| http://lesswrong.com/lw/nf/the_parable_of_hemlock/ > The problem with syllogisms is that they're always valid. [...] > The Bayesian definition of evidence favoring a hypothesis is evidence which we are more likely to see if the hypothesis is true than if it is false. Observing that a syllogism is logically valid can never be evidence favoring any empirical proposition, because the syllogism will be logically valid whether that proposition is true or false. > Syllogisms are valid in all possible worlds, and therefore, observing their validity never tells us anything about which possible world we actually live in. If a proposition is logically possible, there's a non-zero probability it's actually true. E.g. it's possible that God does not exist. It's also possible that God does exist and put dinosaur fossils in the ground to troll us. I say this without sarcasm. Pure Logic(TM) isn't always pragmatic enough to suit our needs because it restricts its inputs and outputs to 100% certainties. In the real world, nothing is ever 100% certain. Maybe we have a lot of life experiences with gravity. Maybe we predict with seven 9's that objects will continue to fall down like they always have. But can we ever be truly-entirely-perfectly certain that tomorrow, gravity won't be around because God forgot to pay the utility bill? No, actually, we can't. We're just really confident because we've experienced evidence of gravity for our entire lives. Likewise, you can never be truly certain that the diodes in your computer won't spontaneously reverse current. But we can still rely on diodes to work properly because we predict that such an event is super-ultra-extremely unlikely (has low probability) given the voltages humanity's electrical engineers decided to ram through our circuits. |