Argument from the laws of logic:
This argument was made popular by Greg Bahnsen in his debate with Gordon Stein. Although Bahnsen's formulations have been often unclear and subject to criticisms we will look at a more precise and clean version of this argument.
P1: If God does not exist then the laws of logic do not exist (Logical Realism)
P2: The laws of logic do exist
C: Therefore God exists
The way this argument is defended is very similar to or analogous to the moral argument. One would argue that the laws of logic are necessary and so they would have to be grounded in some sort of immaterial entity and the only reasonable candidate for that would be God, who would be the foundation of perfect logic and reason (since he is a perfect, personal being).
Here are some of the reason's why atheistic realism cannot account for the laws of logic:
1) It seems that we also have a moral obligation to be reasonable and logical and this seems only possible with persons.
2) there is no guarantee that agents would develop a correct conception of logic because the immaterial abstract objects that would ground logic do not have causal power over the world to guide our faculties.
3) it is hard to conceive of immaterial objects having content apart from a mind with thoughts that possess content.
4) it is difficult to imagine how the metaphysical foundation of logic would itself be non logical (what I mean by this is reasoning correctly), since only persons have logical properties of this sort. Thus, logic would not be logical, which would seem absurd.
5) And finally, it is difficult to see how these logical forms or propositions could relate or connect to the world in any sort of fashion.
Hence, it seems from these considerations that the theistic worldview can account for the laws of logic whereas atheistic realism fails to account for criteria 1-5.