FOM: More on conclusiveness of proofs
F. Xavier Noria
fxn at cambrabcn.es
Wed Dec 17 05:47:37 EST 1997
Hello fom-ers,
In my (student) opinion we can talk about the 'truth' of a proposition
or the correctness of its proof in a statistical-probabilistic-fuzzy
sense, but not boolean.
Let me remind an easy Wittgenstein's proposed exercise:
Let's take a list with the letters of
our alphabet and count how many of them
we have. Let's do this count ten times.
Do we get the same number always?
Is there anyone so that never have done a proof, which he was convinced
that it was right, but it wasn't? (because your best math friend put
his finger on some 'clear' point?) We have examples of 'false'
proofs in math history. How many 'proofs' there exist in this moment
that are incorrect? I don't know, but this might not be
an empty set.
What about the 'completeness' arguments in Euclid's proofs?
Perhaps, what I'm doing it's only a couple of obvious comments, but it
seems to me that we cannot establish the correctness of a proof in an
absolute sense, and so, the 'truth' of the theorem 'proved'
(nevertheless, let me consider my own arguments against my own
explanation in
order to be not completely sure about my opinion :-)
F. Xavier Noria
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