You and Eliezer make good points, thank you. I just started reading about negative probabilities. I don’t believe I’ve heard of them before. Just to be clear, I never claimed that the sum of possibilities would diverge, though I don’t think I gave proper attention to the prior probability distribution summing to 1.
I did not mean to imply that I would individually think up every single impossible possibility. I figured it would be enough to hook into some countably infinite set and show that it is just a subset of all the possible impossibilities we could generate. One could simply tap into the Infinite Earths of DC Comics to construct an argument that resembles the original lack of time camera argument:
The absence of any Superman from Earths 1 through 3^^^^^^^^^^^^3 confirming evolution must elevate the probability that evolution is false.
In my obviously absurd example, I am not sure why Superman from Earth 5000 would be any more complex than Superman from Earth 500. Though I suppose the numbering system would indicate an elevated degree of difficulty crossing over, perhaps. It is true, I didn’t account for all the parallel Earths where Superman is evil, or disinterested in our Earth, or unable to get here. My mind boggles at the possibilities.
I think my original complaint remains, though. Why would the absence of evidence from something that is admittedly impossible increase the probability of something being false? I suppose I am complaining too much for such a tiny marginal increase in probability, since a random person on the street shouting “evolution is false!” is probably going to sway your opinion to a far larger degree than some 1/3^^^^^^^^^^^^^^^^^^^^^^^^^^^3 event.
However, it strikes me as strange that someone should feel obligated to disbelieve (even a tiny bit) evolution on the grounds that Superman 3^^3 didn’t tell him/her that it was true.
(edit: I got the Superman 500 mixed up with 5000)
If this were the case, then what is to stop me from thinking of N>3^^^^^3 impossible methods of gaining evidence (aliens from Mars, or Planet X, or the past, or from Cygnus XJ45, or another dimension...), and then claiming that since these probabilities are mutually independent, summing up the positive probabilities, and claiming evolution (or any theory) to be unlikely to be true? I mean, aside from the thing about probability theory being invalid, which I haven’t seen before.
Also, thank you Eliezer, for explaining why the argument about cryonics is logically rude. I’ve been banging my head on this exact topic with a friend for the past week and have been unable to get past that road block with her.