FOM: Goedel: truth and misinterpretations
Kanovei
kanovei at wmwap1.math.uni-wuppertal.de
Thu Oct 26 13:36:29 EDT 2000
> Date: Thu, 26 Oct 2000 08:52:33 +0200
> From: Torkel Franzen <torkel at sm.luth.se>
> We don't normally express mathematical statements
> "as a single ZFC formula", and it's not clear what you are requiring.
Of course incursions of mathematical English are allowed as
shortcuts, say, "any group contains an element a with aa=a"
is a single ZFC formula,
"modern philosophy likes to refer to chickens" is not.
> You're making a metaphysical counter-claim to the metaphysical claim
> .
I did not make claims, I
only asked that somebody explains what does it mean that
"CH is true or false", and the only coherent explanation was
that this is just the formula "CH or not-CH".
I do not see why I must take on trust the prayer
that either CH is true or CH is false, without any slightest
argument that shows that such a subtle and illusory thing as
the mathematical universe is determinate enough that we can
once figure it out that CH is true or figure it out that not-CH
is true. In this there is nothing metaphysical: not only
mathematics, but all natural science (philosophy not included)
demands proofs of claims, so do I.
> does this mathematical practice have any kind of justification?
This question has been considered by thousands of philosophers
with perhaps dosens of different answers.
What they taught me in my undergrad/grad/PhD philosophy courses
at Moscow State around 1970, is as follows:
1) mathematics develops as a something entire, with common
principles of thinking, rules of deduction, etc.
2) therefore, if something were wrong in a part of it, that
would be reflected in other parts,
3) but some parts of mathematics (finite combinatorics, geometry,
probability, analysis, more) have successfully and undoubtfully
survived harsh practical justification with most perfect mark.
I've never heard of any better explanation.
V.Kanovei
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