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This quantity of modern writings, a few formerly unpublished, follows the series of a customary intermediate or upper-level common sense path and permits lecturers to complement their shows of formal equipment and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

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THE TRUTH FUNCTIONAL ACCOUNT There are sixteen possible truth-functions of A and B. Only one is a candidate for giving the truth-conditions of 'If A, B'. Indeed, the following two assumptions are sufficient to prove that if 'If A, B' is truth-functional, it has the standard truth-function (that is, it is equivalent to '~(A & ~B)' and to '~A v B'). e. are not all tautologies. So we may safely speak of the truth-functional account. It is important to recognize that there are powerful arguments in favour of the truth-functional account.

Two statements are contraries when it is logically impossible for them both to be true; subcontraries when it is logically impossible for them both to be false. These definitions of 'contrary' and 'subcontrary' leave it open whether statements which stand in either of these relations to each other are contradictories or not. Finally, two very useful additions to the logician's vocabulary are the phrases 'necessary condition' and 'sufficient condition'. When one statement entails another, the truth of the first is a sufficient condition of the truth of the second, and the truth of the second a necessary condition of the truth of the first.

I complain to John that he has not replied to my letter. He says he did-he posted the reply some weeks ago. I am not sure whether to believe him. ' Our positive account has it that B is certain on the assumption that A, and so does common sense. But by Assumption 3, I should reason like this: 'I didn't receive the letter. Suppose he posted it: then the conditional is true. But suppose he didn't post it: this, together with the fact that I didn't receive it, is not sufficient for the conditional.

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


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