Re: Help in answering news story on refutation of fermat's last theorem

Torkel Franzen wrote:
> "Mark Nudelman" <markn@xxxxxxxxxxxxxxxxxxxxx> writes:
>
>> I wonder what he thinks it means for an axiom to be "false". Axioms
>> can be inconsistent, but how can they be false?
>
> The same way any other statement can be false. If you take as an
> axiom "0=1", you have a false axiom.

If the statement 0=1 is an axiom, then the symbols 0, 1, and = cannot be
interpreted as they are in normal arithmetic. But if = is interpreted as
"less than", for example, there's nothing wrong with this axiom. The
symbols take their meaning from the axioms, not vice versa. Symbols can't
be interpreted unless you know how they're used in the axiomatic system
which they're part of.

--Mark


.

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