Logic: everywhere or nowhere?

I just finished digesting Dr. Victor Repperts article, "The Argument from Reason", over at http://www.infidels.org/library/modern/victor_reppert/reason.html and was disappointed with one aspect in particular. Dr. Reppert describes how a formal system works in one paragraph, and them much later disregards the same properties when discussing a different formal system.

On the other hand, if I am playing chess, and I am missing a pawn, I can get a penny, a button, a half-eaten carrot, or just about anything else to play the role of a pawn. This is because unlike the frisbee[sic], the pawn's role is purely symbolic, determined by convention.
That seems clear, and I agree. Chess is one type of formal system, basically a instantiation of rules and procedures. Formal systems can be applied to a variety of objects with no change tot he structure of the system. They form a sort of model. Dr. Reppert seems to forget this in a later paragraph, though.

But principles like the laws of non-contradiction apply universally. Contradictions cannot be true in Phoenix, in Houston, in Antarctica, on Venus, in the Virgo cluster, in the furthest nebulae, or even in Southern California. From what particular experience could our knowledge of this have come?
Equally true would be, "But principles like the diagonal movement of bishops apply universally. Bishops cannot move orthogonally in Phoenix, in Houston, in Antarctica, on Venus, in the Virgo cluster, in the furthest nebulae, or even in Southern California. From what particular experience could our knowledge of this have come?" Of course, the obviously true answer would be that we set up the rules of chess the same everywhere, otherwise it's not chess. The same reasoning applies to logic. Any time you set up a system where you only accept two logical values (true or false) and only allow each statement to have one of those values, you get a formal system where the law of non-contradiction obtains. There is no experience this comes from, any more that there is an experience of a real-life bishop that never walks forward straightly. It's a feature that we built into the system, not one innate in the universe.