Inferentialism and the categoricity problem: Reply to Raatikainen

Analysis 69 (3):480-488 (2009)
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It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true that the standard rules of inference" themselves suffice to "determine the meanings of [the] logical constants" (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that "no ordinary formalization of logic ... is sufficient to `fully formalize' all the essential properties of the logical constants" (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists - as proposed by Timothy Smiley and Ian Rumfitt - seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too.



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Author Profiles

Julien Murzi
University of Salzburg
Ole Thomassen Hjortland
University of Bergen

Citations of this work

Logical Consequence.J. C. Beall, Greg Restall & Gil Sagi - 2019 - Stanford Encyclopedia of Philosophy.
Rejection and valuations.Luca Incurvati & Peter Smith - 2010 - Analysis 70 (1):3 - 10.
Classical Harmony and Separability.Julien Murzi - 2020 - Erkenntnis 85 (2):391-415.
Quantifier Variance Dissolved.Suki Finn & Otávio Bueno - 2018 - Royal Institute of Philosophy Supplement 82:289-307.

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1994 - Philosophical Quarterly 44 (177):519-527.
Formalization of logic.Rudolf Carnap - 1943 - Cambridge, Mass.,: Harvard university press.
Yes and no.I. Rumfitt - 2000 - Mind 109 (436):781-823.

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