Tonk Strikes Back∗

Australasian Journal of Logic 3:33-44 (2005)
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Abstract

What is a logical constant? In which terms should we characterize the meaning of logical words like “and”, “or”, “implies”? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Prior’s fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative answer to Belnap’s requirement of conservatity in terms of a local requirement on double line rules.

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Denis Bonnay
Université Paris Nanterre

Citations of this work

Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
Intuitive and reflective inferences.Hugo Mercier & Dan Sperber - 2009 - In Keith Frankish & Jonathan St B. T. Evans (eds.), In Two Minds: Dual Processes and Beyond. Oxford University Press. pp. 149--170.
Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.

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