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LPL 4.1 lecture - Tautologies and logical truth From our...

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Tautologies and logical truth From our discussion of logical consequence, we know that a sentence is a logical consequence of a given set of premises if it is impossible for the conclusion to be false when the premises are true. As we will see, some sentences will turn out to be logical consequences of any set of premises, or of no premises at all. In other words, some sentences will be true regardless of what premises are given, even if no premises are given. Such sentences are said to be logical truths because there are no circumstances in which they could possibly be false. a = a logical possibility vs. logical necessity A sentence is logically possible if, under some set of circumstances, it could be true on purely logical grounds . While physical laws may prevent certain sentences from being true, such limitations have no bearing upon the notion of logical possibility. However, some sentences are not even logically possible. In such cases, the rules of logic prevent a sentence from being true under any circumstances. Such sentences are
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