A Note on Deterministic Updating and van Fraassen's symmetry argument for Conditionalization

Richard Pettigrew*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

33 Downloads (Pure)

Abstract

In a recent paper, Pettigrew (Philos Stud, 2019. https://doi.org/10.1007/s11098-019-01377-y) argues that the pragmatic and epistemic arguments for Bayesian updating are based on an unwarranted assumption, which he calls deterministic updating, and which says that your updating plan should be deterministic. In that paper, Pettigrew did not consider whether the symmetry arguments due to Hughes and van Fraassen make the same assumption (Hughes and van Fraassen in: Proceedings of the Biennial Meeting of the Philosophy of Science Association. pp. 851–869, 1984; van Fraassen in: Rescher N (ed) Scientific inquiry in philosophical perspective. University Press of America, Lanham, pp. 183–223, 1987). In this note, I show that they do. According to Bayesians, when I learn a proposition to which I assign a positive credence, I should plan to update my credences so that my new unconditional credence in a proposition is my old conditional credence in that proposition conditional on the proposition I learned. In other words, if P is my credence function before I learn E, and P⋆ is the credence function I plan to adopt in response to learning E, and P(E)>0, then it ought to be the case that, for all X in F, P⋆(X)=PE(X):=P(X|E):=P(XE)P(E). There are many arguments for this Bayesian norm of updating. Some pay attention to the pragmatic costs of updating any other way (Brown 1976; Lewis 1999); others pay attention to the epistemic costs, which are spelled out in terms of the inaccuracy of the credences that result from the updating plans (Oddie 1997; Greaves and Wallace 2006; Briggs and Pettigrew 2018); some show that updating as the Bayesian requires, and only updating that way, preserves as much as possible about the prior credences while still respecting the new evidence (Diaconis and Zabell 1982; Dietrich et al. 2016). And then there are the symmetry arguments that are our focus here (Hughes and van Fraassen 1984; van Fraassen 1987; Grove and Halpern 1998). In a recent paper, I argued that the pragmatic and epistemic arguments for Bayesian updating are based on an unwarranted assumption, which I called deterministic updating, and which says that your updating plan should be deterministic (Pettigrew 2019). An updating plan specifies how you’ll update in response to a specific piece of evidence. Such a plan is deterministic if there’s a single credence function that it says you’ll adopt in response to that evidence, rather than a range of different credence functions that you might adopt in response. That is, if E is a proposition you might learn, deterministic updating says that your plan for responding to receiving E as evidence should take the form: If I learnE, I’ll adoptP⋆. It should not take the form: If I learnE, I’ll adoptP⋆or I’ll adoptP†or ... or I’ll adoptP∘. In that paper, I did not consider whether the symmetry arguments due to Hughes and van Fraassen make the same assumption. In this note, I show that they do.
Original languageEnglish
Number of pages9
JournalPhilosophical Studies
Early online date18 Apr 2020
DOIs
Publication statusE-pub ahead of print - 18 Apr 2020

Fingerprint Dive into the research topics of 'A Note on Deterministic Updating and van Fraassen's symmetry argument for Conditionalization'. Together they form a unique fingerprint.

Cite this