Ideas by Alex Ahn

The fundamental problem with symbolic AI is that logic is bounded. There is a shape to any corpus of logical expressions that can be programmatically generated via following a set of manipulation rules. And due to the rigid manner in which the corpus evolves, the corpus is bound by its initial position and the rules of manipulation. This is a problem when the corpus has to choose the direction in which it wants to evolve itself further, because the corpus itself is a product of following a set of rigid manipulation rules. Any heuristic rule that can be devised is often not self-referential, and even if it is, it has a limited scope of self-inspection. This is because the heuristic rule itself must be a product of the same mechanism which generated the corpus of logical expressions: the rules of manipulation. And unfortunately, the rules of manipulation are often atomic, often akin to the fundamental laws of logic (e.g. modus ponens). I think it is often hard for people to imagine the s...

I find it distasteful that non-mathematicians think that Gödel's work introduces a level of subjectivity to mathematics. I agree that one can construct an arbitrary number of mathematical universes via selecting an arbitrary set of axioms. But I disagree that they are somehow all equivalent in value or structural consistency. I personally believe that there is one mathematical universe (or category of universes that are structurally equivalent via something like an isomorphism) that has the most structural consistency and can give the human mind the most insight. I personally believe that there are axioms that are representations of structural properties of physical reality. And I believe that there is a set of axioms that aligns perfectly with the physical universe, and subsequently allows the human mind to comprehend its logic to the fullest extent. I believe this because the way that the human mind understands logic is already a consequence of physical reality. Our ability to un...