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george says...
>Peter_Smith wrote:
>
>> Take a language lacking quantifiers and variables,
>
>If only you knew how.
>
>> 0 =/= Sm
>> Sm = Sn -> m = n
>> m + 0 = m
>> m + Sn = S(m + n)
>> m x 0 = 0
>> m x Sn = m x n + n
>> m^0 = S0
>> m^Sn = m^n x n
>>
>> (keep on going in the obvious way ...). Here the m and n are
>> placeholders for standard numerals, not variables:
>
>JEEzus; just go yourself.
>Q: How many legs does a dog have, if you call its tail a leg?
>A: Four. Calling a tail a leg doesn't make it one.
>And calling m and n not-variables here doesn't make them not
>variables.
They are not variables. Is 0 a variable? Is S(0) a variable?
Is S(S(0)) a variable?
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)
Similarly, there are axioms
0 + 0 = 0
S(0) + 0 = S(0)
S(S(0)) + 0 = S(S(0))
which he is summarizing as
m + 0 = m
etc.
Why is it that when you don't understand something,
you start using profanity and insults? Why are you
such a jerk, George?
--
Daryl McCullough
Ithaca, NY
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