On Apr 12, 11:08*pm, Rich Hutnik wrote:

But, if one is working with Chess Variants, then the issue does
arise that if the number of variants is finite, then you can have a
classification system in place that could capture them all, and even
simplify, and perhaps bridge them.

I think that one can always go 'outside the system' and come up with a
reasonable new Chess variant that is not included in any
classification system, even if that system embraces an infinite number
of variants.

Yet, the fact that people can only handle games up to a certain finite
level of complexity means that the number of Chess variants is finite.

A large, but poorly-defined finite set, therefore, can behave for
practical purposes as if it had properties that, in an exact
mathematical sense, can only apply to a set with at least aleph-one
elements. This doesn't defy any law of mathematics (and, indeed, due
to the subject matter, I've pulled sci.math back in, since it's
relevant now).

John Savard