Philosophical Studies

, Volume 162, Issue 2, pp 319–332 | Cite as

Is the Humean defeated by induction?

  • Benjamin T. H. Smart


Many necessitarians about cause and law (Armstrong, What is a law of nature. Cambridge University Press, Cambridge, 1983; Mumford, Laws in nature. Routledge Studies in Twentieth-Century Philosophy. Routledge, Abingdon, 2004; Bird, Nature’s metaphysics: Laws and properties. Oxford University Press, Oxford, 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a Humean attempt at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong.


Humeanism Regularity theory Laws of nature Problem of induction Explanation Hume Armstrong Law of large numbers 



I would like to thank Stephen Barker, Penelope Mackie, Matthew Tugby, and an anonymous referee for their extensive comments. My thanks also to The Bosdet Foundation, The Strasser Foundation, and The States of Jersey’s Department of Education, Sport and Culture.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of NottinghamNottinghamUK

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