Logical proof for the existence of God

1. God by definition is the greatest bieng concievable. Even those individuals who deny that God exists (atheists) outiside of people's minds take the word "god" to mean, among other things, "the greatest bieng concievable." Such people (atheists), then go on to deny that there is anything in external reality corresponding to the word.

therefore...

2. the atheists premise is that GOD DOES NOT EXIST IN THE EXTERNAL WORLD, but only as an concieved entity in people's minds.

3. it is agreed that anything existing in the external world would be greater than it would be if it merely existed as an idea in people's minds.

4. (from 2 and 3) Therefore, a greater bieng than God can be concieved, namely one that exists in the external world.

5. proposition 4 contradicts proposition 1.

6. since proposition 4 follows from propositions 2 and 3, either propositions(s) 1 and/or 2 and/or 3 must be changed to avoid this contradiction.

7. but proposition 1 is simply a definition accepted by both the theist and the atheist, and proposition 3 is granted independently of what is at issue.

therefore...

8. to avoid a contradiction, proposition 2 must be changed.

and...

9. to change proposition 2 is to deny that God is merely an idea in people's minds..

10. therefore, GOD EXISTS IN THE EXTERNAL WORLD, and is not merely an idea in people's minds.

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Arguments for or against this approach?