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Download A Philosophical Companion to First-Order Logic by R. I. G. Hughes PDF

By R. I. G. Hughes

ISBN-10: 0872201821

ISBN-13: 9780872201828

This quantity of contemporary writings, a few formerly unpublished, follows the series of a standard intermediate or upper-level good judgment direction and permits academics to complement their displays of formal tools and effects with readings on corresponding questions in philosophical common sense.

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This measure has the advantage of allowing the probability of the conditional to be independent of the probability of the antecedent. On the truth-functional account, the probability that if you toss the coin it lands heads depends crucially on how probable it is that you toss it. Suppose it is much less likely now that you toss the coin than it was a minute ago. The probability of the material implication, which is equivalent to: Either you won't toss it, or (you will and it will land heads) has greatly increased.

Such a person knows enough to reject the claim that B is true on the assumption that A. 'A & -B' is sufficient to refute 'If A, B'. Assumption 2 is false. Putative possibility 2a does not exist. We have shown, then, that if a conditional has truth conditions, they are truth-functional for the two cases in which A is true. We shall now consider the cases in which A is false. Assumption 3: A conditional has truth-conditions which are not truth-functional when A is false and B is true. 45 Do Conditionals Have Truth-Conditions?

So P(B) = P(A) + P(~A & B) '2: P(A). 35 Do Conditionals Have Truth-Conditions? believing L :J N, that is ~ L, that is very likely. FIG. 1 ~L v N, to be slightly more probable than L ~N r-NN ~L ~L ~N vN j To judge it probable that A :J B is to judge it improbable that A & ~B. To judge it probable that if A, B is not only to judge it improbable that A & ~ B, but to judge this to be less probable than A & B. ' (see Figure 2). FIG. 2 A B A&B A&~B That A & ~ B be small, which is necessary and sufficient for the conditional to be probable on the truth-functional account, is necessary but not sufficient on this account.

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