Abstract

In a series of papers over the past twenty years, and in a new book, Igor Douven (sometimes in collaboration with Sylvia Wenmackers) has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

Highlights

  • Once, when we were young, my friend Robert thought we saw a ghost

  • The explanationist updating rule we just described is a particular case of the following rule, which Bas van Fraassen (1989, Chapter 6) sketched in his early discussion of the tension between inference to the best explanation and Bayesianism, and which Igor Douven (2013, 2021) has made precise and explored in great detail: Explanationist’s Rule If have: pE1 (H1), . . . , