David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 31 (1):1-27 (2002)
The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr( ) ↔ A (understood as the conjunction of Tr( ) → A and A → Tr( )). We also keep the full intersubstitutivity of Tr(>A>)) with A in all contexts, even inside of an →. Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with → as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the →; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary
|Keywords||conditionals law of excluded middle paradoxes truth|
|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
No references found.
Citations of this work BETA
Douglas Patterson (2009). Inconsistency Theories of Semantic Paradox. Philosophy and Phenomenological Research 79 (2):387 - 422.
C. Dutilh Novaes (2008). A Comparative Taxonomy of Medieval and Modern Approaches to Liar Sentences. History and Philosophy of Logic 29 (3):227-261.
Paul �gr� (2005). The Knower Paradox in the Light of Provability Interpretations of Modal Logic. Journal of Logic, Language and Information 14 (1):13-48.
Similar books and articles
Christopher Gauker (2001). T-Schema Deflationism Versus Gödel’s First Incompleteness Theorem. Analysis 61 (270):129–136.
Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.
Hartry H. Field (2008). Saving Truth From Paradox. Oxford University Press.
Lon A. Berk (2004). The Liar, Context and Logical Form. Journal of Logic, Language and Information 13 (3):267-286.
Dale Jacquette (2007). Denying The Liar. Polish Journal of Philosophy 1 (2):91-98.
Noriaki Iwasa (2011). That Truth Exists is More Logical. Think 10 (27):109-112.
R. T. Cook (2012). The T-Schema is Not a Logical Truth. Analysis 72 (2):231-239.
Kevin Scharp (2010). Truth's Saviour? [REVIEW] Philosophical Quarterly 60 (238):183 - 188.
Elia Zardini (2008). Truth and What is Said. Philosophical Perspectives 22 (1):545-574.
Hartry Field (2003). A Revenge-Immune Solution to the Semantic Paradoxes. Journal of Philosophical Logic 32 (2):139-177.
Added to index2009-01-28
Total downloads38 ( #45,980 of 1,102,817 )
Recent downloads (6 months)3 ( #120,475 of 1,102,817 )
How can I increase my downloads?