Abstract
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.
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Notes
See Goodman (1983, ch. III).
Or any other unnatural predicate for that matter.
See Lipton (2004, Chapter 4).
The equivalent of explaining why all the balls in the pot are black, or why all ravens are black.
Let me emphasise that this is not to say that I agree with Armstrong in thinking e → h is always an irrational pattern of inference. I believe that inductive reasoning is, when performed in the right way, perfectly rational. The conclusion h can follow from e, not by deductive logic, but by whatever inductive logic will turn out to be.
Analysis Vol. 51 No. 4 (1991, pp. 206–208).
Importantly, ‘random’ in this sense must mean that every one of these logically possible samples must have an equal probability of being drawn.
Note that a 50/50 proportion will give the lowest probability of a representative sample. A population of 100% ravens will of course give a 100% chance of a representative sample.
This tells us that if we know the number of Xs that are Ys in a population of Xs (where we know the size of the population), then our epistemic probability of a random X being a Y is the number of Xs that are Ys divided by the population size. If 60% of professors are men, our degree of belief that an unknown professor (of whom we have no further information) will be a man should be 0.6.
Assuming an equal probability of choosing any possible sample.
Again, this is on the assumption that there is an equal probability of drawing each of the logically possible samples. This is an assumption I will attempt to justify in Sect. 4.
It has been argued that infinite populations are problematic, but these will not be addressed as there are far stronger objections than this.
Though the Humean questions this idea of ‘ensuring uniformity’. A uniformity just (tenselessly) is the case or is not. There is no question of keeping nature on the rails.
Subsequent subjectivists have substituted this monetary assessment for bets of utility, on the grounds that the value of money differs from the rich to the poor.
See Campbell and Franklin (2004) for a more detailed discussion of this issue.
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Acknowledgments
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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Smart, B.T.H. Is the Humean defeated by induction?. Philos Stud 162, 319–332 (2013). https://doi.org/10.1007/s11098-011-9767-5
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DOI: https://doi.org/10.1007/s11098-011-9767-5