Re: Cranks and errors

On Mon, 18 May 2009 16:57:04 -0700 (PDT) Marshall wrote:

On May 18, 3:44 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

I've given you all you need to know that with a language with '+' and
'0' and the axiom "Axy x=y" we may derive, with first order logic with
identity, "Axy x+y=0".

See Endertons' logic book or any number of other textbooks on
mathematical logic (or even just read your own copy of Shoenfield
without burdening it with all the extra garbage you demand it say).

Or, if I may be so bold, and without meaning any disrespect,
work it out for one's own self. Can we come up with a model
for that theory in which it is *not* the case that x+y=0? (For
example.) No, we cannot. (I think this completely escapes
Nam's attention, even when it is specifically pointed out.)

Marshall, I don't think that the notion of model has any relevance for the
"problem" discussed here. (Though I might err, of course.)

(Briefly:) IF "x+y" is a term, and IF "0" is a term, clearly there is no
interpretation (in the context of FOPL=) such that "x+y=0" is not
satisfied/true.

Again pointing out why we have the "paradigm" "language first" in this
context. ;-)


Herb
.

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