Abstract
So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in particular we give an example in which the effect occurs in a larger domain, according to Shogenji justification, than Carnap’s measure of confirmation would have led one to expect.
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References
Atkinson D., Peijnenburg J., Kuipers T. (2009) How to confirm the conjunction of disconfirmed hypotheses. Philosophy of Science 76: 1–21
Carnap R. (1962) Preface to the second edition of Logical foundations of probability. University of Chicago Press, Chicago
Hawthorne J., Fitelson B. (2004) Re-solving irrelevant conjunction with probabilistic independence. Philosophy of Science 71: 505–514
Keynes J. (1921) A treatise on probability. Macmillan, London
Shogenji, J. (2009). The degree of epistemic justification and the conjunction fallacy. Synthese (this number).
Acknowledgements
I would like to thank Tomoji Shogenji for his most stimulating paper and for fruitful email correspondence. I am also indebted to Theo Kuipers for pointing out that the proof of ordinal uniqueness depends crucially on the requirement that the measure of justification was not allowed to depend on the choice of the threshold of justification.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Atkinson, D. Confirmation and justification. A commentary on Shogenji’s measure. Synthese 184, 49–61 (2012). https://doi.org/10.1007/s11229-009-9696-4
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DOI: https://doi.org/10.1007/s11229-009-9696-4