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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. It doesn't even make them non-quantified; in fact,
they are universally quantified bound variables, and this
treatment IS NOT quantifier-free. If you have books that say
otherwise then you are perfectly welcome to burn them for all I care.
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