## Blindness

17 Jul

(Three unfalsifiable mice)

It is a mathematical axiom that P(E | H) + P(~E | H) = 100%. That is, the probability of having the evidence at hand given the truth of the hypothesis plus the probability of not having the evidence at hand given the truth of the hypothesis equals 100%. The two have to exhaust all possibilities. E and ~E aren’t necessarily binary; it could represent the entire range of the types of evidence we would see given H (like, say, numbers 1 – 6 for the roll of dice).

Why am I pointing this out? Well, in What Is Evidence, Yudkowsky writes:

This is why rationalists put such a heavy premium on the paradoxical-seeming claim that a belief is only really worthwhile if you could, in principle, be persuaded to believe otherwise. If your retina ended up in the same state regardless of what light entered it, you would be blind. Some belief systems, in a rather obvious trick to reinforce themselves, say that certain beliefs are only really worthwhile if you believe them unconditionally— no matter what you see, no matter what you think. Your brain is supposed to end up in the same state regardless.

What would it look like, from a Bayesian-hypothetical model, to have your retina end up in the same state regardless of what light entered it? P(E | H) and P(~E | H) would reach maximum entropy; meaning that P(E | H) = P(~E | H). Or, if there are 100 types of evidences to be found, P(E | H) = 1/100 and each instance of P(~E | H) other than P(E | H) are equal. Again, like rolling dice; each number 1 – 6 is equally likely (unless the die is weighted).

As I’ve hammered on multiple times, this is the Bayesian definition of unfalsifiable; also as the blog Maximum Entropy points out. This just means that if your hypothesis is unfalsifiable, it is no different than being blind, since there isn’t any type of light (evidence) that would have a different effect on your retina (hypothesis). And this means that to have blind faith is to have a faith that is unfalsifiable. They are metaphorically equal.

So if you don’t want to have “blind faith” in some hypothesis (like god), then believe in a hypothesis that can be disproved. Or to reword it, you can’t both believe in a hypothesis that is unfalsifiable and claim to not have blind faith in said hypothesis.

Posted by on July 17, 2013 in Bayes

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