# on 24-Dec-2018 (Mon)

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 [unknown IMAGE 3711651155212] #chapter-1 #has-images #jaynes_probability_theory The evidence does not prove that A is true, but verification of one of its consequences does give us more confidence in A. For example, let

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Distributivity rule in logic

#chapter-1 #jaynes_probability_theory

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one would take ‘A implies B’ to mean that B is logically deducible from A.
What's wrong?
"A implies B" really does not mean that there is a chain of arguments so you can derive B from what's inside the statement A. "A implies B" indeed only means "whenever A, then B". You can say "the fact that the number 3 is odd implies that the number 100 is bigger than the number 50". "Implies" here really doesn't mean that you can derive size relations of numbers from the oddness of other numbers by looking at the concepts of "size" and "oddness". These statements haven't anything special to do with each other, they just happen to be both true.

And every true statement "follows from" / "is implied by" every other true statement in the sense of formal logic.
every statement (be it true or false) "is implied by" / "follows from" any false statement.

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Note carefully that in ordinary language one would take ‘A implies B’ to mean that B is logically deducible from A. But, in formal logic, ‘A implies B’ means only that the propositions A and AB have the same truth value.

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