What Gödel does is the following: he constructs a sequence of symbols which is not decidable (i.e. there is no “proof” of it or of its negation). Then (and thi

What Gödel does is the following: he constructs a sequence of symbols which is not decidable (i.e. there is no “proof” of it or of its negation). Then (and this is super important) he explains that IN THE STANDARD INTERPRETATION that sequence of symbols can be translated to “the sequence of symbols corresponding to the number XXXXX is a statement which has no proof” (and has to be true) and that very sequence corresponds to that number XXXXX. But those two things (the construction and the interpretation) are totally separated, and goes to great lengths to keep them so.