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

Let me correct my previous post:

Torkel Franzen wrote:

> anzaurr...@xxxxxxxxxxx writes:

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

> Not at all. I simply mean a statement which is false and is an axiom
> of the theory. An example is the theory obtained by adding "PA is
> inconsistent" as a new axiom to PA.

That's exactly my point: the statement S = "PA is inconsistent" by
itself is neither self-contradictory nor false. In fact, if you let PA
denote any set of mutually contradictory statements, the statement S
itself will be true, not false.

Only if you combine S with the set PA, will you get a contradiction.

> > Most statements, on their own, are neither false nor true.

> It's unclear to me what you mean by this. Is your quoted
> statement an
> example of a statement that is neither false nor true "on its own"?

Which quoted statement? The one that you conveniently deleted from your

post? I don't remember. You deleted it.

> What about "The Eiffel tower is larger than a banana"?

I don't know what "Eifel Tower" is. It's not in the USA, is it? Nor do
I know
what's a "banana". Is it some kind of a fruit? Like most
mathematicians,
I don't travel abroad and I eat only carmelized frog legs.

But if you define to me what you mean by a "banana" and the "Eifel
Tower", I will try to tell you whether, given your definitions, the
Eiffel tower is larger than a banana.

Don't forget to tell me what you mean by "larger". Does it mean having
a larger volume or a larger surface area?

My guess is that the answer will depend on how large of a banana you
think biologists can grow.

> What is an
> example of a statement that *is* true or false "on its own"?

I gave you an example but you chose to cut it out without understanding

it. Any statement of the form

A and (not A)

where A is pretty much any statement of your choice, is "false" on its
own.

In any case, you seem to agree with my point that there are few
"axioms" that
are false "on its own".

.

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