any() and all() on empty list?

Alex Martelli aleaxit at
Fri Mar 31 07:43:42 CEST 2006

Fredrik Lundh <fredrik at> wrote:

> Marcin Ciura wrote:
> >>>all(flying elephants which are not pink) => true
> >>>
> >>>So, these flying elephants -- are they pink or not?
> >>
> >> No, you ask two different sets whether they are true.
> >
> > No, there is only one empty set.
> who said anything about empty sets ?

Universally-false predicate <--> empty set Cantor's/Frege's world, which is commonly accepted as equivalent
to Aristotle's Logic.  Modal logic is a different kettle of fish (and,
in retrospect, what Dodgson [aka Carroll] was groping towards)... but I
know of no programming paradigm based on it (even Turing's and Church's
map more easily to naive set theory//logic, give or take a Zermelo or
so;-). I would in fact challenge the assertion that a useful programming
paradigm COULD be based on modal logic, hoping for proof of the


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