By R. I. G. Hughes
This quantity of modern writings, a few formerly unpublished, follows the series of a standard intermediate or upper-level common sense direction and permits academics to counterpoint their displays of formal equipment and effects with readings on corresponding questions in philosophical good judgment.
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Additional resources for A Philosophical Companion to First-Order Logic
If I think it is 50:50 that if you toss this coin, it will land heads, then, whatever the probability that you toss it, the probability that (you toss it and it lands heads) is half as much: the ratio is 1 :2. 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.
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. It depends (say) on whether in the closest possible words in which he did post it, I still didn't receive it. ' Assumption 3, then, is incompatible with our positive account, and once more, intuition vindicates our account.
Putative possibility 3b does not exist. Finally, Assumption 4: Truth-functionality fails when 'Nand 'B' are both false. Now consider someone who is sure that A and B have the same truth-value, but is uncertain which. For example he knows that John 46 Dorothy Edgington and Mary spent yesterday evening together, but doesn't know whether they went to the party. According to our positive account and according to common sense, he knows enough to be sure that if John went to the party (J), Mary did (M).