In Bob Hale, Crispin Wright & Alexander Miller (eds.), The Blackwell Companion to the Philosophy of Language. Blackwell (forthcoming)

Ian Rumfitt
Oxford University
Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also had an influence on the philosophy of language: some prominent writers in that area, notably Dummett and Robert Brandom, have taken it to be a special case of a more general requirement that the grounds for asserting a statement must cohere with its consequences. This essay considers various ways of making the Harmony Thesis precise and scrutinizes the most influential arguments for it. The verdict is negative: all the extant arguments for the Thesis are weak, and no version of it is remotely plausible.
Keywords Logical connectives  Sequent calculus  Inversion Principle  Proof-theoretic semantics  Proof-theoretic harmony  Dag Prawitz  Michael Dummett  Gerhard Gentzen  Neil Tennant
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Making It Explicit.Isaac Levi & Robert B. Brandom - 1996 - Journal of Philosophy 93 (3):145.
Truth.Michael Dummett - 1959 - Proceedings of the Aristotelian Society 59 (1):141-62.
A Counterexample to Modus Ponens.Vann McGee - 1985 - Journal of Philosophy 82 (9):462-471.
Anti-Realism and Logic: Truth as Eternal.Neil Tennant - 1987 - Oxford, England: Oxford University Press.

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Citations of this work BETA

Classical Harmony and Separability.Julien Murzi - 2020 - Erkenntnis 85 (2):391-415.
Logical Form and the Limits of Thought.Manish Oza - 2020 - Dissertation, University of Toronto

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