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

Jesse F. Hughes wrote:

> > If you don't know what an axiom is, ask your mommy.

> Really, you are embarrassing yourself with this line.

You are right. But I don't understand the purpose of your previous post
to me. Is this top show that we non-logicians don't understand the
concept of proof?

>anzaurres1@xxxxxxxxxxx wrote:

> > Torkel Franzen wrote:

> > > "Mark Nudelman" <markn@xxxxxxxxxxxxxxxxxxxxx> writes:

> > > > If the statement 0=1 is an axiom, then the symbols 0, 1, and =
> > > > cannot be interpreted as they are in normal arithmetic.
> > > > Symbols can't be interpreted unless you know
> > > > how they're used in the axiomatic system
> > > > which they're part of.

> > > So what axiomatic system are the symbols in your statement above a
> > > part of?

> > You can pick any axiomatic system you want. In some the statement 0=1
> > will be true. In others - false.

> > As the previous poster told you, take the usual axioms of integers,
> > including inductive ordering, and let the symbol "=" denote what we
> > usually denote as "<". Then "0=1" is a correct statement.

> There is no concept of a statement being true or false "in an
> axiomatic system" in logic.

So, what's your point? That it's wrong for a mathematician to say that,
given some particular set of axioms, the statement "0=1" is false?

Don't other mathematicians say "Such and such statement is true" or
"Such and such statement is false" each and every day? Are you saying
that mathematicians have no right to say such things?

I assure you that, given the usual definitions and axioms of integers,
the statement "0=1" is false, no matter how much you object.

Or were you making an irrelevant comment?

.

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