Logical systems based on the principle that logical consequence, or entailment, only holds between propositions which are relevant to each other.
They were developed, notably by Alan Ross Anderson and Nuel D Belnap (1920- ), as a reaction to the claim of Clarence Irving Lewis and Cooper H. Langford (in Symbolic Logic (1932), chapter 8) that logical entailment is the same as strict implication, where this is defined so that (where P and Q are propositions) P strictly implies Q if and only if it is logically impossible (that is to say a contradiction) for P to be true and Q false.
A contradiction therefore strictly implies any proposition, and any proposition strictly implies a logical truth. These so-called paradoxes of strict implication seem counterintuitive, and relevance logics restrict entailment to apply more narrowly than strict implication. The need to do this, however, is disputed.
Also see: connexive implication, paraconsistency
Source:
J Bennett, ‘Entailment’, Philosophical Review (1968); general survey, questioning need for relevance logics
Table of Contents
- 1 Videos
- 2 Related Products
- 2.1 Entailment, Vol. 1: The Logic of Relevance and Necessity
- 2.2 Entailment, Vol. 2: The Logic of Relevance and Necessity (Princeton Legacy Library)
- 2.3 Joy of Logic
- 2.4 Relevance Outside Logic (Circuito Cerrado Remix)
- 2.5 The Structural-Anarchism Manifesto: (The Logic of Structural-Anarchism Versus The Logic of Capitalism)
- 2.6 The Concept of Relevance and the Logic Diagram Tradition
- 2.7 Relevance Outside Logic
- 2.8 Patient Safety: The Relevance of Logic in Medical Care (Studies in Medical Philosophy)
- 2.9 Larisa Maksimova on Implication, Interpolation, and Definability (Outstanding Contributions to Logic)
- 2.10 Relevance
Videos
Entailment, Vol. 1: The Logic of Relevance and Necessity
- Hardcover Book
- Alan Ross Anderson (Author)
- English (Publication Language)
- 578 Pages - 01/21/1976 (Publication Date) - Princeton University Press (Publisher)
Entailment, Vol. 2: The Logic of Relevance and Necessity (Princeton Legacy Library)
- Used Book in Good Condition
- Hardcover Book
- Anderson, Alan Ross (Author)
- English (Publication Language)
- 787 Pages - 04/06/1992 (Publication Date) - Princeton University Press (Publisher)
Joy of Logic
- Amazon Prime Video (Video on Demand)
- Catherine Gale (Director)
- English (Playback Language)
- English (Subtitle)
The Structural-Anarchism Manifesto: (The Logic of Structural-Anarchism Versus The Logic of Capitalism)
- Amazon Kindle Edition
- Bellemare, Michel Luc (Author)
- English (Publication Language)
- 01/20/2019 (Publication Date)
The Concept of Relevance and the Logic Diagram Tradition
- Used Book in Good Condition
- Dejnožka, Jan (Author)
- English (Publication Language)
- 170 Pages - 07/31/2012 (Publication Date) - CreateSpace Independent Publishing Platform (Publisher)
Patient Safety: The Relevance of Logic in Medical Care (Studies in Medical Philosophy)
- Gungov, Alexander L. (Author)
- English (Publication Language)
- 120 Pages - 10/30/2018 (Publication Date) - ibidem Press (Publisher)
Larisa Maksimova on Implication, Interpolation, and Definability (Outstanding Contributions to Logic)
- Hardcover Book
- English (Publication Language)
- 371 Pages - 02/01/2018 (Publication Date) - Springer (Publisher)
Last update 2020-06-17. Price and product availability may change.