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May 17, 2022 at 22:19 comment added J Kusin Yes abstraction does those wonderful things. But listing all even numbers like you say is probably very particular. “Give me a probably consistent formalism which allows me to write the most Arabic numerals in base 10 such that [some formalism for evens], without duplication, in the shortest time, smallest memory, which if run forever will produce more new numbers”. If we have a specific question, we don’t need more abstraction almost. And a specific pluralism puts the ceiling on.
May 17, 2022 at 21:41 comment added emesupap how would you ever state all even numbers? Not by listing, surely. Being able to abstract away performs a pragmatic function in opening up new roads of discovery and conjecture, as well.
May 17, 2022 at 18:59 comment added J Kusin But it seems like ultimately everything collapses and stagnates into situation-> x. And then there I go again wondering why use abstraction. It’s like every specific question has a specific answer.
May 17, 2022 at 18:35 comment added emesupap perhaps you wish to say that in exactly 1000 different cases, some wff holds. will you state them each individually, or say that all 1000 x, that satisfy some property, also satisfy another property?
May 17, 2022 at 18:34 comment added emesupap you are requiring a very strong condition on your epistemology, roughly corresponding to knowing that you know. This is roughly a strong internalism, and, by my lights, fairly implausible. in addition, a logic need not function as just stating that x holds, for a particular x. you might wish to say that all x of a certain type hold.
May 17, 2022 at 18:17 comment added J Kusin I guess I want to say, by knowing this is the best model, the best abstraction, you’d have to have such complete knowledge there’d be no need for “abstracting”. Complete knowledge would be just stating something is the case, with nothing to abstract.
May 17, 2022 at 17:44 history answered emesupap CC BY-SA 4.0