FOM: Goedel: truth and misinterpretations
Torkel Franzen
torkel at sm.luth.se
Tue Oct 24 03:31:04 EDT 2000
V.Kanovei says:
>Now, how can it be claimed that any given mathematical
>statement is either true or false?
>Not, and exactly by a very
>elementary reason: the Structure is not fully determined.
Sure, but that's no obstacle to statements that refer only to a
determinate part of that indeterminate structure being determinately
true or false.
>Any further reference to "true but not provable" is a misconception,
>whose philosophical nature is the misidentification of the
>Human and ZFC-dweller as Observers.
That's a very odd statement, since after all it is mathematically
provable that if ZFC is consistent then there is a true arithmetical
sentence A such that the canonical translation A* of A into the
language of ZFC is not a theorem of ZFC. Apparently you don't regard
this particular result as even meaningful. Why not?
>Since Euclid, "we *know*" well that a mathematical statement is true
>if there is a (mathematically sound) PROOF of the statement -- this
>is by the way why Mathematics has been called EXACT science.
Right, but what is your view of the axioms used in this proof?
______
Torkel Franzen, University of Luleå
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