PHILOSOPHY OF RELIGION: A contemporary introduction

200 ARGUMENTS: MONOTHEISTIC CONCEPTIONS

Cosmological Argument, stage four

It is at least not unreasonable to accept PSR*, and it is worth seeing how the
argument that requires it continues. A few additional definitions will serve the
familiar service of simplifying the statement of the argument.

D4 Being X has necessary existential security = X exists, and X is caused to
exist or depends for its existence on something else is self-contradictory.
D5 Q is a basic property of X = X has Q, and X has no property Q such that
X has Q explains the truth of X has Q.
D6 Q is a non-basic property of X = X has Q, and X has some property Q
such that X has Q explains the truth of X has Q.
D7 X has logically necessary existence = X exists, our concept of X is accurate
relative to X’s existence and X does not exist is self-contradictory.
D8 X has logically contingent existence = X exists, our concept of X is
accurate relative to X’s existence, and neither X exists nor X does not
exist is self-contradictory.

Note that:

(i) X has necessary existential security does not entail X has logically
necessary existence;
(ii) X has logically necessary existence does entail X has necessary
existential security;
(iii) whatever exists has either logically necessary or logically contingent
existence;
(iv) while if it is logically possible that the existence of something be
explained, it follows that it is logically possible that the thing not exist, it
is not true that if it is logically possible that it not exist, then it is
logically possible that its existence be explained;
(v) while it is true that if it is logically possible that the truth of a
proposition be explained, it is logically possible that the proposition not
be true, it does not follow that if it is logically possible that a proposition
not be true, then it is logically possible its truth be explained.

Now we can begin stage four.

11 X’s existence is logically impossible to explain and its existence can
explain the existence of things whose existence it is logically possible
to explain is true only if X has necessary existential security is true.
12 If something exists whose existence it is logically impossible to
explain and whose existence can explain the existence of things