>Can you deduce the majority of the C language from these initial axioms?
Well, no. You can deduce A language but it might not be C.
I sense we're going down a fruitless path here. In my first post I was only giving an analogy of someone understanding math at a fundamental level to someone understanding a programming language at a fundamental level and how they could inform similar abilities/prowess in people when it comes to dealing with complex problems/etc.
You misunderstand the usage of consistency regarding mathematics. It is not the same. These rules which compose C are design decisions, and whether they are entirely artificial. Mathematical consistency arises from imposing axioms, following which there are no decisions to be made.