How do you deal with Munchhausen trilemma? It used to not bother me much, and I think my (axiomatic-argument based) reasoning was along the lines of "sure, the axioms might be wrong, but look at all the cool things that come out of them." The more time passes, though, the more concerned I become. So, how do you deal?
Fine, Eliezer, as someone who would really like to think/believe that there's Ultimate Truth (not based in perception) to be found, I'll bite.
I don't think you are steelmanning post-modernists in your post. Suppose I am a member of a cult X -- we believe that we can leap off of Everest and fly/not die. You and I watch my fellow cult-member jump off a cliff. You see him smash himself dead. I am so deluded ("deluded") that all I see is my friend soaring in the sky. You, within your system, evaluate me as crazy. I might think the same of you.
You mig...
Oops, misread that as sum(1/(2n))[1:infinity] (which it wasn't), my bad.
Hate to nitpick myself, but 1/2+1/4+1/8+... diverges (e.g., by the harmonic series test). Sum 1/n^2 = 1/4 + 1/9 + ... = (pi^2)/6 is a more fitting example.
An interesting question, in this context, is what it would mean for infinitely many possibilities to exist in a "finite space about any point that can be reached at sub-speed of light times." Would it be possible under the assumption of a discrete universe (a universe decomposable no further than the smallest, indivisible pieces)? This is an issue we don't have to worry about in dealing with the infinite sums of numbers that converge to a finite number.
If this wasn't clear: responses would be much more helpful than up/down votes.