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 Mathematical Logic for Computer Science: Third Edition
- 2.2 Joy of Logic
- 2.3 Relevance Outside Logic (Circuito Cerrado Remix)
- 2.4 Entailment, Vol. 1: The Logic of Relevance and Necessity
- 2.5 Relevance Outside Logic
- 2.6 Entailment, Vol. 2: The Logic of Relevance and Necessity (Princeton Legacy Library)
- 2.7 Can Man Live Without God
- 2.8 The Concept of Relevance and the Logic Diagram Tradition
- 2.9 The Relevance of Royce (American Philosophy)
- 2.10 Relevance
Videos
Mathematical Logic for Computer Science: Third Edition
- Springer
- Ben-Ari, Mordechai (Author)
- English (Publication Language)
- 361 Pages - 06/17/2012 (Publication Date) - Springer (Publisher)
Joy of Logic
- Amazon Prime Video (Video on Demand)
- Catherine Gale (Director)
- English (Playback Language)
- English (Subtitle)
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)
Can Man Live Without God
- Amazon Kindle Edition
- Zacharias, Ravi (Author)
- English (Publication Language)
- 206 Pages - 08/30/2004 (Publication Date) - Thomas Nelson (Publisher)
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)
The Relevance of Royce (American Philosophy)
- Hardcover Book
- English (Publication Language)
- 340 Pages - 02/03/2014 (Publication Date) - Fordham University Press (Publisher)
Last update 2020-04-06. Price and product availability may change.