Paradoxes and Failures of Cut

Australasian Journal of Philosophy 91 (1):139 - 164 (2013)
Abstract
This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning?one which takes meaning to be constituted by assertibility and deniability conditions?and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system?ST?that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to
Keywords No keywords specified (fix it)
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
    Michael Dummett (1976). What is a Theory of Meaning? (II). In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.

    View all 20 references

    Citations of this work BETA
    Lionel Shapiro (2013). Validity Curry Strengthened. Thought: A Journal of Philosophy 2 (1):100-107.
    Similar books and articles
    Leon Horsten (2006). Axiomatizing Kripke's Theory of Truth. Journal of Symbolic Logic 71 (2):677 - 712.
    Hartry Field (2002). Saving the Truth Schema From Paradox. Journal of Philosophical Logic 31 (1):1-27.
    Elia Zardini (2008). A Model of Tolerance. Studia Logica 90 (3):337 - 368.
    Wenfang Wang (2011). Against Classical Dialetheism. Frontiers of Philosophy in China 6 (3):492-500.
    Analytics

    Monthly downloads

    Added to index

    2012-01-07

    Total downloads

    29 ( #50,772 of 1,088,372 )

    Recent downloads (6 months)

    1 ( #69,449 of 1,088,372 )

    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.