Abstract
In robustness analysis, hypotheses are supported to the extent that a result proves robust, and a result is robust to the extent that we detect it in diverse ways. But what precise sense of diversity is at work here? In this paper, I show that the formal explications of evidential diversity most often appealed to in work on robustness – which all draw in one way or another on probabilistic independence – fail to shed light on the notion of diversity relevant to robustness analysis. I close by briefly outlining a promising alternative approach inspired by Horwich’s (Probability and evidence. Cambridge University Press, Cambridge, 1982) eliminative account of evidential diversity.
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- 1.
For clarity and ease of exposition, I leave the background beliefs term implicit in all Bayesian formulations.
- 2.
Orzack and Sober also criticize an alternative explication according to which two models are diverse only if they are logically independent. The fact that RA-diverse models may involve contrary simplifying assumptions spells trouble for this account; e.g., “A model with the assumption of random mating is not logically independent of a model with the assumption that mating is assortative; the reason is that the truth of one entails the falsity of the other.”
- 3.
- 4.
Notation: c(x, y) measures the degree of confirmation that y lends to x; c(x, y | z) measures the degree of confirmation that y lends to x, conditional on (or given that) z.
- 5.
I have replaced Fitelson’s notation with our own. It should be noted that Fitelson suggests this relation as a condition of adequacy on measures of confirmation, as opposed to proving and presenting it as a theorem that follows robustly (!) for all candidate measures.
- 6.
I have since developed such an account in (Schupbach Forthcoming).
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Acknowledgements
I am grateful for the helpful conversations I have shared on this topic with Aki Lehtinen, Chiara Lisciandra, Gerhard Schurz, Jacob Stegenga, and Ioannis Votsis. Also, thanks to two anonymous referees for their helpful suggestions, which allowed me to improve an earlier draft of this paper. Research for this article was supported by an Aldrich Fellowship from the University of Utah’s Tanner Humanities Center, and was conducted during a visit to the Düsseldorf Center for Logic and Philosophy of Science.
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Schupbach, J.N. (2015). Robustness, Diversity of Evidence, and Probabilistic Independence. In: Mäki, U., Votsis, I., Ruphy, S., Schurz, G. (eds) Recent Developments in the Philosophy of Science: EPSA13 Helsinki. European Studies in Philosophy of Science, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-23015-3_23
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