This thread has probably been done many times before, but oh well.
I've been thinking about this quite a lot today; here are my ideas:
Leaving aside for the moment exactly what the term 'principles of logic' means, I want to posit the existence of a God that lies beyond the 'rules' of sense and congency; indeed, a God that created these 'rules' to aid us in our understanding of the world.
If this God exists, surely we, as logical beings, could never justify our belief that he exists. To say that the world is so complex as to warrant a creator by necessity, for example, implies a logical relation between the creator and the created, and even that God recognises his abilty to create complexity over our own ability. This latter idea implies that God thinks logically, which contradicts the initial premise that he lies beyond it.
We could solve these issues by saying that he is subject to logic, and that he did create the world logically. However, this would apparently remove him of omnipotence. And we can't have the best of both theories, as it's contradictory to say that he is governed by the 'principles' that he 'created'.
Does my argument demonstate a misunderstading of the entirely inconceivable in relation to the logical principles that 'govern' (for want of a better word) what I can conceive of?