FOM: Reply to Franzen on Cantor and Hilbert
jshipman@bloomberg.net
jshipman at bloomberg.net
Thu Dec 4 17:42:24 EST 1997
Torkel raises an interesting philosophical point. Can a proposition be
meaningful to us if we can never have any hope of deciding it even in principle?
"The 2^2^1000 decimal place of pi is odd" is obviously meaningful, and I
suspect it is incapable of ever being decided by intelligent beings in this
universe, but it is not "essentially undecidable" because it is decidable "in
principle".
"Every finite subsequence of digits appears in the decimal expansion of pi"
is also obviously meaningful (to most of us), and not obviously decidable "in
principle", but it would seem presumptuous to call it "essentially incapable of
being decided". Who can say we'll never improve our mathematical understanding
to the point where we can settle this question? Why should we give up trying?
I would say, contra Torkel, that there is indeed a sense in which a question
"*essentially* incapable of being decided" is meaningless. I also claim that if
we can KNOW that it is essentially undecidable, then it is meaningless in a much
stronger sense. But for CH I see no need to give up trying yet! -- Joe Shipman
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