Is the infinitude of “how should one think?” the “main reason” why philosophy is infinite? Is it the main reason for most particular infinite philosophical problems being infinite? I would guess that it is not — that there are also other important reasons; in particular, if a philosophical problem is infinite, I would expect there to at least also be some reason for its infinitude which is “more internal to it”. In fact, I suspect that clarifying the [reasons why]/[ways in which] endeavors can end up infinite is itself an infinite endeavor :).
Attribution is probably very (plausibly infinitely) tricky here, similar to how it’s tricky to state why certain facts about mathematical structures are true while others are false. Sure, one can point to a proof of the theorem and say “That’s why P is true.” but this is conflating the reason for why one knows/believes P versus the reason for why P, especially when there are multiple, very different ways to prove the same proposition.[1] Or at least that’s how it feels to me.
I don’t know how often it is the case. It would be fun to see something like a distribution of proof diversity scores for some quasi-representative set of mathematical propositions where by “proof diversity” I mean something like information diameter (Li & Vitányi, Def 8.5.1).
Attribution is probably very (plausibly infinitely) tricky here, similar to how it’s tricky to state why certain facts about mathematical structures are true while others are false. Sure, one can point to a proof of the theorem and say “That’s why P is true.” but this is conflating the reason for why one knows/believes P versus the reason for why P, especially when there are multiple, very different ways to prove the same proposition.[1] Or at least that’s how it feels to me.
I don’t know how often it is the case. It would be fun to see something like a distribution of proof diversity scores for some quasi-representative set of mathematical propositions where by “proof diversity” I mean something like information diameter (Li & Vitányi, Def 8.5.1).