Not every picture of a pipe is a pipe but it's at least conceivable that an actual working pipe can be constructed out of something which happens to be a pictur

Not every picture of a pipe is a pipe but it's at least conceivable that an actual working pipe can be constructed out of something which happens to be a picture of a pipe. Similarly Godel isn't proving that all statements in a system are paradoxically self-referential. Only that given any system of sufficient complexity, one can conceivably be constructed. In any event, all of our mathematical proofs are predicated upon the idea that the representation of a mathematical object can be treated in terms of proof as equivalent to the mathematical object. Is "2" the number 2 or is it just a glyph that non-representationally depicts the successor of the first counting number? And if you believe the latter, then how do you go about proving anything about the actual successor of the first counting number without resorting to glyphs?