Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-12T20:49:15.540Z Has data issue: false hasContentIssue false

THE META-INDUCTIVE JUSTIFICATION OF INDUCTION

Published online by Cambridge University Press:  07 February 2019

Abstract

I evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that rests on results from the machine learning branch of prediction with expert advice.

My conclusion is that the argument, suitably explicated, comes remarkably close to its grand aim: an actual justification of induction. This finding, however, is subject to two main qualifications, and still disregards one important challenge.

The first qualification concerns the empirical success of induction. Even though, I argue, Schurz's argument does not need to spell out what inductive method actually consists in, it does need to postulate that there is something like the inductive or scientific prediction strategy that has so far been significantly more successful than alternative approaches. The second qualification concerns the difference between having a justification for inductive method and for sticking with induction for now. Schurz's argument can only provide the latter. Finally, the remaining challenge concerns the pool of alternative strategies, and the relevant notion of a meta-inductivist's optimality that features in the analytic step of Schurz's argument. Building on the work done here, I will argue in a follow-up paper that the argument needs a stronger dynamic notion of a meta-inductivist's optimality.

Type
Articles
Copyright
Copyright © Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arnold, E. 2010. ‘Can the Best-alternative Justification solve Hume's problem? On the Limits of a Promising Approach.’ Philosophy of Science, 77(4): 584–93.CrossRefGoogle Scholar
Carnap, R. 1947. ‘On the Application of Inductive Logic.’ Philosophy and Phenomenological Research, 8(1): 133–48.CrossRefGoogle Scholar
Cesa-Bianchi, N. and Lugosi, G. 2006. Prediction, Learning and Games. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Cesa-Bianchi, N., Freund, Y., Haussler, D., Helmbold, D. P., Schapire, R. E. and Warmuth, M. K. 1997. ‘How to use Expert Advice.’ Journal of the ACM, 44(3): 427485.CrossRefGoogle Scholar
Dawid, A. P. 1984. ‘Present Position and Potential Developments: Some Personal Views. Statistical Theory: The Prequential Approach.’ Journal of the Royal Statistical Society A, 147: 278–92.CrossRefGoogle Scholar
De Rooij, S., Van Erven, T., Grünwald, P. D. and Koolen, W. M. 2014. ‘Follow the Leader if you Can, Hedge if you Must.’ Journal of Machine Learning Research, 15: 1281–316.Google Scholar
Dietrich, F. and List, C. 2016. ‘Probabilistic Opinion Pooling.’ In Hájek, A. and Hitchcock, C. (eds), The Oxford Handbook of Probability and Philosophy, pp. 519–41. Oxford: Oxford University Press.Google Scholar
Feigl, H. 1950. ‘De Principiis non Disputandum … ? On the Meaning and the Limits of Justification.’ In Black, M. (ed.), Philosophical Analysis, pp. 119156. New York, NY: Cornell University Press.Google Scholar
Freund, Y. and Schapire, R. E. 1997. ‘A Decision-theoretic Generalization of On-line Learning and an Application to Boosting.’ Journal of Computer and System Sciences, 55: 119–39.CrossRefGoogle Scholar
Goodman, N. 1947. ‘On Infirmities of Confirmation-theory.’ Philosophy and Phenomenological Research, 8(1): 149–51.CrossRefGoogle Scholar
Goodman, N. 1954. ‘Fact, Fiction, and Forecast.’ London: The Athlone Press.Google Scholar
Grünwald, P. D. 2007. The Minimum Description Length Principle. MIT Series in Adaptive Computation and Machine Learning. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Herz, P. 1936. ‘Kritische Bemerkungen zu Reichenbachs Behandlung des Humeschen Problems.’ Erkenntnis, 6: 2531.CrossRefGoogle Scholar
