Re: Cantor's circular "proof" that evens = integers

On 2007-05-24, in sci.logic, Daryl McCullough wrote:
<george-like>
It is IDIOTIC to start with an interpretation of a LANGUAGE!!
How can someone possibly have a preferred interpretation of
a FUNCTION SYMBOL, if you don't ALREADY have in mind the AXIOMS
governing that symbol. The symbol "+" ONLY MEANS addition if
it is accompanied by the AXIOMS OF ADDITION!!! To say that
the intended interpretation of the SYMBOL "+" is given by
a set-theoretic model makes NO SENSE. Someone can just as
well use "*" or "&" or "@*$!!!" as the symbol for addition!
The symbol means NOTHING without accompanying axioms. The
choice of a symbols is COMPLETELY ARBITRARY!!! So SHUT THE
*** UP about "interpretations of a language"!!!!
</george-like>

How did I do?

Pretty well, but I find you haven't quite captured the spirit of George's
thought in some subtle and hard to pin down way.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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