I hold the logic is a prerequisite and component of existence, as is material reality. The supernatural is nonsensical in itself. An omniscient/omnipotent being is nonsense by its own definition. And a mind prior to and outside the material universe is nonsense on several levels, not the least of which is the idea of a mind (or anything) without material existence and causational determination cannot be upheld as existing.
Even if every known law of science were wrong, or if we were incapable of ultimately determining what makes the Universe real as it is, this would not make contradictory things possible, nor would it repudiate causation and material reality as the ultimate prerrequisites to anything.