ARGUMENTS FOR MONOTHEISM 1975 That a logically contingent existential proposition is true can only
be explained by some other existential proposition being true.
If, in the relevant sense of explanation, P’s truth entails Q’s truth, then
P entails Q. No existential proposition is entailed by a set of
propositions that does not contain any existential propositions.
6 If an existential proposition does not concern something whose
existence it is logically possible to explain, it concerns something
whose existence is logically impossible to explain.
These exhaust the possibilities.
7 The truth of There exist things whose existence it is logically
possible to explain can only be explained by a true existential
proposition concerning something whose existence it is logically
impossible to explain (from 4, 5, 6).
8 Some existential proposition concerning something whose
existence it is logically impossible to explain, and whose existence
can explain the existence of things whose existence it is logically
possible to explain, is true (from 3, 7).
Premise 4 is plainly true; whatever Xs are, there being Xs cannot explain
there being Xs. Nor can the existence of something that might not have
existed be explained other than by reference to things that exist; the
existence of contingent things can only be explained by reference to
something that exists, not by reference to something that doesn’t exist.
So premise 5 is true. Necessarily, for anything X that exists, either it is
logically possible that X’s existence be explained or it isn’t; that is what
premise 6 says. If (i) X’s existence can be explained, and (ii) can be
explained only by the truth of a type A proposition or by the truth of a
type B proposition, and (iii) cannot be explained by the truth of a type A
proposition, then it follows that (iv) X’s existence can be explained by
the truth of a type B proposition. Premise 7 applies this reasoning to the
notions of propositions concerning the existence of things whose
existence can be explained and propositions concerning the existence of
things whose existence cannot be explained. Premises 4, 5, 6 entail 7 and
3 and 7 entail 8; if they are true (and they are) so is it. Hence stage two
is successful.