PEP 354: Enumerations in Python

[Alex Martelli]

Terry Reedy <tjreedy at udel.edu> wrote:
   ...
> I suspect that the notion of empty  set was once controversial.

Yep: Reverend Dodgson (best known by his pen name of Lewis Carroll, and
as the author of the Alice novels, but a logician and mathematician IRL)
fought long and hard against Cantor's set theory, focusing on "the empty
set" (singular: in Cantor's theory there can be only one) but not
managing to build an actual contradiction around it.  The poor man died
just before his compatriot Bertrand Russell found "Russell's Paradox"
(which destroyed Frege's logic -- but is quite applicable to destroying
a foundation stone of Cantor's set theory as well).

I personally believe that Dodgson was reaching towards what today we
call modal logic (particularly intensional logic), though he could
hardly get there with such encumbrances as his fiction writing, his
photography, his heavy smoking of cannabis, etc, etc. But, that's just
me, and I can't claim to be an expert at modern set theory (though I do
know enough of it to see that it's quite different from Cantor's "naive"
version that's still taught in most schools...!-), much less of the
subtleties of modal logic.  Still, if you give a set interpretation of
modal logic, there isn't ONE empty set: the crucial point of modal
logic, from my semi-learned POV, is that it distinguishes what JUST
HAPPENS to be false, from what MUST INTRINSICALLY be false (and ditto
for true).  In set terms, say, "all integers x such that x>x" would be
an *intrinsically* empty set, while "all dogs that are in this house
right now" would be a set which *just happens* to be empty -- they
aren't "one and the same, the sole empty set" any more than they are in
commonsense (the notion Dodgson fought against).


Alex