Download e-book for iPad: A Philosophical Companion to First-Order Logic by R. I. G. Hughes

By R. I. G. Hughes

ISBN-10: 0872201821

ISBN-13: 9780872201828

This quantity of modern writings, a few formerly unpublished, follows the series of a standard intermediate or upper-level good judgment direction and permits lecturers to counterpoint their shows of formal equipment and effects with readings on corresponding questions in philosophical common sense.

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Answer: very unlikely. On the other hand, he is committed to 5. The principle is provable in probability theory: writing ,_, for logical equivalence, B - (A & B) v (~A & B). So P(B) = P(A & B) + P( ~A & B). If A entails B, A- A & B. 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.

THE POSITIVE ACCOUNT CONTINUED I outlined my positive account of belief in a conditional in Sect. 3. In considering how likely it is that if A, B, one assumes A, that is, ignores the possibility that ~A. Relative to that assumption, one . considers how likely it is that B (see Figure 2). This yields the following criterion: X believes that Gudges it likely that) if A, B, to the extent that he judges that A & B is nearly as likely as A or, roughly equivalently, to the extent that he judges A & B to be more likely than A & -B.

I conclude, therefore, that the mistake philosophers have made, in trying to understand the conditional, is to assume that its function is to make a statement about how the world is (or how other possible worlds are related to it), true or false, as the case may be. Along the way (Sects. 3 and 5) I develop a positive account of what it is to believe, or to be more or less confident, that if A, B, in terms of which an adequate logic of conditionals can be developed. The argument against truth-conditions is independent of this positive account of the conditional, as I show that any truthconditional account has counterintuitive consequences, as well as clashing with my positive thesis.

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

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