Comments on Greg Restall & Gillian Russell's “barriers to implication”
| Abstract | I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier the- ses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Con- struction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, I am satisfied with its treatment of the first three topics, namely generality, necessity, and time. But I am not satisfied with its treatment of normativity, so my comments are exclusively on that topic. | |||||||||
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Peter Milne (2008). Russell's Completeness Proof. History and Philosophy of Logic 29 (1):31-62.
Susan Rogerson & Sam Butchart (2002). Naïve Comprehension and Contracting Implications. Studia Logica 71 (1):119-132.
Greg Restall (1996). Truthmakers, Entailment and Necessity. Australasian Journal of Philosophy 74 (2):331 – 340.
M. Campercholi, D. Castaño & J. P. Díaz Varela (2011). Quasivarieties and Congruence Permutability of Łukasiewicz Implication Algebras. Studia Logica 98 (1-2):267-283.
Gabriel Rabin (2007). Full-Blooded Reference. Philosophia Mathematica 15 (3):357--365.
Gillian Russell & Greg Restall (forthcoming). Barriers to Implication. In Charles Pigden (ed.), Hume on Is and Ought. Palgrave MacMillan.
Gillian Russell (2011). Indexicals, Context-Sensitivity and the Failure of Implication. Synthese 183 (2):143-160.
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