[FOM] response to Sam Sanders' intriguing recent post on reductionism

[Tom Dunion]

On Feb 28, Sam Sanders said:

>> Biology  < Chemistry < Physics < Mathematics < Mathematical Logic

Everyone will agree that Biology is not just the study of some particular
chemical reactions. Similarly, Chemistry (resp. Physics) is not just the
study of some particular physical (resp. mathematical) systems.

In each case, if X<Y, then X cannot be *reduced* to some subset of Y.  Obviously
X does take place in a subset of Y, but it is more than just a subset of Y.
something "holistic" is going on.

A good example is Biology: the notion of "living matter" is not
well-defined or understood yet, and has no reduction
(to the best of my knowledge) to simple chemical reactions. <<

That's spot on!   And I would suspect that "Mr. Z" of ZFC fame was
indeed motivated by some such holistic approach to (at that time) Cantor's
very new realm of set theory and not merely trying to silence the critics of
his proof of his well-ordering theorem.

The early paradoxes were known, and had to be avoided, but whether or not
one believes Cantor was (as he himself believed) the tribune of some
divine revelation, it does not follow that there cannot be any reality
"out there" un-captured by ZFC (or by ZFC + large cardinals, or...)

- TD