Proving God's Existence

Two definitions:

an argument is valid =df it's not possible that the premisses of the argument are true while the conclusion is false (or, it must be the case that if the premisses are true, then the conclusion is true as well)
an argument is invalid =df it's not valid

In terms of the former definition we can say the following: a conclusion follows from some premisses just in case the argument with those premisses and that conclusion is valid.

Example 1

Every human being is mortal.
Socrates is a human being.
Therefore,
Socrates is mortal.

Example 2

If you study hard, you will pass the course.
You study hard.
Therefore,
You will pass the course.

Example 3

If you study hard, you will pass the course.
You don't study hard.
Therefore,
You won't pass the course.

Example 4

Every UR student was denied admission to an Ivy League school.
Jane is a UR student.
Therefore,
Jane was denied admission to an Ivy League school.

Two more definitions:

an argument is sound =df it's valid and all of its premisses are true.
an argument is unsound =df it's not sound

An Important Consequence:

It follows from the definitions of sound' and valid' that a sound argument has a true conclusion.

A useful principle:

To show that an argument is invalid it suffices to exhibit another argument of the same form with true premisses and a false conclusion.

The form of examples 1 and 4:

Every F is G.
a is F.
Therefore,
a is G.

Example 5

If it's warmer than 100 F. today, then it's warmer than 60 F. today.
It's not warmer than 100 F. today.
Therefore,
It's not warmer than 60 F. today.

Example 6

Either God exists or the Taj Mahal is green.
The Taj Mahal isn't green.
Therefore,
God exists.

Perhaps what we are looking for is a sound argument the conclusion of which is that God exists and the premisses of which are acceptable to nearly every sane and reasonably intelligent person who thinks about them. (Similar standards should apply, of course, to the attempt to prove that God doesn't exist.)

A Final Distinction:

revealed theology: the attempt to discover things about God by appealing to a special source of revelation, e.g., biblical theology.

natural theology: the attempt to discover things about God by appealing to propositions that are either self-evident or acceptable to most sane and reasonably intelligent people.