ChrisHallquist comments on No Universally Compelling Arguments in Math or Science - Less Wrong
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Well, if they're logically inconsistent, but nothing you can say to them will convince to give up YECism in order to stop being logically inconsistent... then that particular chain of reasoning, at least, isn't universally compelling.
Or, if they have an undefeatable hypothesis, if that's literally true... doesn't that mean no argument is going to be compelling to them?
Maybe you're thinking "compelling" means what ought to be compelling, rather than what actually convinces people, when the latter meaning is how Eliezer and I are using it?
I am at a loss about the true meaning of a "universally compelling argument", but from Eliezer's original post and from references to things such as modus ponens itself, I understood it to mean something that is able to overcome even seemingly axiomatic differences between two (otherwise rational) agents. In this scenario, an agent may accept modus ponens, but if they do, they're at least required to use it consistently. For instance, a mathematician of the constructivist persuasion denies the law of the excluded middle, but if he's using it in a proof, classical mathematicians have the right to call him out.
Similarly, YEC's are not inconsistent in their daily lives, nor do they have any undefeatable hypotheses about barbeques or music education: they're being inconsistent only on a select set of topics. At this point the brick wall we're hitting is not a fundamental difference in logic or priors; we're in the domain of human psychology.
Arguments that "actually convince (all) people" are very limited and context sensitive because we're not 100% rational.