Re: Delusions and occasional bleak truth

On Nov 27, 9:47 pm, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit
You'd just blow it off? Even if it's 100% valid?
How would you know it is 100% valid?

I believe what mike3 is saying is, suppose someday,
someone discovers a proof of "1=0" in ZFC. As he
emphasizes, he doesn't mean VR or, for that matter,
anyone who regularly posts in this newsgroup. He
means a _real_ proof, a proof that all of the
mainstream mathematicians agree is a valid proof
of "1=0" in ZFC. As Goedel once proved, it's
impossible to prove that ZFC is consistent, so it
is impossible to rule out that someday, someone
will prove that ZFC is inconsistent.

Do you realize this stuff has been
studied, checked and rechecked for hundreds (not to mention thousands)
of years by some of the most brillant minds of humanity ?

And here we reach the crux of the matter -- time.

When Cantor first proposed his _naive_ set theory,
it was quickly proved inconsistent by Russell. But
since then, no one has proved ZFC inconsistent. I
disagree with Feldmann's reference to millennia,
but certainly a century is long enough, especially
when compared to the lifespan of naive set theory,
to believe that if ZFC were inconsistent, one of
the "brilliant minds" would have discovered it
well before now.

Suppose I were to ask mainstream mathematicians
which of the following is the _least_ likely to be
discovered in his/her lifetime:

1. A proof/counterexample of Goldbach
2. A proof/counterexample of P = NP
3. A proof/counterexample of Riemann
4. A proof/counterexample of Twin Primes
5. A proof that ZFC is inconsistent

I bet most would choose 5. Indeed, the more time
passes, the _more_ likely we are to resolve 1-4,
but the more time passes, the _less_ likely we
are to prove ZFC inconsistent.

One opponent of ZFC (_not_ a sci.math poster)
once said it best:

"ALL mathematicians believe that it is
_theoretically_ possible that set theory is
inconsistent, but NO mathematicians believe it is
_actually_ possible that set theory is inconsistent."
.

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