David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 35 (6):653 - 660 (2006)
Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number of simple observations is made showing that the unwanted phenomenon exemplified by tonk in some logics also occurs in contexts in which tonk is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives
|Keywords||proof-theoretic semantics trivializing connectives|
|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
Arthur Prior (1967). The Runabout Inference Ticket. In Peter Strawson (ed.), Analysis. Oxford University Press 38-9.
N. D. Belnap (1977). A Useful Four-Valued Logic. In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel
Neil Tennant (1987). Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic. Journal of Symbolic Logic 52 (3):665-680.
Stephen Read (1994). Thinking About Logic: An Introduction to the Philosophy of Logic. Oxford University Press.
Roy T. Cook (2005). What's Wrong with Tonk(?). Journal of Philosophical Logic 34 (2):217 - 226.
Citations of this work BETA
David Ripley (2015). Anything Goes. Topoi 34 (1):25-36.
Heinrich Wansing & Yaroslav Shramko (2008). Suszko's Thesis, Inferential Many-Valuedness, and the Notion of a Logical System. Studia Logica 88 (3):405 - 429.
Heinrich Wansing & Yaroslav Shramko (2008). Suszko’s Thesis, Inferential Many-Valuedness, and the Notion of a Logical System. Studia Logica 88 (3):405-429.
Similar books and articles
Lloyd Humberstone (2007). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 36 (5):435 - 487.
James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
Jean-Baptiste Joinet, Harold Schellinx & Lorenzo Tortora de Falco (2002). SN and CR for Free-Style LKtq: Linear Decorations and Simulation of Normalization. Journal of Symbolic Logic 67 (1):162-196.
Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
Xavier Caicedo (2004). Implicit Connectives of Algebraizable Logics. Studia Logica 78 (1-2):155 - 170.
By Neil Tennant (2005). Rule-Circularity and the Justification of Deduction. Philosophical Quarterly 55 (221):625–648.
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
Lloyd Humberstone (2006). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 35 (5):435 - 487.
Added to index2009-01-28
Total downloads32 ( #124,997 of 1,907,142 )
Recent downloads (6 months)1 ( #467,610 of 1,907,142 )
How can I increase my downloads?