FOM: Reply to Franzen on Cantor and Hilbert
martind at cs.berkeley.edu
Thu Dec 4 18:57:39 EST 1997
At 05:42 PM 12/4/97 -0500, jshipman at bloomberg.net wrote:
> 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
>we can KNOW that it is essentially undecidable, then it is meaningless in a
>stronger sense. But for CH I see no need to give up trying yet! -- Joe Shipman
Here are two examples.
1. I toss a coin, and without me or anyone else looking at it, I put it in
my pocket. The sentence "That coin fell with HEADS up" would seem to be
essentially undecidable (how will we ever know its truth value), but is it
2. Consider the class of all sentences of the form:
"The number of people who entered Macy's 34th Street in New York during the
hours it was open on May 1, 1995 was exactly n."
There is exactly one integer n for which this sentence is true, but (unless
Macy's has installed counting devices I don't know about) we will never know
thw correct value on n. For n sufficiently small or large, we do know the
sentence is false. So for these values, the sentence is meaningful. As we
enter the range for which we can't be sure, do the sentences become
"meaningless"? Strange semantics.
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