Abstract
The Problem of Old Evidence (POE) states that Bayesian confirmation theory cannot explain why a theory H can be confirmed by a piece of evidence E already known. Different dimensions of POE have been highlighted. Here, I consider the dynamic and static dimension. In the former, we want to explain how the discovery that H accounts for E confirms H. In the latter, we want to understand why E is and will be a reason to prefer H over its competitors. The aim of the paper is twofold. Firstly, I stress that two recent solutions to the dynamic dimension, recently proposed by Eva and Hartmann, can be read in terms of Inference to the Best Explanation (IBE). On this base, I gauge the weaknesses and strengths of the two models. Namely, I show that the two authors endorse a particular IBE’s formulation, and that it is still unsure if it is the one descriptively used. Moreover, I contend that, while one condition of their first model is not expression of this formulation, the only condition of their second model is. Secondly, I focus on the static dimension of POE which, now, has to be expressed in IBE terms. To solve it, I rely on the counterfactual approach, and on a version of IBE in which explanatory considerations help to evaluate the terms in Bayes’ theorem. However, it turns out that the problems of the counterfactual approach recur even when it is used to solve the static POE in IBE terms.
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Notes
Eells refers to hypotheses or, equivalently, theories, by using the capital letter T and not H. However, for consistency, I replaced T with H.
The first problematic case is also considered by Glymour (1980, p. 89), who, however, does not provide any example. Moreover, Glymour (1980, pp. 87–91) makes other arguments in favour of the claim that it is problematic to have particular degrees of belief in E, or in H given E, had our degrees of belief in E been less than 1.
For the proof, see Eva and Hartmann (2020), footnote n. 4, p. 491.
To expand on the distinction between these two senses of confirmation, see Hartmann and Sprenger 2019, variation 1.
I say that t is a high value because in E&H Idea, it is said that H receives strong confirmation.
Lipton (2001, p. 106) explains why each of these virtues is an explanatory virtue by saying, respectively: “better explanations explain more types of phenomena, explain them with greater precision, provide more information about underlying mechanisms, unify apparently disparate phenomena, or simplify our overall picture of the world”.
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Acknowledgements
I would like to thank my Ph.D supervisor, Jan Sprenger, and my supervisor during the period abroad, Stephan Hartmann, for the numerous, helpful, and insightful discussions about the subject of this paper.
Funding
This work was carried out during the author’s Ph.D program. However, the paper was first submitted to the journal while the author was receiving the scholarship funded by Compagnia di San Paolo, whereas the revisions of the paper were made after the scholarship ended.
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Sagrafena, C. The old evidence problem and the inference to the best explanation. Euro Jnl Phil Sci 13, 2 (2023). https://doi.org/10.1007/s13194-022-00507-4
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DOI: https://doi.org/10.1007/s13194-022-00507-4