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Raiden comments on If there was one element of statistical literacy that you could magically implant in every head, what would it be? - Less Wrong
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Comments (67)
The idea of ALL beliefs being probabilities on a continuum, not just belief vs disbelief.
Doesn't the word "ALL" make your statement self-contradictory?
The statements being believed in don't have to be on continuums (continui?) for belief in them to be represented as probabilities on a continuum; "I am X% certain that Y is always true".
continua.
My statement itself isn't something I believe with certainty, but adding that qualifier to everything I say would be a pointless hassle, especially for things that I believe with a near-enough certainty that my mind feels it is certain. The part with the "ALL" is itself a part of the statement I believe with near certainty, not a qualifier of the statement I believe. Sorry I didn't make that clearer.
OK, and appropriate when writing on LW. But I wonder if part of the reason most people don't think of "beliefs being probabilities on a continuum" is that even statistically literate people don't usually bother qualifying statements that if taken literally would mean they held some belief with probability 1.
No, it just makes it something other than a belief: an axiom, a game-rule, a definition, a tautology, etc.
It's a belief about beliefs.
That's true, but it's hard to see why that means that it would be a contradiction. It's true that there is a contradiction if you say that all beliefs have a specific mathematical probability of less than one (e.g. including that 1+1=2), since probability theory also assumes that the probability of a mathematical claim is 1. But probability theory isn't supposed to be an exact representation of human beliefs in the first place, but a formalized and idealized representation. In reality we are not always completely certain even of mathematical truths, and this does not cause the existence of a contradiction, because this uncertainty, considered in itself, is not something mathematical.
You could say in the same way that all beliefs are uncertain, including this one, without any contradiction, just as it is not a contradiction to say that all sentences are made of words, including this one.
I interpreted the statement as basically "I am CERTAIN that you can never be certain of anything." I almost didn't post a response because I thought the author might have been deliberately being sarcastic.
This a million times!
How many bias are based on this alone? It's discomforting...