David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Philosophical Logic 39 (5):557-76 (2010)
Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions.
|Keywords||Harmony Inferentialism Autonomy Validity Tonk Dummett Gentzen Prawitz Lorenzen|
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References found in this work BETA
Robert Brandom (2000). Articulating Reasons: An Introduction to Inferentialism. Harvard University Press.
Michael A. E. Dummett (1991). The Logical Basis of Metaphysics. Harvard University Press.
Michael A. E. Dummett (1993). The Seas of Language. Oxford University Press.
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Citations of this work BETA
David Ripley (2015). Anything Goes. Topoi 34 (1):25-36.
Alberto Naibo & Mattia Petrolo (2015). Are Uniqueness and Deducibility of Identicals the Same? Theoria 81 (2):143-181.
Allen P. Hazen & Francis Jeffry Pelletier (2014). Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different. Studia Logica 102 (6):1103-1142.
Florian Steinberger (2011). What Harmony Could and Could Not Be. Australasian Journal of Philosophy 89 (4):617 - 639.
Nils Kürbis (2015). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic 44 (6):713-727.
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