Abstract
Evidentiary propositions E 1 and E 2, each p-positively relevant to some hypothesis H, are mutually corroborating if p(H|E 1 ∩ E 2) > p(H|E i ), i = 1, 2. Failures of such mutual corroboration are instances of what may be called the corroboration paradox. This paper assesses two rather different analyses of the corroboration paradox due, respectively, to John Pollock and Jonathan Cohen. Pollock invokes a particular embodiment of the principle of insufficient reason to argue that instances of the corroboration paradox are of negligible probability, and that it is therefore defeasibly reasonable to assume that items of evidence positively relevant to some hypothesis are mutually corroborating. Taking a different approach, Cohen seeks to identify supplementary conditions that are sufficient to ensure that such items of evidence will be mutually corroborating, and claims to have identified conditions which account for most cases of mutual corroboration. Combining a proposed common framework for the general study of paradoxes of positive relevance with a simulation experiment, we conclude that neither Pollock’s nor Cohen’s claims stand up to detailed scrutiny.
I am quite prepared to be told…”oh, that is an extreme case: it could never really happen!” Now I have observed that this answer is always given instantly, with perfect confidence, and without any examination of the proposed case. It must therefore rest on some general principle: the mental process being something like this—“I have formed a theory. This case contradicts my theory. Therefore, this is an extreme case, and would never occur in practice.”
Rev. Charles L. Dodgson
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Bickel P. J., Hammel E. A., O’Connell J. W. (1975) Sex bias in graduate admissions: Data from Berkeley. Science 187: 398–404
Blyth C. R. (1972) On Simpson’s paradox and the sure thing principle. Journal of the American Statistical Association 67: 364–366
Chung K.-L. (1942) On mutually favorable events. Annals of Mathematical Statistics 13: 338–349
Cohen L. J. (1977) The probable and the provable. Clarendon Press, Oxford
Cohen L. J. (1980) Bayesianism versus Baconianism in the evaluation of medical diagnoses. British Journal for the Philosophy of Science 31: 45–62
Pollock J. (1990) Nomic probability and the foundations of induction. Oxford University Press, New York
Pollock, J. (2009). Probable probabilities, available online at: http://oscarhome.soc-sci.arizona.edu/ftp/PAPERS/ProbableProbabilitieswithproofs.pdf.
Rényi A. (1970) Foundations of probability. Holden Day, San Francisco
Schlesinger G. (1988) Why a tale twice told is more likely to take hold. Philosophical Studies 54: 141–152
Shafer G. (1976) A mathematical theory of evidence. Princeton University Press, Princeton
Simpson E. H. (1951) The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society (Series B) 13: 238–241
Wagner C. (1991) Corroboration and conditional positive relevance. Philosophical Studies 61: 295–300
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Wagner, C.G. The corroboration paradox. Synthese 190, 1455–1469 (2013). https://doi.org/10.1007/s11229-012-0106-y
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DOI: https://doi.org/10.1007/s11229-012-0106-y