Fixing a hole in the ground of induction

Australasian Journal of Philosophy

Volumn 79, Issue 4, 2001, Pages 553-563

  Campbell, Scott ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751188900     PISSN: 00048402     EISSN: None     Source Type: Journal    
DOI: 10.1080/713659309     Document Type: Article

References (14)

1. D.C. Stove, The Rationality of Induction (Oxford: Clarendon Press, 1986); D.C. Williams, The Ground of Induction (New York: Russell and Russell, 1963; first pub. 1947). All references to Stove and Williams will be, respectively, to these works.
2. Patrick Maher, 'The Hole in the Ground of Induction', Australasian Journal of Philosophy 74 (1996), pp. 423-32. All references to Maher will be to this paper.
3. The subset needs to be large-e.g., 3000. But the subset does not have to be a large percentage of the population-in fact, the population can be as big as you like, as long as it is finite (which all actual populations are).
4. This is all rather roughly put (I shall avoid technicality in this paper), but these matters can be made mathematically precise. The details can be found in Williams.
5. For a recent defence of logical probability, see James Franklin, 'Resurrecting Logical Probability', Erkenntnis, forthcoming, v. 55.
6. Not that the initial unlikeliness of the raven population being mostly black is not raised by our sample being mostly black, says Maher-it is, but only very slightly.
7. Maher doesn't say so, but presumably he thinks his objection sinks notjust this inductive inference, but all, or at least most, of the inductive inferences we make.
8. Essentially the same mistake occurs in the so-called 'lottery paradox', where it is claimed that the a priori unlikelihood of the winning numbers gives you reason to doubt the newspaper report. But of course this improbability is irrelevant, because some numbers were going to be drawn-what matters is therefore how likely it was that the paper would misreport these numbers, whatever they happened to be.
9. It would also involve Maher in an inconsistency, for he would himself accept that 99% was the initial probability
10. After all, we could have said 'Most numbers in Situation B lie between 1 and 99 million, so only the numbers outside that range are a priori unlikely, so 3 468 792 is in fact a priori likely'. Obviously this sort of reasoning allows any number in Situation B to be made a priori likely or unlikely, depending on how you carve things up.
11. Suppose an objector continued to insist that the multi-coloured response defeats my §VI argument against Maher. In that case, consider the coloured dartboard again. Whatever is true of black in regard to a priori probabilities is true of any other colour, yet there is no possible analogue of the multi-coloured response to save Maher here, so his view must be false.
12. What if it is objected that it is a least a possibility that you have ESP, and can know that you will pick out the non-red ball? The problem with this claim is that if there is reason to think that you have ESP, then we are no longer dealing with the a priori probabilities. By definition, we are concerned with the case where we have no reason to suppose that any one ball is any more likely to be drawn than any other.
13. There will of course be other reasons as well for rejecting the occasional sighting, such as that we would expect a few spurious sightings anyway, especially given the understandable fascination that the topic has for many people who live in the area.
14. I would like to thank Jim Franklin and Stephen Hetherington for their very helpful comments, and an anonymous referee for this journal. This paper was started while I was a Visiting Fellow in the Philosophy Programme, School of Advanced Study, University of London, in 1999. Thanks also to the School of Philosophy at the University of New South Wales for assistance in the writing of this paper in 2000.