David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Analysis 69 (3):480-488 (2009)
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.
|Keywords||Categoricity Problem Logical inferentialism Bilateralism Fundamental Assumption Intuitionism External negation|
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References found in this work BETA
I. Rumfitt (2000). Yes and No. Mind 109 (436):781-823.
Dag Prawitz (2006). Meaning Approached Via Proofs. Synthese 148 (3):507 - 524.
Lloyd Humberstone (2000). The Revival of Rejective Negation. Journal of Philosophical Logic 29 (4):331-381.
Kent Bendall (1979). Negation as a Sign of Negative Judgment. Notre Dame Journal of Formal Logic 20 (1):68-76.
Citations of this work BETA
Luca Incurvati & Peter Smith (2010). Rejection and Valuations. Analysis 70 (1):3 - 10.
Denis Bonnay & Dag Westerståhl (2016). Compositionality Solves Carnap’s Problem. Erkenntnis 81 (4):721-739.
Jaroslav Peregrin (2010). Inferentializing Semantics. Journal of Philosophical Logic 39 (3):255 - 274.
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