92 CONCEPTIONS OF ULTIMATE REALITYTex/Tim*
Tex: It is self-contradictory that there be no frogs. [Necessarily, not(not-
F)]
Tim: It is not self-contradictory that there be no frogs. [Not-(Necessarily,
not(not-F)]
Tex thinks something logically impossible that Tim thinks logically possible.
Logical necessity and logical possibility are modalities. We can put the
difference between the disagreements in yet another way: the Tim/Tom
disagreement is about the truth of There are frogs; the Tex/Tim dispute is
about the modality of There are frogs. Disputes about whether there are
frogs has, of course, no religious content. But the pretend disputes about
frogs are paralleled by disputes about God.
The NN principle
A final point will place us in position to complete our discussion. A modal
proposition is a second-order proposition^7 that says about some first-order
proposition that it is necessarily true, necessarily false, or logically contingent.
Here is a bit of the logic of modal propositions.^8 Where P is any proposition:
1 Necessarily, P (= It is not possible that P be false).
2 Necessarily, not-P (= It is not possible that P be true).
3 Contingent, P (= It is not impossible that P be true and it is not impossible
that P be false)
express the possible modalities regarding P. They entail, respectively,
4 Possibly, P.
5 Not-(Possibly, P).
6 Possibly, P.
where “possibly” means not “maybe” but “it is logically possible that” or “P
is not self-contradictory.” A proposition of the form expressed in 1 through
6 is a second-order proposition; it says of a first-order proposition that it is
necessary, contingent, or possible.
What the NN thesis tells us is this:
NN: Every true modal proposition is necessarily true, and every false
modal proposition is necessarily false; it is logically impossible
that there be a contingently true or a contingently false modal
proposition.