You’re welcome :) to be honest it’s my first for this as well 😂, but I do have experience with math.
The one thing that ticked me with your proof, was about your phrasing. You were trying to prove !(p=>q)
i.e. p^!q
by a counter example, but your wrote “suppose we have p^!q
”, which is already the thesis of the proof. So what you wrote is essentially “We will proof A is false. Suppose !A, then !A.” which is not proving !A. What you should have done is to remove the “suppose” part and say if p=>q
then if I nothing to hide I should not be concerned, but I can have nothing to hide and be concerned, which is a contradiction. Then your proof would be somewhat correct but my last two arguments still hold. The issue could be solved woth some modals or quantifiers to express the different people.
Sure you can always infinitely define what is behind but I don’t think it is relevant here or you couldn’t do any moral logic.
The two axioms I assumed are A1 a proven fact and A2 the very defintion of having something to hide. It is enough for this specific problem.
I don’t see how Gödel’s theorems are useful since they say that a given system of actions is either incomplete or inconsistent. With these two axioms it’s hardly inconsistent and we don’t care about it being incomplete since we only have one theorem to prove