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The Material Theory of Induction at the Frontiers of Science

Published online by Cambridge University Press:  06 July 2020

William Peden Open the ORCID record for William Peden [Opens in a new window]
William Peden*
Affiliation:
Università Politecnica delle Marche, Italy
*
Email: w.j.peden@durham.ac.uk
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Abstract

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such an absence of circumstances ‘the frontiers of science', where background scientific theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science.

Keywords

Inductionthe Material Theory of InductionJohn Nortonstatistical reasoningscientific reasoning
Type
Article
Information
Episteme , Volume 19 , Issue 2 , June 2022 , pp. 247 - 263
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Achinstein, P. (2010). ‘Norton's “Intractable Problem of Induction”.’ In Morgan, G.J. (ed.), Philosophy of Science Matters: The Philosophy of Peter Achinstein, pp. 284–5. Oxford: Oxford University Press.Google Scholar
Campbell, S. (2001). ‘Fixing a Hole in the Ground of Induction.’ Australasian Journal of Philosophy 79, 553–63.CrossRefGoogle Scholar
Campbell, S. and Franklin, J. (2004). ‘Randomness and the Justification of Induction.’ Synthese 138, 79–99.CrossRefGoogle Scholar
Craig, R.V. and Hogg, A.T. (1965). Introduction to Mathematical Statistics. New York, NY: The Macmillan Company.Google Scholar
Cunningham, C.J. (2017). Bode's Law and the Discovery of Juno: Historical Studies in Asteroid Research. Cham: Springer.CrossRefGoogle Scholar
Dawid, R. (2015). ‘Turning Norton's Dome Against Material Induction.’ Foundations of Physics 45, 1101–9.CrossRefGoogle Scholar
Descartes, R. (1952). Descartes’ Philosophical Writings (ed. and trans. Kemp Smith, N.). London: Macmillan.Google Scholar
Ducheyne, S. (2008). ‘Some Worries for Norton's Theory of Induction.’ Philosophia Naturalis 45, 37–46.CrossRefGoogle Scholar
Goodman, N. (1954). Fact, Fiction, and Forecast. Cambridge, MA: Harvard University Press.Google Scholar
Indurkhya, B. (1990). ‘Some Remarks on the Rationality of Induction.’ Synthese 85, 95–114.CrossRefGoogle Scholar
Jackson, A. (2019). ‘How to Solve Hume's Problem of Induction.’ Episteme 16, 157–74.CrossRefGoogle Scholar
Kelly, T. (2010). ‘Hume, Norton, and Induction without Rules.’ Philosophy of Science 77, 754–64.CrossRefGoogle Scholar
Kyburg, H.E. (1956). ‘The Justification of Induction.’ Journal of Philosophy 53, 394–400.CrossRefGoogle Scholar
Lange, M. (2002). ‘Okasha on Inductive Scepticism.’ Philosophical Quarterly 52, 226–32.CrossRefGoogle Scholar
Lange, M. (2011). ‘Hume and the Problem of Induction.’ In Gabbay, D., Hartmann, S. and Woods, J. (eds), Handbook of the History of Logic, Volume 10: Inductive Logic, pp. 43–91. Amsterdam: Elsevier.Google Scholar
Leavitt, H.S. and Pickering, E.C. (1912). ‘Periods of 25 Variable Stars in the Small Magellanic Cloud.’ Harvard College Observatory Circular 173, 1–3.Google Scholar
Maher, P. (1996). ‘The Hole in the Ground of Induction.’ Australasian Journal of Philosophy 74, 423–32.CrossRefGoogle Scholar
Nieto, M.M. (1972). The Titius–Bode Law of Planetary Distances: Its History and Theory. Oxford: Pergamon Press.Google Scholar
Norton, J.D. (2003). ‘A Material Theory of Induction.’ Philosophy of Science 70, 647–70.CrossRefGoogle Scholar
Norton, J.D. (2006). ‘How the Formal Equivalence of Grue and Green Defeats What is New in the New Riddle of Induction.’ Synthese 150, 185–207.CrossRefGoogle Scholar
Norton, J.D. (2007). ‘Probability Disassembled.’ British Journal for the Philosophy of Science 58, 141–71.CrossRefGoogle Scholar
Norton, J.D. (2010). ‘Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist.’ In Morgan, G.J. (ed.), Philosophy of Science Matters: The Philosophy of Peter Achinstein, pp. 284–5. Oxford: Oxford University Press.Google Scholar
Norton, J.D. (2011). ‘Challenges to Bayesian Confirmation Theory.’ In Bandyopadhyay, P.S. and Forster, M.R. (eds), Philosophy of Statistics, pp. 391–440. Oxford: Elsevier B.V.CrossRefGoogle Scholar
Norton, J.D. (2014). ‘A Material Dissolution of the Problem of Induction.’ Synthese 191, 671–90.CrossRefGoogle Scholar
Okasha, S. (2001). ‘What Did Hume Really Show about Induction?’ Philosophical Quarterly 51, 307–27.CrossRefGoogle Scholar
Okasha, S. (2005). ‘Does Hume's Argument Against Induction Rest on a Quantifier-shift Fallacy?’ Proceedings of the Aristotelian Society 105, 237–55.CrossRefGoogle Scholar
Peden, W. (2019). ‘Direct Inference in the Material Theory of Induction.’ Philosophy of Science 86, 672–95.CrossRefGoogle Scholar
Pollock, J.L. (1983). ‘Epistemology and Probability.’ Synthese 55, 231–52.CrossRefGoogle Scholar
Pollock, J.L. (1990). Nomic Probability and the Foundations of Induction. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Reichenbach, H. (1949). The Theory of Probability. Berkeley, CA: University of California Press.Google Scholar
Ross, W.D. (1930). The Right and the Good. Oxford: Clarendon Press.Google Scholar
Russell, B. (1912). The Problems of Philosophy. London: Williams and Norgate.Google Scholar
Saatsi, J. (2010). ‘Form-Driven vs. Content-Driven Arguments for Realism.’ In Magnus, P.D. and Busch, J. (eds), New Waves in Philosophy of Science, pp. 8–28. London: Palgrave-Macmillan.CrossRefGoogle Scholar
Smart, B.T. (2013). ‘Is the Humean Defeated by Induction?’ Philosophical Studies 162, 319–32.CrossRefGoogle Scholar
Steel, D. (2010). ‘What if the Principle of Induction is Normative? Formal Learning Theory and Hume's Problem.’ International Studies in the Philosophy of Science 24, 171–85.CrossRefGoogle Scholar
Stove, D.C. (1986). The Rationality of Induction. Oxford: Oxford University Press.Google Scholar
Whately, R. (1855). Elements of Logic. Boston, MA: James Monroe and Company.Google Scholar
Williams, D.C. (1947). The Ground of Induction. New York, NY: Russell & Russell.CrossRefGoogle Scholar
Worrall, J. (2010). ‘For Universal Rules, Against Induction.’ Philosophy of Science 77, 740–53.CrossRefGoogle Scholar