Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics?
Does a proof of a conjecture, say FLT, which is essentially an arranged (legal) collection of mathematical symbols, by itself, without our interpretation, means a proof of FLT? If it doesn't, does there exist a possibility that WE, within the same calculus, can provide it some other justified meaning, one which is very different from FLT?
That is: does meaning of mathematical propositions, of whatever sort it may be, reside solely with in the mathematical propositions: how the proposition is structured, and relations between symbols and their relative positions? (Loosely, think Wittgenstein's Picture Theory). OR only a natural language can provide any meaning to it? (If this is the case, aren't mathematical statements tautologies?)
The issue I am concerned with is if description of mathematical results in natural language is a valid exercise, and if it is of any concrete importance to a
- And, in principle, to God (an infinitely intelligent being who can compute infinite operations concurrently and instantly).
Will be helpful if answers to this question also include remarks on the above two points on mathematician and God.