David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 88 (2):263 - 294 (2008)
The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered
|Keywords||Philosophy Computational Linguistics Mathematical Logic and Foundations Logic|
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References found in this work BETA
Robert B. Brandom (1994). Making It Explicit: Reasoning, Representing, and Discursive Commitment. Harvard University Press.
Robert Brandom (2000). Articulating Reasons: An Introduction to Inferentialism. Harvard University Press.
Bertrand Russell (2005). On Denoting. Mind 114 (456):873 - 887.
Michael A. E. Dummett (1991). The Logical Basis of Metaphysics. Harvard University Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Citations of this work BETA
Allen P. Hazen & Francis Jeffry Pelletier (2014). Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different. Studia Logica 102 (6):1103-1142.
Jaroslav Peregrin (2015). Logic Reduced To Bare Bones. Journal of Logic, Language and Information 24 (2):193-209.
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