Out of curiosity, how would Hintikka (or you if you share their views) justify axioms if not through intuitions? I am asking with the assumption that all knowledge is built upon axioms (which I can provide an argument for if necessary). It seems to me that intuitions are the only possible source of axioms and thus we must assume some connection between them and truth if we are to avoid scepticism, though I am still struggling with the nature of that connection... any insights would be appreciated.

I am by no means an expert on quantum physics so please correct me if I am wrong, but my understanding of the double slit experiment is that the particle acts as a wave when unobserved and as a particle when observed. Such a conclusion is unintuitive (as mentioned earlier) because it implies that our observations can affect reality and that particles can act as both particles and waves under different circumstances. It seems a leap, however, to go from this point to arguing that it does both simultaneously (which would imply a contradiction). As far as I can tell, the only statement we can make is that it's nature is undetermined as it approaches the slit because it has the potential to be both a particle and a wave, but both are not actualized simultaneously.

Regardless, I would agree with the original argument that if something appears to violate the PNC, we should disbelieve it rather than disbelieving the PNC. The reason for this is that without the PNC everything becomes trivial. A tree is both a tree and not a tree. Everything is everything and nothing at once. Logic becomes impossible. As Aristotle would put it, we would become vegetables rather than human beings. If something appears to violate the PNC, then we should examine it closely and seek out any potential errors. Given that we are here dealing with empirical experiments that are at the forefront of science (and thereby not very well understood), I don't think we have any justification for believing the PNC is violated even if I have massively misrepresented the experiment and the article is right on that point.