|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.|
|Geach, Peter T.
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Entailment/Quine/Geach: Quine used "implies" instead of "entails". - Geach: Entailment requires nouns - Quotes are nevertheless noun-similar. - Entailment requires quotes to include sentences. - GeachVsPropositions: "entails": is an artificial word instead you can also use "an if" - example: "A. if Russell is a brother, Russell is male": that avoids looking at partial sentences as a blackening of the paper (letters). - (Otherwise "The proposition that Russell is a Brother ...").
Entailment/Geach: truth conditions: thesis: "p entails q" iff and only if there is an a priori possibility to know that Cpq, which is not to find out whether either p or q is true. - Problem: that implies a possibility that we have: "p" is false and "it is possible to find out that p" is true. - One can know necessary things without facts and without conceptual analysis. - Lewy's First Paradox: Entailment cannot be fully transitive.
Entailment/Lewy's 1. Paradox: Summary: 1. One can know a priori that Cpq without knowing p v q. - 2. one can know a priori that Cqr without knowing p v r. We can conclude from these premises: Conclusion: one can know a priori that Cpr - N.B.: but we cannot add safely: without knowing ("which is not a way to find out") whether p v r. - We have the a priori way of finding out that Cpr, derived from our a priori knowledge that Cpq and that Cqr. - But that does not allow to answer if p, and figure out that Cqr allows not to figure out whether r. - If the truth table provides the same truth values anyway, you cannot speak of a link. There is no reason to believe that we have any knowledge a priori that both Cp(Kpq) and C(Kpq)r, and such that Cpr, with the exception of a priori knowledge, that r. - Therefore, there is no reason to believe p entails r.
Transitivity/Geach: Entailment is not transitive, but validity of evidence is transitive. - FitchVs: Evidence is not transitively valid in order to solve paradoxes of set theory.
Logic Matters Oxford 1972