|Entailment: material relationship between statements, unlike the formal implication. I.e. the content of the partial statements is relevant for the truth value of the composed statement. See also conditional, implication paradox._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Entailment: consists in the interpretation - inference: in the underlying natural language - logical consequence/Cresswell: but, of course, there is even in intensional logic the concept of logical consequence and e.g. Montague has made use of it. For example, if p and q are propositional variables, then neither is a logical consequence of the other because it is always possible to attribute truth values to the variables so that p is true in a possible world, but q is not.
VsEntailment: it may be in many interpretations that the set of possible worlds, in which p is true, is entailed in the set of possible worlds, in which q is true. And in all these interpretations, applies: p entails q.
Logic/some authors: thesis: logic is concerned primarily with what is true in all interpretations, not merely in one.
CresswellVs: even if this is true, this cannot apply in an analysis of the natural language. It is also simply not true that logic deals with all interpretations. For example, the logical constants are only interpreted in one way and not in others - it must be ensured that the meaning postulates do not provide an analysis of what it means for an inference to be valid. ((s) Otherwise circular).
HC I 265
Entailment/Ackermann/Hughes/Cresswell: from criticising paradoxes of strict implication: even weakest systems contain them. - This makes it impossible to interpret "strimp" as "follows from" or "follows logically from".
Solution: Entailment: as a calculus of logical continuity - Ackermann: "strict implication" - Belnap, Anderson: Entailment._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984