Saving the truth schema from paradox

Journal of Philosophical Logic 31 (1):1-27 (2002)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,351
External links
  •   Try with proxy.
  • Through your library Configure
    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.
    Similar books and articles
    Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.
    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.
    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.
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    35 ( #41,655 of 1,088,389 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,389 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.