Theoria 81 (2):143-181 (2015)

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Abstract
A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of analysis is driven by exploiting the Curry–Howard correspondence. In particular, deducibility of identicals is shown to correspond to the computational property of eta expansion, which is essential in the characterization of propositional identity
Keywords logical constants  propositional identity  Curry–Howard correspondence  uniqueness  deducibility of identicals  inferentialism
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DOI 10.1111/theo.12051
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Truth and Other Enigmas.Michael Dummett - 1978 - Cambridge, MA, USA: Harvard University Press.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Elements of Intuitionism.Michael Dummett - 1977 - Oxford University Press.

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