Connectives stranger than tonk

Journal of Philosophical Logic 35 (6):653 - 660 (2006)
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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



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Heinrich Wansing
Ruhr-Universität Bochum

Citations of this work

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.
.Luca Incurvati & Julian J. Schlöder - 2023 - New York: Oxford University Press USA.

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References found in this work

A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
The runabout inference ticket.Arthur Prior - 1967 - In P. F. Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.

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