mattes at math.ucdavis.edu
Fri Oct 31 16:48:17 EST 1997
>I hate to be repetitive, but sometimes I find telling quotes that are much
>stronger than anything I am saying - from people you would least expect. I
>would like your reaction to the Morriss Kline quote from Mathematics from
>Ancient to Modern Times, Chapter 51, pp. 1182:
>"By far the most profound activity of twentieth-century mathematics has
>been the research on the foundations."
There are other interesting passages by Morris Kline. E.g. in
"Mathematics, the loss of certainty", p.331, he quotes Goedel as saying in
"the role of the alleged "foundations" is rather comparable to the
function discharged, in physical theory, by explanatory hypotheses. . . .
The so-called logical or set-theoretical foundations for number theory or
of any other well established mathematical theory is explanatory, rather
than foundational, exactly as in physics where the actual function of
axioms is to explain the phenomena described by the theorems of this
system rather than to provide a genuine foundation for such theorems."
Do you agree with this statement?
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