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Re: [ontolog-forum] Inconsistent Theories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 09 Feb 2010 01:11:55 -0500
Message-id: <4B70FCAB.5090902@xxxxxxxxxxx>
Chris,    (01)

JFS>>  Theory T1:  (Ex)(Ay)(y=x).
 >>     Theory T2:  (Ex)(Ey)~(x=y).    (02)

CM> I don't understand how the truth recursion will work for these
 > sentences.    (03)

I don't understand what you are objecting to.    (04)

Theory T1 is true of any model that contains exactly one individual
in the domain.  Theory T2 is true of any model that contains two or
more individuals.  There is no model that can make both theories true.    (05)

CM> The variables "x" and "y" drop out of the picture and ultimately
 > play no role whatever in the truth conditions of the sentence.    (06)

I agree.  That's what I was trying to say, and what I interpreted
Wittgenstein as saying:    (07)

LW> 4.242 Expressions of the form "a=b" are therefore only expedients
 > in presentation (Behelfe der Darstellung).    (08)

CM> 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)".    (09)

No.  I meant that the variable names are artifacts of the notation,
since they disappear in notations such as existential graphs.    (010)

John    (011)

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