I believe there is a sense in which the laws of thought follow from our created finiteness. It is provable in first order logic that if we allow one contradiction, then we can prove anything at all. In the remarks below I use the rules of inference of first order logic, but without the quantifiers, that is in a propositional schema, for the sake of simplicity.
Negation is denoted by the tilde.
From a metaphysical point of view, this argument is in one sense circular, because the absurdity I claim for the argument comes from LC, which the argument assumes. Let us try to eliminate idempotency of negation and any kind of remotion from the proof and argue constructively. But this is a tautology, and we can write permutations of it ceaselessly and get nothing productive. No inconsistency will arise, but proving the absence of inconsistency throws us back on idempotency, and reasoning by negation. Over and above this, we are also unable to act on them.