FOM: Questions for Hersh
rhersh at math.unm.edu
Tue Jan 20 16:09:12 EST 1998
On Tue, 20 Jan 1998 JSHIPMAN at bloomberg.net wrote:
> Are the following statements "mathematics" by your definition? Why or why not?
> 1) White wins in chess if you remove Black's Queen from the initial position.
YES IT'S ABOUT SOMETHING NONPHYSICAL (ABSTRACT) AND HAS A
CONVINCING, ACCEPTED PROOF.
> 2) Mozart was a greater composer than Salieri
NO "GREATER" IS SUBJECT TO UNDECIDABLE DIFF OF OPINION
TRUE, THE STATEMENT MAY GET UNIVERSAL CONSENSUS,
BUT NOT ON THE BASIS OF CONVINCING REASONING OR
3) Chopin's preludes are more difficult to play than Czerny's
DON'T KNOW HOW PRECISE "DIFFICULT TO PLAY" WOULD BE
4) Chopin's preludes are more complex than Czerny's
DON'T KNOW, LIKE 3
5) There exist 5 subsets of 3-dimensional Euclidean space R3 whose union is the
> unit ball and which can be transformed by rigid motions to 5 subsets of R3 whose
> union is two unit balls, one centered at (0,0,0) and one centered at (0,0,2)
YES, NO PROBLEM, JUST STANDARD MATH
> 6) If there is a function defined on nonempty sets of reals such that f(X) is
> always contained in X, then 5) is true.
YES, AS IN 5
7) There is a nonconstructible set of real numbers.
DON'T KNOW IF NONCONSTRUCTIBLE IS MATHEMATIALLLY PRECISE
IF YOU MEAN NONMEASURABLE, THEN YES
8) If there is a measurable cardinal then 7) is true.
I BELIEVE ON AUTHORITY THAT MEASURABLE CARDINAL IS
MATH, BUT THEN THE SAME COMMENT AS ON 7.
> I am sorry to quiz you in such a peremptory Harveyish fashion, but I think this
> will clarify things for everybody very quickly. Thanks! -- Joe Shipman
> YOU'RE WELCOME
More information about the FOM