Suppose you find yourself convinced that the laws of logic are objective and that they have a positive ontological status. With their immutability in mind, the laws of logic cannot be grounded in a dynamic universe. Consider this:
1. The universe and everything contained within it are mutable. (Premise)
2. The laws of logic are immutable. (Premise)
3. Therefore, the laws of logic cannot be contained within the universe. (From 1 and 2)
The objectivity and existence of laws of logic necessitate that they be necessary, eternal, immutable and immaterial. Now, do these objects fit better within a theistic worldview or an atheistic worldview? Obviously, naive materialism is ruled out as a plausible (possible?) worldview, and materialism is one of the most predominant atheistic worldviews.
Technically, an atheist could adopt a version of Platonism. It's at this point that I would exhort the believer to stress the advantages of conceptualism over against Platonism. To continue:
4. The laws of logic are abstract objects. (Premise)
5. Abstract objects are either mind-independent or mental concepts. (Premise)
6. Abstract objects cannot be mind-independent. (Premise)
7. Therefore, the laws of logic are mental concepts. (From 4 - 6)
Now, the laws of logic cannot be the concepts of just any mind. For, there are possible worlds in which contingent minds do not exist. Yet, the laws of logic still obtain in those possible worlds. Hence, the laws of logic must be the concepts of a necessary mind (e.g. God).
Premise (6) might be the most controversial of the argument. I would stress the causal impotence of abstract objects, and the fact that there is a causal relation between mind-independent realities and the mind that knows them. In other words, if the laws of logic were mind-independent, then they could not be known. However, they certainly are known. Therefore, the laws of logic are not mind-independent, but conceptual in nature.
As for the positive ontological status of the laws of logic and other abstract objects, I would appeal to their indispensability. It is impossible to reason apart from laws of logic. A thing cannot possess the attribute of indispensability and be non-existent. After all, non-existent entities do not possess any attributes. A parody of this argument might go something like this: unicorns possess the attribute of being magical. Yet, that doesn't mean unicorns exist.
The problem with the above objection is that unicorns really don't possess the attribute of being magical. The quality of being a magical horse with a horn is not instantiated, whereas the indispensability of logic is instantiated. It really is necessary for us to use logic whenever engaging in rational inquiry. In sum, there is no parity between the argument and its parody.
If this argument is sound, as I maintain it is, then we have a definitive proof in favor of theism and against atheism. Far from there being a conflict between faith and reason, it turns out that reason actually presupposes faith.