Tonk Strikes Back
Australasian Journal of Logic 3:33-44 (2005)
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.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.Author's Profile
DOI
10.26686/ajl.v3i0.1771
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Citations of this work
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.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
Logicality, Double-Line Rules, and Modalities.Norbert Gratzl & Eugenio Orlandelli - 2019 - Studia Logica 107 (1):85-107.
Double-line Harmony in a Sequent Setting.Gratzl Norbert & Orlandelli Eugenio - 2017 - In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016.