His problem is even more basic than that. Axioms+rules+theorems make up a formal system, not a universe. (I can see how it's easy to confuse the two.) At some point, you must use induction & associate/identify some of its elements with observable quantities; that's what makes it a physical theory instead of a purely mathematical theory. Deduction alone gets you nowhere in the real world. And in its own domain the most it gives is consistency, not truth. I can't for the life of me understand why it's desired, or why its absence is relevant.