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george says...
>> Peter is saying that the (infinitely many) axioms of his
>> theory are
>>
>> 0 =/= S(0)
>> 0 =/= S(S(0))
>> 0 =/= S(S(S(0)))
>> etc.
>> which he summarizes in the metalanguage (the language he
>> is using to *describe* the language) as
>>
>> 0 =/= S(m)
>
>His decision to do that MAKES m a VARIABLE, DUMBASS.
Yes, but once again, m is *not* a term in the language
that Peter is describing (the object language). It is a
term in the *metalanguage*. Peter is describing a language
(the object language) whose axioms have no variables.
He's using a *different* language (one that has variables)
in order to describe the object language.
--
Daryl McCullough
Ithaca, NY
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