The truth of the principle of non-contradiction [PNC] isn’t a matter of mere opinion (try denying the principle of noncontradiction without using it!). It is widely held that the PNC and all logical principles are objectively and universally true. Many philosophers will say they are true in all possible worlds! This means that logic is not tied to the way our world is. Whatever it is, it exists as a feature of reality that couldn’t not be the case and it is used every time we make and support a claim. If logic is this real thing that exists outside time and space, then this entails that the natural world is not all there is. In other words, the supernatural (as in supra-natural) must exist.—Travis Dickinson (from, God Makes Sense Of The Logic Used To Reject Him)