The C preprocessor is a pushdown automaton, which if you add fixpoints (unbounded recursion) becomes a bounded storage machine. Our actual computers are such machines, which if you give them an infinite amount of memory are Turing machines. A language can be Turing-complete even if the implementation of that language is not.
Interestingly, any physical, finite machine can be modelled as a finite state automaton (which is even more limited than a pushdown automaton) with a large enough state space. The distinction only comes up when you consider idealized infinite machines.
Can C be implemented such that pointers do not have a fixed size? That is to say, suppose you have a hypothetical machine that uses bignum memory addresses. Can C be implemented to run on that machine without cheating and using a fixed pointer size?
You don't need to reason about C's pointers to consider its Turing Complete. That it allows arbitrary storage, it has conditionals and allows full looping (either unbounded loops or full recursion) is enough. That is, a language that had C's semantics sans pointers would still be Turing Complete.
I actually pondered on this for a long time, and I haven't come to a conclusion. I cannot, however, counter any of your arguments, as I thought some of the same things myself.
