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

Torkel Franzen wrote:
> anzaurres1@xxxxxxxxxxx writes:
>
> > When we, mathematicians, say that a statement is true in a given
> > axiomatic system, we mean that one can logically derive this statement
> > from the axioms.
>
> People do indeed often speak of a statement being "true in a given
> axiomatic system" when they mean that it is provable in that system.
> While mostly harmless, this terminology promotes needless confusion.
> For example, it sometimes prompts them to contradict the simple
> observation that there are theories with false axioms.

I assume by a "false" axiom you mean a statement that is
self-contradictory in itself. Like

A AND (NOT A)

where A is a statement of your choice.

Right?

But how many theories, created by educated mathematicians, that contain
self-contradictory statements, are there? Probably none.

Most statements, on their own, are neither false nor true. For
example, is the statement "1 + 1 + 1 = 0" a "false axiom"?

.

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