Comment author:Vaniver
25 May 2013 10:38:31PM
*
3 points
[-]
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.
Comment author:jshibby
29 May 2013 05:26:26PM
0 points
[-]
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.
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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.
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.