How to Learn from Theory-Dependent Evidence; or Commutativity and Holism: A Solution for Conditionalizers

Gallow, J. Dmitri

doi:10.1093/bjps/axs045

Cited by 14 publications

(14 citation statements)

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“…16 These alternative rules include Jeffrey conditioning (or probability kinematics) (Jeffrey, 1992) and various parameterizations thereof (Field, 1978;Wagner, 2002), imaging (Lewis, 1976;Leitgeb, 2016), and Gallow's rule for learning theory-dependent evidence (Gallow, 2014).…”

Section: Deterministic Convergencementioning

confidence: 99%

Deterministic Convergence and Strong Regularity

Nielsen¹

2020

The British Journal for the Philosophy of Science

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Bayesians since Savage ([1972]) have appealed to asymptotic results to counter charges of excessive subjectivity. Their claim is that objectionable differences in prior probability judgements will vanish as agents learn from evidence, and individual agents will converge to the truth. Glymour ([1980]), Earman ([1992]) and others have voiced the complaint that the theorems used to support these claims tell us, not how probabilities updated on evidence will actually behave in the limit, but merely how Bayesian agents believe they will behave, suggesting that the theorems are too weak to underwrite notions of scientific objectivity and intersubjective agreement. I investigate, in a very general framework, the conditions under which updated probabilities actually converge to a settled opinion and the conditions under which the updated probabilities of two agents actually converge to the same settled opinion. I call this mode of convergence ‘deterministic’, and derive results that extend theorems in (Huttegger [2015b]). The results here lead to a simple characterization of deterministic convergence for Bayesian learners and give rise to an interesting argument for what I call ‘strong regularity’, the view that probabilities of non-empty events should be bounded away from zero. 1Introduction2Preliminaries3Deterministic Convergence4Consensus in the Limit5Strong Regularity6ConclusionAppendix

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Section: Deterministic Convergencementioning

confidence: 99%

Deterministic Convergence and Strong Regularity

Nielsen¹

2020

The British Journal for the Philosophy of Science

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“…Gallow () argues that learning scenarios like these arise in cases involving theory‐dependent evidence. In such cases, you could be in a position in which, if the background theory t is true, then experience will deliver either the evidence e or the evidence ¬ e .…”

Section: Diachronic Dutch Book Argumentsmentioning

confidence: 99%

Diachronic Dutch Books and Evidential Import

Gallow

2017

Philos Phenomenol Research

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A handful of well-known arguments (the 'diachronic Dutch book arguments') rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not 'diachronically Dutch bookable') if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non-trivial assumptions about which evidence you might acquire-in the case of conditionalization, the assumption is that, if you might learn that e , then it is not the case that you might learn something else that is consistent with e . These assumptions may not be relaxed. When they are, not only will non-(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid.

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“…A different proposal for making the information that it was Sophia's vision that caused her increase in confidence in D available to Sophia is presented in Gallow (2014). Gallow (2014) first proposes the following update rule:…”

Section: Appendixmentioning

confidence: 99%

“…For this reason Gallow (2014) generalizes his first update rule to the following second update rule:…”

Section: Appendixmentioning

confidence: 99%