Logical abductivism and non-deductive inference
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Logical abductivism and non-deductive inference Graham Priest1,2 Received: 6 June 2020 / Accepted: 20 October 2020 © Springer Nature B.V. 2020
Abstract Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters. Keywords Logical abductivism · Abduction · Induction · Problem of indiction · Logical revision
1 Introduction Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction; and over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. In this paper I discuss the matter, clarifying and examining. A central issue that will appear is that of the circularity involved in using abduction to determine a theory of
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Graham Priest [email protected]
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Departments of Philosophy, The CUNY Graduate Center, New York, USA
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The University of Melbourne, Melbourne, Australia
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Synthese
abduction. As we will see, the issue fragments into a number of different scenarios. Some of them are relatively straightforward, and some of them are not. I shall make comments on the latter ones, but I warn the reader that definitive solutions are not to be found in this paper. The best I can do is put the issues on the table as a prolegomenon to further discussion.
2 Logical abductivism First, let us get some background straight. Logic—for the moment, deductive logic—in one of the many senses of that term, is, as I noted, an account, or theory, about what follows from what and why.1 As anyone who knows a little of the history of Western logic can see, there have been numerous such, very different, theories: those of Aristotle, the Stoics, Abelard, Buridan, Frege, Heyting, to name but a few of many.2 Why was one theory deemed (hopefully, rationally!) preferable to another? More generally, given a bunch of such theori
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