[inopinatus]

The first statement is either wholehearted agreement with my remark or a rejection of Gödel numbering.

The second statement is similar but highlights the problematic distinction of the terms, since in such a framing they ascribe meaning solely and specifically to human intellectual processes, so one must also show either that we are alone in the universe, or (perhaps equally) that all cognitive entities share the same processes. This is of course merely dancing around questions of the universality of truth. Alas, only Wittgenstein knew the answer.

[wavesonthing]

I didn't attempt to delve into that, so ...

With Gödel, there is the space of the possible, the invention indeed being the axiomatic foundation that engenders the space of possibilities. If the space of possibilities is disconnected, intuitive jumps are required to arrived at unreacheable truths. So yes, here we are 'discovering' -- learning the membership set of true statements -- but these are existing things only in the context of the invention, which is why it is correct to say they are discovered in a relative sense.