The consequence relation of tautological entailment is maximally relevant: Answering a question of Graham Priest
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Graham Priest has asked whether the consequence relation associated with the Anderson–Belnap system of Tautological Entailment,1 in the language with connectives ¬, ∧, ∨, and countably many propositional variables as tomic formulas, maximal amongst the substitution-invariant relevant consequence relations on this language. Here a consequence relation is said to be relevant just in case whenever for a set of formulas Γ and formula B, we have Γ B only if some propositional variable occurring in B occurs in at least one formula in Γ. (It follows that relevant consequence relations are atheorematic in the sense that whenever Γ B for some such consequence relation , Γ = ∅.) Here I write up in more detail the upshot of the conversation – returning an aﬃrmative answer to Priest’s question – about this in the common room that Greg Restall and I were participating in last Friday [ = October 6, 2006], dotting some “i”s and crossing some “t”s (and adding the odd further reﬂection).
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Philip Kremer & Michael Kremer (2003). Some Supervaluation-Based Consequence Relations. Journal of Philosophical Logic 32 (3):225-244.
Beata Konikowska (1990). A Two-Valued Logic for Reasoning About Different Types of Consequence in Kleene's Three-Valued Logic. Studia Logica 49 (4):541 - 555.
Luca Moretti (2003). Why the Converse Consequence Condition Cannot Be Accepted. Analysis 63 (4):297–300.
Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
I. L. Humberstone (1993). Functional Dependencies, Supervenience, and Consequence Relations. Journal of Logic, Language and Information 2 (4):309-336.
Matthew W. McKeon (2010). The Concept of Logical Consequence: An Introduction to Philosophical Logic. Peter Lang Pub..
Dag Westerståhl (2012). From Constants to Consequence, and Back. Synthese 187 (3):957-971.
Daniel N. Osherson & Scott Weinstein (1993). Relevant Consequence and Empirical Inquiry. Journal of Philosophical Logic 22 (4):437 - 448.
Added to index2009-01-28
Total downloads4 ( #251,104 of 1,098,129 )
Recent downloads (6 months)0
How can I increase my downloads?