Thursday, October 25, 2007

5.152 We call propositions that have no truth-arguments in common with one another independent of one another.

Propositions independent of one another (e.g. any two elementary propositions) give one another the probability ½.

If p follows from q, then the proposition “q” gives the proposition “p” the probability 1. The certainty of a logical conclusion is a limiting case of probability.

(Application to tautology and contradiction.)

Does probability thus conceived make any sense? Independent propositions cannot give each other any probability they do not already have, i.e. they cannot give them any probability at all. So does talk of probability belong in logic?

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