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Vaniver comments on Evidence and counterexample to positive relevance - Less Wrong
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Comments (37)
Your interpretation about g is correct.
The high probability interpretation is not a useful interpretation of "evidence," and there's a much easier way to discuss why: implication. P("A or ~A"|"My socks are white")=1, because P("A or ~A") is 1, and conditioning on my socks being white cannot make that less true. It is not sensible to describe the color of my socks as evidence for the truth value of "A or ~A".
The increase in probability definition is sensible, and what is used locally for Bayesian evidence.
Thanks Vaniver. Doesn't your example shows something unsatisfactory about the High Probability interpretation also? Given that P(A or ~A|My socks are white)>1/2, that my socks are white would also count as evidence that A or ~A. Your point seems to suggest that there must be something having to do with content in common between the evidence and the hypothesis.
Actually, early empiricists wanted to consider tautologies just those that were confirmed by any evidence whatsoever. (This enables an empiricist to have a pure evidential base of only empirical events.) It doesn't sound great, but some folks like the conclusion that anything (or anything possible) is evidence for a tautology.