[FOM] re "understanding Putnam on understanding mathematics
gstolzen at math.bu.edu
Wed Jul 25 19:24:52 EDT 2007
On July 24, Karin Verelst asked,
> In the post by Gabriel Stolzenberg occurs a quotation:
> "The laws of logic, the very laws that Aristotle taught us, do not
> hold beyond the domain of the finite."
> Where exactly did Hilbert make that remark?
He didn't make exactly that remark. Note that I prefaced it with
"something like." (I was doing it from memory.) I wrote,
Hilbert, who said something like, "The laws of logic,
the very laws that Aristotle taught us, do not hold
beyond the domain of the finite."
The exact remark is in "On the Infinite." In "From Frege to Goedel,"
it's in the second paragraph on p. 379. Here is part of it.
In any case, those logical laws that man has always used
since he began to think, the very ones that Aristotle
taught, do not hold.
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