Are Uniqueness and Deducibility of Identicals the Same?
Alberto Naibo, Mattia Petrolo · Theoria · 2014
Abstract A comparison is given between two conditions used to define logical constants:Belnap's uniqueness andHacking'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 theCurry–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.