Lipton, P. 2004. Inference to the Best Explanation, 2nd edition. London: Routledge.Google Scholar
Littlestone, N. and Warmuth, M. K. 1994. ‘The Weighted Majority Algorithm.’ Information and Computation, 108: 212–61.CrossRefGoogle Scholar
Putnam, H. 1983. ‘Foreword to the Fourth Edition.’ In Goodman, N. (ed.), Fact, Fiction, and Forecast, 4th edition. Cambridge, MA: Harvard University Press.Google Scholar
Reichenbach, H. 1933. ‘Die Logischen Grundlagen des Wahrscheinlichkeitsbegriffs.’ Erkenntnis, 3: 401–25.CrossRefGoogle Scholar
Reichenbach, H. 1935. Wahrscheinlichkeitslehre: eine Untersuchung Über die Logischen und Mathematischen Grundlagen der Wahrscheinlichkeitsrechnung. Leiden: Sijthoff.Google Scholar
Reichenbach, H. 1938. Experience and Prediction. Chicago, IL: University of Chicago Press.Google Scholar
Salmon, W. C. 1957. ‘The Predictive Inference.’ Philosophy of Science, 24(2): 180–90.CrossRefGoogle Scholar
Salmon, W. C. 1967. The Foundations of Scientific Inference. Pittsburgh, PA: University of Pittsburgh.CrossRefGoogle Scholar
Schurz, G. 2004. ‘Der Metainduktivist: Ein spieltheoretischer Zugang zum Induktionsproblem.’ In Bluhm, R. and Nimtz, C. (eds), Selected Papers Contributed to the Sections of GAP.5, Fünfter Internationaler Kongress der Gesellschaft für Analytische Philosophie, Bielefeld, 22–26 September 2003, pp. 243–57. Paderborn: Mentis Verlag.Google Scholar
Schurz, G. 2008. ‘The Meta-inductivist's Winning Strategy in the Prediction Game: A New Approach to Hume's Problem.’ Philosophy of Science, 75(3): 278305.CrossRefGoogle Scholar
Schurz, G. 2009. ‘Meta-induction and Social Epistemology: Computer Simulations of Prediction Games.’ Episteme, 6(2): 200–20.CrossRefGoogle Scholar
Schurz, G. 2017. ‘No Free Lunch Theorem, Inductive Skepticism, and the Optimality of Meta-induction.’ Philosophy of Science, 84(4): 825–39.CrossRefGoogle Scholar
Schurz, G. 2018. ‘Optimality Justifications: New Foundations for Foundation-oriented Epistemology.’ Synthese, 195(9): 3877–97.CrossRefGoogle Scholar
Schurz, G. Ms. ‘Hume's Problem Solved: The Optimality of Meta-Induction.’ Manuscript in preparation.Google Scholar
Schurz, G. and Thorn, P. D. 2016. ‘The Revenge of Ecological Rationality: Strategy-selection by Meta-induction Within Changing Environments.’ Minds and Machines, 26(1–2): 3159.CrossRefGoogle Scholar
Sellars, W. 1964. ‘Induction as Vindication.’ Philosophy of Science, 31(3): 197231.CrossRefGoogle Scholar
Shalev-Shwartz, S. and Ben-David, S. 2014. Understanding Machine Learning: From Theory to Algorithms. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Skyrms, B. 1965. ‘On Failing to Vindicate Induction.’ Philosophy of Science, 32(3): 253–68.CrossRefGoogle Scholar
Skyrms, B. 2000. Choice and Chance: An Introduction to Inductive Logic, 4th edition. Belmont, CA: Wadsworth.Google Scholar
Sterkenburg, T. F. 2018. Universal Prediction: A Philosophical Investigation. PhD Dissertation, University of Groningen.Google Scholar
Sterkenburg, T. F. 2019. ‘The Meta-inductive Justification of Induction: The Pool of Strategies.’ Philosophy of Science, in press.CrossRefGoogle Scholar
Vovk, V. G. 1990. ‘Aggregating Strategies.’ In Fulk, M. and Case, J. (eds), Proceedings of the Third Annual Workshop on Computational Learning Theory (COLT90), pp. 371–83. San Mateo, CA: Morgan Kaufmann.Google Scholar
Vovk, V. G. 1998. ‘A Game of Prediction with Expert Advice.’ Journal of Computer and System Sciences, 56: 153–73.CrossRefGoogle Scholar
Vovk, V. G. 2001. ‘Competitive On-line Statistics.’ International Statistical Review, 69(2): 213–48.CrossRefGoogle Scholar