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## Re: [ontolog-forum] Inconsistent Theories

 To: "[ontolog-forum] " Christopher Menzel Tue, 9 Feb 2010 10:24:23 -0600 <069F1022-07E1-462A-9FAB-51A03E78051D@xxxxxxxx>
 ```On Feb 9, 2010, at 12:11 AM, John F. Sowa wrote: > Chris, > > JFS>> Theory T1: (Ex)(Ay)(y=x). >>> >>> Theory T2: (Ex)(Ey)~(x=y). > > CM> I don't understand how the truth recursion will work for these >> sentences. > > I don't understand what you are objecting to. > > 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.    (01) Well, I'm certainly not objecting to *that*. My question is simply what the actual clause for an identity statement looks like and how it functions in the overall definition of the truth conditions for an arbitrary sentence. As I understood you, you said that identity statements "x=y" involving variables x and y are in fact about the variables x and y themselves. I simply don't understand how any such account is to be woven into a standard Tarski-style definition of truth in an interpretation since, in such a definition, variables ultimately disappear from a sentence's truth conditions.    (02) > CM> The variables "x" and "y" drop out of the picture and ultimately >> play no role whatever in the truth conditions of the sentence. > > I agree. That's what I was trying to say, ...    (03) Oh. I missed that. :-)    (04) > ...and what I interpreted Wittgenstein as saying: > > LW> 4.242 Expressions of the form "a=b" are therefore only expedients >> in presentation (Behelfe der Darstellung). > > 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)". > > No. I meant that the variable names are artifacts of the notation, > since they disappear in notations such as existential graphs.    (05) Well, that's good, but then I still don't quite understand what you are saying when you say that "x=y" is about the variables x and y themselves. But pretty clearly we're not arguing about anything of genuine substance here.    (06) -chris    (07) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (08) ```
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