170 ARGUMENTS: MONOTHEISTIC CONCEPTIONS(vii) Argument A has the form: 1. Either G or N; 2. Not-N; so 3.G.
(viii)Argument B has the form: 1. Not-G or N; 2. Not-N; so 3. Not-G.
(ix) Thus either Argument A is valid and has only true premises or
Argument B is valid and has only true premises.
(x) Exactly one of these arguments is a proof in the sense of proof in
logic: one of these argument not only is valid but also has only
true premises.
Unless we know, independently of these arguments, whether God exists
or not we cannot tell which argument is a proof. The simple notion of a
proof in logic is perfectly proper for some purposes. But having a proof
in that, and no stronger, sense for some conclusion C is of no help in
deciding whether C is true. Mavrodes notes that we need a notion of a
proof that extends our knowledge. Perhaps something along these lines
will do.
Argument A is an argument that extends our knowledge relative to
its conclusion C only if:
(i) A is a proof in logic;
(ii) we know that A is valid (that its premises entail its conclusion);
(iii) we know that A is sound (that its premises are true);
(iv) for each premise P of A, we can know whether or not P is true
without having to know whether C is true (our knowledge of each
of the argument’s premises is independent of our knowing whether
the argument’s conclusion is true);
(v) for the conjunct of all of the premises of A (premise one and
premise two and premise three, etc.) we can know whether or not
that conjunct is true without having to know whether C is true
(our knowledge of all of the argument’s premises together is
independent of our knowing whether the argument’s conclusion is
true);
(vi) for each premise P of A, our knowledge of P is better founded than
our knowledge of C;
(vii)for the conjunct of all of the premises of A (premise one and
premise two and premise three, etc.), our knowledge of that
conjunct is better founded than our knowledge of C.
This, or something much like it, is the sense of “proof” in which we seek
proofs that religious beliefs are true. In what follows, we will consider
some of the more interesting of the many attempts to provide such
proofs.