Philosophy Lexicon of Arguments

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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.

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I 174
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 ...").
I 180
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.
I 183
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.
I 184
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.

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.

Gea I
P.T. Geach
Logic Matters Oxford 1972

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Ed. Martin Schulz, access date 2018-05-23