New PDF release: A Philosophical Companion to First-Order Logic

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This quantity of modern writings, a few formerly unpublished, follows the series of a regular intermediate or upper-level common sense direction and permits academics to counterpoint their shows of formal equipment and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

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Additional resources for A Philosophical Companion to First-Order Logic

Example text

It is evident that the purposes which I have said might be served by making a logically necessary statement in the form of a contradictory of an inconsistent statement could be served equally well by making it in the form of a second-order statement of logical appraisal. These would, in fact, be different ways of saying the same thing, or of making the same appraisal. Instead of saying 'He is not both over and under six foot tall', we could say 'The statement that he is over six foot 6. The symbol 'S 1' changes its character.

Some historical background: Robert Stalnaker (1970) was, I believe, the first to suggest that insight into the semantics of conditionals might be gained from the probability theorist's notion of a conditional probability, P(B/A) (the probability of B given A). Judgements about how probable it is that if A, B, seem to coincide with judgements about the 28 Do Conditionals Have Truth-Conditions? 29 the negative result too, but hardly perspicuously. My aim, in trying to extract an intuitively compelling argument from a somewhat baffling piece of algebra, is not only to make this way of thinking about conditionals more widely, and more deeply, appreciated.

It is also, by weakening the assumptions, to provide a stronger proof of the negative result. I hope to render the positive thesis more plausible, too, by presenting it less technically. It should not need emphasis that in the conditional we have an indispensable form of thought, which plays a large part in both theoretical reasoning about what is the case and practical reasoning about what to do. Its basic role may be described thus: we are not omniscient; we do not know as much as it would be useful for us to know.

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


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