Hmm, why is this the case? I think I'm missing background knowledge here.
Think of it like this: say you're flipping a coin and want the probability of heads. The only way you can think of to not get heads or tails is if an alien swaps the coin with something else when you toss it, and you assign that a tiny probability. Then suddenly you realize that there's a 1/10000 chance to land on the edge!
Now, factor by which this changes your probability estimates for heads and tails is really small. 0.499999999999 is pretty much the same as 0.49995, if you were betting on heads, your expected payoff would barely shiver. But if you w...
Advanced apologies if this has been discussed before.
Question: Philosophy and Mathematics are fields in which we employ abstract reasoning to arrive at conclusions. Can the relative success of philosophy versus mathematics provide empirical evidence for how robust our arguments must be before we can even hope to have a non-negligible chance of arriving at correct conclusions? Considering how bad philosophy has been at arriving at correct conclusions, must they not be essentially as robust as mathematical proof, or correct virtually with probability 1? If so, should this not cast severe doubt on arguments showing how, in expected utility calculations, outcomes with vast sums of utility can easily swamp a low probability of their coming to pass? Won't our estimates of such probabilities be severely inflated?
Related: http://lesswrong.com/lw/673/model_uncertainty_pascalian_reasoning_and/