and thanks to @ZzzoneiroCosm as well for trying to straighten me out...gave me one more opportunity to see I was misreading...but I just doubled down on making an ass of myself :grin:

↪Valentinus
I don't know. I haven't been able to follow your line of thought. It feels like you are only posting half of what you are saying. As if I am missing half of the conversation. — Banno

Okay. I will try to do better.

Kant objected to Hume's view of causality because it did not give a way to rank different explanations.
The objection on Kant's side was not so much about whether there were any way thinkers who could assign one agent or another as the cause of something but that Hume was cutting the enterprise off at the knees. Because every story as a story is just a story, there is no way to connect it to some kind of necessity that could provide proof of some explanation being more than that. A story.

So, on one level, the whole effort to object to an idea became a comprehensive theory of what could replace the disagreed thing.

As a matter of one thesis supplanting another, that is rather odd. The contestants are arguing about the rules of a fight rather than who has the correct view of a matter.

and thanks to ZzzoneiroCosm as well for trying to straighten me out...gave me one more opportunity to see I was misreading...but I just doubled down on making an ass of myself :grin: — ZhouBoTong

Fun with anonymity.

Critical thinking without context is dangerous. — Banno

I think you're missing something about crackpots. For example, I struggled with the concept of compactness when learning topology. For some time, I thought: surely this isn't the natural complement to discreteness when generalizing finiteness to infinite sets. It wasn't until I learned topology from the perspective of computability theory that I understood the concept. Despite lacking knowledge and thinking critically, I don't think I ever became a crackpot about compactness.

Similarly, I read about the Riemann hypothesis before learning complex analysis. It never occurred to me to question whether the problem was actually within my grasp. I knew that thousands of people much smarter and more informed than myself have worked on the problem, and in order to fully understand let alone approach it I would have years of work ahead of myself. On another note, I avoid talking about the foundations of physics because I'm almost completely ignorant about the subject.

For whatever reason, crackpots focus on specific topics: the axiom of infinity, the Riemann hypothesis, P=NP, the ABC conjecture, and so forth. It's rare to find crackpots discussing the axiom of choice, the mean value theorem, the reality of transcendental numbers, or other actually problematic topics in mathematics (in particular, from the perspective of constructive mathematics). It must be a sociological phenomenon, but I'm not sure how to explain the choice of topics. Surely everyone learned mathematics in high school that are highly suspect and revised in more advanced courses; but those usually aren't the topics they choose to target. Anyways, my two cents.