Logic as instrument: the millian view on the role of logic

History and Philosophy of Logic 17 (1-2):73-83 (1996)
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Abstract

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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Ken Akiba
Virginia Commonwealth University

Citations of this work

The Metaphysical Commitments of Logic.Thomas Brouwer - 2013 - Dissertation, University of Leeds

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Conditionals.Frank Jackson (ed.) - 1991 - New York: Oxford University Press.
Truth by Convention.W. V. Quine - 1936 - In Philosophical Essays for Alfred North Whitehead. London: Longmans, Green & Co.. pp. 90–124.

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