ARGUMENTS FOR MONOTHEISM 195examining these arguments has not been very positive; none seems even close to
a proof that God exists. But rearrangement and revision of the materials these
arguments contain provide something stronger.
Some further definitions
If these materials do yield a stronger – even a successful – argument, perhaps
they do so via the following argument. Once again, some definitions will make it
possible to state the argument less complexly than otherwise. Further, the way
the premises are stated is intended to keep them from being open to various
standard objections. Note that nothing in the following argument requires that
there not be various sorts of self-motion or self-change and it requires no
assumptions about whether there is an infinite series of anything.
By way of reminder:
Definition 1: P is a logically contingent proposition = neither P nor not-P
is self-contradictory.
Definition 2: P is a logically necessary proposition = not-P is self-
contradictory.
Further:
Definition 3: P is an existential proposition = P entails a proposition of
the form X exists.
Definition 4: It is logically possible that P’s truth be explained = There is
some proposition Q such that Q’s truth explains P’s truth is
not self-contradictory.
To give an analysis: if it is logically possible that the existence of something X be
explained, then it is logically possible that X not exist, and if it is logically
possible that the truth of a proposition P be explained, it is logically possible that
it not be true.
Given these definitions, we can state another version of the Cosmological
Argument.
Cosmological Argument, stage one
1 If it is logically possible that the truth of a logically contingent
existential proposition be explained, then there actually is an
explanation of its truth (whether we know what it is or not).