@cwage Cox was not confused about this. The error seems to have been introduced by ET Jaynes, who knew no logic and missed the point.
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Replying to @Meaningness
@Meaningness@cwage Hmm. I was extremely surprised by this statement. Say more?1 reply 0 retweets 0 likes -
Replying to @GrumplessGrinch
@GrumplessGrinch@cwage If I write this up, I’ll need to go back and read Jaynes carefully to make sure I understand exactly how he got >1 reply 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage > confused, but I think the phrase “Aristotelian logic” was what tripped him up. https://en.wikipedia.org/wiki/Term_logic1 reply 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage Anyway, the upshot is that Jaynes didn’t understand that Cox’s theorem applies only to boolean algebra, which >1 reply 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage > is a system with (1) binary values and (2) no quantification. PT generalizes (1) but doesn’t deal with (2).1 reply 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage Aristotelian logic does have quantification (as well as binary values), and PT does not generalize it.2 replies 0 retweets 0 likes -
Replying to @Meaningness
@Meaningness@cwage Okay, why do we need quantification?1 reply 0 retweets 0 likes -
Replying to @GrumplessGrinch
@GrumplessGrinch@cwage If you want to say “any time you see a snark, it might be a boojum” you need quantification.1 reply 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage Because this is a universally quantified (“for all”) statement; it’s not just about a particular snark.1 reply 0 retweets 0 likes
@GrumplessGrinch @cwage PT can only say P(boojum(s0)|snark(s0))>0, for some particular snark s0.
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Replying to @Meaningness
@GrumplessGrinch@cwage Statistical inference (which is *not* the same as PT) gives you limited quantification, which is what you want.2 replies 0 retweets 0 likes -
Replying to @Meaningness
@GrumplessGrinch@cwage Statistical inference starts with a model (which falls out of the sky—this is why PT + logic < epistemology).1 reply 0 retweets 1 like - 5 more replies
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