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Re: [ontolog-forum] Inconsistent Theories

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 8 Feb 2010 23:26:23 -0600
Message-id: <70346279-5B15-4EA1-8B3B-8C4E8E6947A0@xxxxxxxx>
On Feb 8, 2010, at 10:56 PM, John F. Sowa wrote:
> Chris
> JFS>> I agree with Wittgenstein that x=y is a statement about the
>>> names x and y, rather than a statement about the subject domain.
>>> In any case, I don't want to get into metaphysical arguments
>>> about the nature of identity.
> CM> Good thing, John, since you're wrong.    (01)

Bad form, John, you left off the smiley! :-) <-- LEAVE THAT ALONE    (02)

> Please note that I was making a comment about the expression "x=y",
> not about the following two statements, which are definitely
> about the the subject domain:
>    Theory T1:  (Ex)(Ay)(y=x).
>    Theory T2:  (Ex)(Ey)~(x=y).    (03)

I don't understand how the truth recursion will work for these sentences.  
Consider     (04)

  (*)  (Ex)(y)Pxy.    (05)

Unpacked according to Tarski, (*) is true just in case, for some object b (in 
the domain of the model), for every object c, <b,c> is in the set assigned to 
"P".  The variables "x" and "y" drop out of the picture and ultimately play no 
role whatever in the truth conditions of the sentence.  According to your 
suggest, if I'm understanding, "x" and "y" themselves occur in the truth 
conditions of "x=y" and, hence, I assume in the truth conditions of 
"(Ex)(Ay)(y=x)".  I just don't see how that's going to work.  Choice of 
variables is incidental; that is reflected in et fact that they don't occur in 
Tarskian truth conditions.    (06)

-chris    (07)

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