Classically, an argument A therefore B is ‘valid’ (or A is said to ‘entail’ B) if and only if (iff) each situation (model) is such that either A is false or B is true. This fits well with so-called ‘tableau’ methods for showing that A entails B by working out the mutual inconsistency of A and ~B. But both the classical notion of validity and the corresponding tableau methods allow that A may entail B because of some feature of A alone, irrespective of B, and vice versa. Thus if A is a contradiction, then each situation is such that A is false, and so a fortiori is such that A is false or B is true. And if A is a contradiction, then a tableau construction will show that A is inconsistent, and so a fortiori that A and ~B are inconsistent. Of course, the same points can be made dually when B is a logical truth.
CITATION STYLE
Dunn, J. M. (2019). Intuitive Semantics for First-Degree Entailment and ‘Coupled Trees.’ In Synthese Library (Vol. 418, pp. 21–34). Springer Science and Business Media B.V. https://doi.org/10.1007/978-3-030-31136-0_3
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