Revisiting the Justification of Deduction

Greg Restall (University of Melbourne)

Abstract: In “The Justification of Deduction,” Michael Dummett explores what it might be to give a justification for the rules of inference used in deductive logic. He argues that if we understand these rules of inference as means of transforming warrants, we can see how deductive reasoning is both valid (the conclusion does not go beyond what we are warranted to assert on the basis of the warrant for the premises, and informative (we can nonetheless learn things by way of deductive reasoning).  There is a lot to like in Dummett’s account of deductive logic, but I will argue that there is a serious shortcoming, focussed on the role of warrant in the analysis. I will show that the account of the normatvity of logic couched in terms of the norms governing assertion and denial not only has all the virtues of Dummett's account, it also allows for a much smoother picture of the role of both proofs and counterexamples in drawing the distinction between valid and invalid arguments. (For light relief, these points will be illustrated with examples from the development of logic and mathematics in the 18th and 19th Centuries.)