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How Bayesian Confirmation Theory Handles the Paradox of the Ravens

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The Place of Probability in Science

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 284))

Abstract

The Paradox of the Ravens (aka, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens.

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Acknowledgements

We would like to thank the following people for useful conversations about the paradox of confirmation: Luc Bovens, Fabrizio Cariani, Kenny Easwaran, Ted Hailperin, Alan Hájek, Stephan Hartmann, Chris Hitchcock, Colin Howson, Franz Huber, Jim Joyce, Patrick Maher, Chad Mohler, Brad Monton, Mike Titelbaum, and Brian Weatherson. Special thanks to Jan Sprenger, whose critique of the implications of an earlier version of the results in Sections “A New Bayesian Approach to the Paradox” and “Quantitative Results” spurred us to make significant improvements.

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Authors and Affiliations

  1. Dept. of Philosophy, University of California, CA, 947202390, Berkeley, USA

    Branden Fitelson

  2. Dept. of Philosophy, University of Oklahoma, Norman, OK, 73019, USA

    James Hawthorne

Authors
  1. Branden Fitelson
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  2. James Hawthorne
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Correspondence to Branden Fitelson .

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Editors and Affiliations

  1. Springer, Dordrecht, 3311 GC, Netherlands

    Ellery Eells

  2. Dept. Philosophy, University of Minnesota, Duluth, 55812, USA

    J.H. Fetzer

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Fitelson, B., Hawthorne, J. (2010). How Bayesian Confirmation Theory Handles the Paradox of the Ravens. In: Eells, E., Fetzer, J. (eds) The Place of Probability in Science. Boston Studies in the Philosophy of Science, vol 284. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3615-5_11

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