object(x)'.  Neat - in Frege-Russell 'for all x F(x)' is true even when nothing exists.  But unsatisfying, because there remains the difficulty of negative existential singular sentences.  How do we translate 'Pegasus does not exist'?  If 'Pegasus' is a name at all, then Object(Pegasus), which translates to 'Pegasus exists', which is false.

I prefer a non-standard logic which (as David knows) extends the Frege approach from general existential statements to singular statements.  For Frege, 'serpents exist' means that the concept 'serpent' is instantiated.  If we accept singular concepts, it follows that 'Pegasus exists' means that the concept Pegasus is instantiated, and 'something exists' means that some concept is instantiated.

For more on singular concepts, use this search key.  Maverick has objected to the notion of singular concepts many times, but has failed to address any of my masterful replies.

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8 Comments:

Blogger Anthony said...

Bill seems to be equivocating on "exists". In part 1, he says that "There is no such propositional function as 'x exists.'" So in part 1, he is using exists=exists-simpliciter.

But in part 2, he talks about "when Tom ceases to exist". In part 2, he is using exists=exists-presently.

The solution, it seems, is quite simple. Something exists-simpliciter is "For some x, x=x". Something exists-presently is "For some x, x exists-presently".

What am I missing?

2:54 am  
Blogger Edward Ockham said...

The problem is the same if we restrict 'exists' to your 'exists presently'.

9:32 am  
Blogger Anthony said...

So don't do that?

Really, I'm not sure what you mean, though.

11:23 am  
Blogger Edward Ockham said...

>>What am I missing?

You seem to be missing the point of Bill's post. Perhaps I haven't understood your point, though.

3:25 pm  
Blogger Anthony said...

I don't see what's wrong with "For some/all x, x = x."

Granted, this doesn't answer the question of how to add time into the mix, which is the problem with trying to translate "You still exist!" into formal logic. But I don't think that's the question.

Anyway, is my comment that he is equivocating not clear? Bill accepts the distinction between "exists presently" and "exists simpliciter". If he is not equivocating, which one is he using?

4:29 pm  
Blogger David Brightly said...

Ed, do you think perhaps that part of the problem for Bill is that he sees concepts as multiply instantiable, or 'repeatable' as he puts it, in essence? 'Singular concept' is then oxymoronic, unless we can somehow see 'singular' as alienans.

10:35 am  
Blogger Edward Ockham said...

>>Ed, do you think perhaps that part of the problem for Bill is that he sees concepts as multiply instantiable, or 'repeatable' as he puts it, in essence? 'Singular concept' is then oxymoronic, unless we can somehow see 'singular' as alienans.

Probably, but then he would have to prove that multiple instantiation was an essential or necessary part of a concept.

I think one of his posts made that very argument, but I havent' looked for it (all help welcome, of course).

3:50 pm  
Blogger Anthony said...

>> Probably, but then he would have to prove that multiple instantiation was an essential or necessary part of a concept.

David said multiply instantiable, not multiply instantiated.

Anyway, I'd love to hear any alternate theories. At least, ones which don't involve magic.

12:57 am  

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