At what point is an independent fact introduced? (never)
I’m not sure how to interpret this thought experiment, but it seems that you could still produce indistinguishable-from-independent-fact-in-the-eyes-of-in-world-observers -like things.
Like, if we take empty set, set that contains empty set, then form a set that contains all earlier sets, and this way construcy natural numbers, and then produce a function that takes one set and gives it’s “successor”, as in, the next natural number. F(1) = 2, F(11) = 12 and so forth.
This could be taken as “natural, simple world”, where there are no surprises, like, F(15) giving 1337 as a result, or anything. That F(15) = 1337 would count as an independent fact. But obviously rule like could be formulated, and I’m really unsure about what’s there to prevent this “add one expect if 15, give 1337″ rule from happening, given that the original successor function did ‘happen’.
But then again, maybe I just misunderstood, I got kind of an impression that you’re thinking Universe as some sort of limit as length of deduction chains approach infinity, but this idea seems counter-intuitive to me.
I’m not sure how to interpret this thought experiment, but it seems that you could still produce indistinguishable-from-independent-fact-in-the-eyes-of-in-world-observers -like things.
Like, if we take empty set, set that contains empty set, then form a set that contains all earlier sets, and this way construcy natural numbers, and then produce a function that takes one set and gives it’s “successor”, as in, the next natural number. F(1) = 2, F(11) = 12 and so forth.
This could be taken as “natural, simple world”, where there are no surprises, like, F(15) giving 1337 as a result, or anything. That F(15) = 1337 would count as an independent fact. But obviously rule like could be formulated, and I’m really unsure about what’s there to prevent this “add one expect if 15, give 1337″ rule from happening, given that the original successor function did ‘happen’.
But then again, maybe I just misunderstood, I got kind of an impression that you’re thinking Universe as some sort of limit as length of deduction chains approach infinity, but this idea seems counter-intuitive to me.