Bayesian Convergence to the Truth and the Metaphysics of Possible Worlds

Abstract

Belot (2013) argues that Bayesians are epistemologically flawed because they believe with probability one that they will learn the truth about observational propositions in the limit. While Belot's considerations suggest that this result should be interpreted with some care, the concerns he raises can largely be defused by putting convergence to the truth in the context of learning from an arbitrarily large but finite number of observations.

On the role of explanatory and systematic power in scientific reasoning

“…Here is not the place to take up the discussion of in how far the convergence results, given the presuppositions that they make, provide a vindication for Bayesian norms of reasoning. For detailed discussion of the claim that these convergence results (at least partially) vindicate the Bayesian norms of reasoning, see Belot (2013), Earman (1992), Hawthorne (2014), and Huttegger (2015aHuttegger ( , 2015b. For applications of these results in Bayesian philosophy of science see for example Brössel (2008Brössel ( , 2014Brössel ( , 2015, Huber (2008), and Huttegger (2015aHuttegger ( , 2015b).…”

“…For detailed discussion of the claim that these convergence results (at least partially) vindicate the Bayesian norms of reasoning, see Belot (2013), Earman (1992), Hawthorne (2014), and Huttegger (2015aHuttegger ( , 2015b. For applications of these results in Bayesian philosophy of science see for example Brössel (2008Brössel ( , 2014Brössel ( , 2015, Huber (2008), and Huttegger (2015aHuttegger ( , 2015b). The following theorem shows that systematic power as a criterion of theory choice is vindicated by the convergence theorems to the same extent as Bayesian norms of reasoning in general are vindicated by these theorems:…”

An Axiomatic Theory of Inductive Inference

“…The debate has spurred different views. Huttegger (2015) argued that the issue of convergence to the truth should be put in the context of a long, but finite horizon. Weatherson (2015) revisited Belot's argument from the perspective of Bayesian imprecise probability.…”

Pride and Probability

“…This objection has received considerable attention in the literature, 4 and many of the available responses recommend substantial modifications of the Bayesian framework in order to evade Belot's conclusion. For instance, Huttegger (2015) proposes to use metric Boolean algebras, which allow to avoid drawing distinctions between events that can only be made by infinitely many observations, Weatherson (2015) advocates passing to imprecise Bayesianism, while Elga (2016) and Nielsen and Stewart (2019) suggest dropping countable additivity in favour of finite additivity.…”

“…3 See (Oxtoby, 1980). 4 See (Huttegger, 2015), (Weatherson, 2015), (Elga, 2016), (Belot, 2017), (Cisewski et al, 2018), (Pomatto and Sandroni, 2018), (Nielsen and Stewart, 2019), and (Gong et al, 2021). 5 The computability-theoretic approach advocated in this paper is in line with (Huttegger et al, 2023) (see also (Zaffora Blando, 2020)), where Lévy's Upward Theorem is studied through the lens of computability theory and the theory of algorithmic randomness-a branch of computability theory on which we rely here, as well.…”