David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Logica Universalis 4 (1):67-135 (2010)
What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains.
|Keywords||Alan Ross Anderson Nuel D. Balnap Gottlop Frege Bertrand Russell Ludwig Wittgenstein W. V. O. Quine Aristotle Charles Sanders Peirce relevance/relevant logic entailment logic diagrams modus ponens (ponendum) disjunctive syllogism truth tables truth-grounds Venn diagrams|
|Categories||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
Panayot Butchvarov (1970). The Concept of Knowledge. Evanston,Northwestern University Press.
Gottlob Frege (1991). Posthumous Writings. Wiley-Blackwell.
Martin Gardner (1958/1968). Logic Machines, Diagrams and Boolean Algebra. New York, Dover Publications.
Stephen Gaukroger (1989). Cartesian Logic: An Essay on Descartes's Conception of Inference. Clarendon Press.
Citations of this work BETA
No citations found.
Similar books and articles
Luca Viganò (2000). An o(N Log N)-Space Decision Procedure for the Relevance Logic B+. Studia Logica 66 (3):385-407.
Stephen Read (2006). Monism: The One True Logic. In D. de Vidi & T. Kenyon (eds.), A Logical Approach to Philosophy: Essays in Memory of Graham Solomon. Springer.
Yao-Hua Tan (1997). Is Default Logic a Reinvention of Inductive-Statistical Reasoning? Synthese 110 (3):357-379.
C. J. Nix & J. B. Paris (2006). A Continuum of Inductive Methods Arising From a Generalized Principle of Instantial Relevance. Journal of Philosophical Logic 35 (1):83 - 115.
C. Kenneth Waters (1987). Relevance Logic Brings Hope to Hypothetico-Deductivism. Philosophy of Science 54 (3):453-464.
James P. Delgrande & Francis Jeffry Pelletier (1998). A Formal Analysis of Relevance. Erkenntnis 49 (2):137-173.
J. J. Moreso (1996). On Relevance and Justification of Legal Decisions. Erkenntnis 44 (1):73 - 100.
Added to index2010-03-13
Total downloads21 ( #81,620 of 1,101,573 )
Recent downloads (6 months)3 ( #117,010 of 1,101,573 )
How can I increase my downloads?