Abstract
Bayesians regard their solution to the paradox of confirmation as grounds for preferring their theory of confirmation to Hempel’s. They point out that, unlike Hempel, they can at least say that a black raven confirms “All ravens are black” more than a white shoe. However, I argue that this alleged advantage is cancelled out by the fact that Bayesians are equally committed to the view that a white shoe confirms “All non-black things are non-ravens” less than a black raven. In light of this, I reexamine the dialectic between Hempel and the Bayesians.
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Notes
As should be clear by now, there are many different versions of Bayesianism. Indeed, early Bayesian champion, I.J. Good (1971), once playfully demonstrated that, in principle, there are over forty-thousand varieties of Bayesianism. With so many options then, it is not surprising that there are different sorts of practicing Bayesians and—at a detailed level—more than one Bayesian solution to the paradox. My focus here will simply be the standard Bayesian response to the puzzle. Vranas (2004) provides an immense, near-exhaustive bibliography of Bayesian treatments of the paradox.
Bayesians have proposed multiple measures of incremental confirmation. Fitelson (1999) presents an illuminating overview.
Fitelson (2002) provides a good summary and important recent discussion of the problem.
References
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, S362–S378.
Fitelson, B. (2002). Putting the irrelevance back into the problem of irrelevant conjunction. Philosophy of Science, 69, 611–622.
Fitelson, B., & Hawthorne, J. (2010). How Bayesian Confirmation Theory Handles the Paradox of the Ravens. In E. Eells & J. Fetzer (Eds.), The Place of Probability in Science. Chicago, IL: Open Court.
Good, I. J. (1961). The paradox of confirmation II. British Journal for the Philosophy of Science, 12, 63–64.
Good, I. J. (1967). The white shoe is a red herring. British Journal for the Philosophy of Science, 17, 322.
Good, I. J. (1971). 46656 varieties of Bayesians. American Statistician, 25, 62–63.
Hempel, C. G. (1945). Studies in the logic of confirmation. Mind 54, 1–26 & 97–121.
Vranas, P. (2004). Hempel’s Raven paradox: a lacuna in the standard Bayesian solution. British Journal for the Philosophy of Science, 55, 545–560.
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Brian Laetz died in a traffic accident on March 18th, while this article was still under review. The editors wish to express their condolences to Mr. Laetz’s friends and family. We thank Mr. Laetz’s family for permission to proceed with publication of this article, and thank Paul Bartha for correcting the page proofs.
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Laetz, B. Does the Bayesian solution to the paradox of confirmation really support Bayesianism?. Euro Jnl Phil Sci 1, 39–46 (2011). https://doi.org/10.1007/s13194-010-0007-1
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DOI: https://doi.org/10.1007/s13194-010-0007-1