10

Arguments for monotheism

Proof

P

roof is a complex notion. In simplest terms, a proof is a valid
argument with true premises. This is the standard notion of proof in
logic. An argument consists of premises intended to provide support
for a conclusion. An argument is valid if it is logically impossible that the
premises be true and the conclusion be false.^1 Any argument of the form If
A then B, A; therefore B, for example, will be valid.
Given this basic notion of a proof, the contemporary philosopher George
Mavrodes has noted that one of the following arguments is a proof and the
other is not:^2

Argument A

1. Either God exists or nothing exists.


2. Something exists.
   So: 3. God exists.

Argument B

1*. Either God does not exist or nothing exists.

2. Something exists.
   So: 3*. God does not exist.^3

Note that:

(i) Premises 1 and 1 are disjunctions. They have the forms, respectively,
Either G or N and Either not-G or N.
(ii) It is false that nothing exists. So the N disjunct is false.
(iii) Necessarily, either God exists or God does not exist; either G is true
or else not-G is true.
(iv) A disjunction is true so long as at least one of its members is true. So
either 1 is true or else 1 is true.
(v) Premise 2, which appears in both arguments, is true.
(vi) Both arguments are valid.