The articles and essays in this blog range from short pieces to long ones. Many of the posts are also introductory (i.e., educational) in nature; though, even when introductory, they still include additional commentary. The material dates back to 2005.
Wednesday, 29 April 2015
Necessity & Possibility are Interdefinable
modal theory, necessity and possibility are inter-definable. We can
define or explain necessity in terms of possibility, and possibility
in terms of necessity.
say that something is possible isn't really to say that it's likely
(or unlikely, for that matter); or that it probably will happen some
time in the future. What is important about X is that its
non-happeningness (as it were) isn't necessary. There's
nothing necessary about there being no unicorns or no five-foot high
cats. There are no unicorns, indeed; though it's not necessary that
there are no unicorns. There probably couldn’t be five-foot high
cats; though it isn’t necessary that there aren’t any or that
there won't be any in the future.
can kind of invert this possibility-necessity relation by making it a
of defining possibility in terms of necessity (or non-necessity), we
can now define necessity in terms of possibility (or
is necessary if it has to be the case or if it must happen. In terms
of possibility, we can say, “that its failure to happen is not
possible” (182). So if we drop a stone, it must fall to the ground
(if there is nothing material stopping it). It's not possible that it
would, or could, just float in the air. This is natural necessity.
we can say that it is necessary that all bachelors are unmarried
because married bachelors are not possible. This is the case simply
because the word ‘bachelor’ is a synonym for ‘unmarried man’.
Thus, if we say that
the bachelor is married.”
we're also saying that
the unmarried man is married.”
with the substitution of synonym for synonym we arrive at a
straightforward assertion of a logical contradiction. We're saying
that John can be both unmarried and married at one and the same time.
Thus John’s unmarried status is necessary precisely because he's a
bachelor. Therefore his being a married bachelor isn't possible. The
the bachelor is unmarried.”
true is because of the impossibility of
the bachelor is married.”
this it isn't surprising that “musts and mights are really two
sides of the same coin” (182). We wouldn’t have necessity without
possibility (or something’s impossibility). Similarly, we wouldn’t
have possibility with necessity (or something’s being necessary).