Is logic empirical? Is logic to be found in the world? Or is logic rather a convention, a product of conventions, part of the many rules that regulate the language game? Answers fall in either camp. We like the linguistic answer. In this paper, we want to analyze how a linguistic community would tackle the problem of developing a logic and show how the linguistic conventions adopted by the community determine the properties of the local logic. Then show how to move from a notion of logic that varies from community to community to a notion of logic that is in a sense universal. The framework is conventional up to a point: we have sentences, atomic and composite, the connectives are interpreted, values are computed, and the value of a composite sentence is a function of the values of its subsentences. Less conventional is the use of a plurality of truth values, and the sharp distinction we draw between sentences and statements, in the spirit of the distinction between proposition and judgment that one may find in proof theory. The linguistic community will face many choices. What are the good ones, the ones to avoid? Are there, in some sense, optimal choices? These are the kind of issues we are addressing. Where do we end up? With some kind of universal bivalent logic, ironically enough. We start from an arbitrarily large number of truth values, atomic sentences and connectives, construct a generic many-valued logic, recover more or less the usual results and issues, and in the end it all comes down to a positive bivalent logic with two connectives, `and' and `or', as if logic is nothing more than a mere accounting of possibilities.
Keywords many-valued logic  satisfiability  Galois connection  Bivalence  AI  Cognitive agent  truth  Logical connectives  Logic and information
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

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

Carnap and Logical Truth.Willard van Orman Quine - 1960 - Synthese 12 (4):350--74.
Logical Consequence.Patricia Blanchette - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. pp. 2001--115.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Completeness and Super-Valuations.Gary M. Hardegree - 2005 - Journal of Philosophical Logic 34 (1):81 - 95.
Entailment and Bivalence.Fred Seymour Michael - 2002 - Journal of Philosophical Logic 31 (4):289-300.
Propositional Logic.Kevin C. Klement - 2004 - Internet Encyclopedia of Philosophy.
Many-Valued Logics.Nicholas J. J. Smith - 2012 - In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge. pp. 636--51.
Classical Logic and Truth-Value Gaps.Philip Hugly & Charles Sayward - 1992 - Philosophical Papers 21 (2):141-150.
First-Order Fuzzy Logic.Vilém Novák - 1987 - Studia Logica 46 (1):87 - 109.
Three-Valued Logics in Modal Logic.Barteld Kooi & Allard Tamminga - 2013 - Studia Logica 101 (5):1061-1072.
How to Avoid Deviance (in Logic).Walter Sinnott-Armstrong & Amit Malhotra - 2002 - History and Philosophy of Logic 23 (3):215--36.


Added to PP index

Total views
270 ( #39,335 of 2,499,277 )

Recent downloads (6 months)
18 ( #46,498 of 2,499,277 )

How can I increase my downloads?


My notes