FOM: Is chess as interesting as mathematics? JoeShipman at
Thu Feb 21 20:35:50 EST 2002

Silver misrepresents Grandy's argument by supposing that Grandy's finite-infinite distinction concerns the objects of discourse rather than the questions that can be asked about them. 

The point is not to compare questions about finite numbers or sets with questions about infinite numbers or sets; the point is that chess deals only with delta_0 questions while Peano Arithmetic deals with questions (that are ABOUT finite sets and numbers) of arbitrary logical complexity, for which there is not necessarily a reduction to a finite problem.  I think it IS fair to say that the well-known "Open Questions" that are pi^0_1 or pi^0_2 are indeed more interesting than the delta_0 ones (the most interesting of which, in my opinion, are questions about the value of Ramsey numbers, but which do not approach the interest of pi^0_1 questions like the Poincare Conjecture or the Riemann Hypothesis or pi^0_2 questions like P=?NP).

-- Joe Shipman

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