David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 17 (1-2):73-83 (1996)
I interpret Mill?s view on logic as the instrumentalist view that logical inferences, complex statements, and logical operators are not necessary for reasoning itself, but are useful only for our remembering and communicating the results of the reasoning. To defend this view, I first show that we can transform all the complex statements in the language of classical first-order logic into what I call material inference rules and reduce logical inferences to inferences which involve only atomic statements and the material inference rules. Then I explain why we introduce logical operators and logical inference rules into a system of the latter kind. In the end I determine what kind of negation is justified from this point of view
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Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Stephen Read (1994). Formal and Material Consequence. Journal of Philosophical Logic 23 (3):247 - 265.
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