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"It could be that Walter's horse has wings" does not imply that there is
any such animal as Walter's horse, only that there could be; but "Walter's
horse is a thing which could have wings" does imply Walter's horse's
existence. But the conjunction "Walter's horse exists, and it could be
that Walter's horse has wings" still does not imply "Walter's horse is a
thing that could have wings", for perhaps it can only be that Walter's
horse has wings by Walter having a different horse. Nor does "Walter's
horse is a thing which could have wings" conversely imply "It could be that
Walter's horse has wings"; for it might be that Walter's horse could only
have wings by not being Walter's horse.
I would deny, though, that the formula [Necessarily if some x has property P
then some x has property P] expresses a logical law, since P(x) could stand
for, let us say "x is a better logician than I am", and the statement "It is
necessary that if someone is a better logician than I am then someone is a
better logician than I am" is false because there need not have been any me.
-- A.N. Prior, "Time and Modality"
I do hate sums. There is no greater mistake than to call arithmetic an
exact science. There are permutations and aberrations discernible to minds
entirely noble like mine; subtle variations which ordinary accountants fail
to discover; hidden laws of number which it requires a mind like mine to
perceive. For instance, if you add a sum from the bottom up, and then again
from the top down, the result is always different.
-- Mrs. La Touche
