Bradley Lucier scripsit:
> In mathematics, statements about the (nonexistent) elements of the
> empty set are taken to be true; such statements are called "vacuously
> true". "All witches are green" => #t; "all dragons are over 6 feet
> tall" => #t; "all dragons are under 6 inches tall" => #t.
ObDigression: This is only true on the assumption of unrestricted
quantification, which translates "All witches are green" as (Ax)(Wx->Gx).
We call this kind of quantification unrestricted because it quantifies
over all objects whatsoever, and then makes the claim "if a witch, then
green" which is equivalent to "either not a witch or green", which is
obviously true in a universe in which all objects are not witches.
Restricted quantification, however, is (AWx)(Gx), and is *false* if
there are no witches, just as "Each rhinoceros in my workplace is painted
purple" is false. There are no such rhinocerotes, and so the claim fails.
(It took several hours of one-on-one with a logician for me to understand
this, having been brought up in the unrestricted-quantification faith,
which is closely related to "sola scriptura" and possibly to total
depravity. :-) )
--
Possession is said to be nine points of the law, John Cowan
but that's not saying how many points the law might have. [EMAIL
PROTECTED]
--Thomas A. Cowan (law professor and my father)
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