Another way of phrasing this is that I am pessimistic about the prospects of conceptual thinking, which seems to be the main way by which we could find a fundamental obstruction. (Theory and empirical experiments can build intuitions about what is and isn’t hard, but given the complexities of the real world it seems unlikely that either would give us the sort of crystallized knowledge that Paul is aiming for.) Phrased this way, I put less credence in this opinion, because I think there are a few examples of conceptual thinking being very important, though not that many.
Can you expand on your reasons for pessimism?
Idk, it seems hard to do, I personally have had trouble doing it, the future is vast and complex and hard to fit in your head, when trying to make an argument that eliminates all possible bad behaviors while including all the good ones it seems like you’re going to forget some cases, which proofs let you avoid because they hold you to a very high standard but there’s no equivalent with conceptual thinking.
(These aren’t very clear/are confused, if that wasn’t obvious already.)
Another way of putting it is that conceptual thinking doesn’t seem to have great feedback loops, which experiments clearly have and theory kind of has (you can at least get the binary true/false feedback once you prove any particular theorem).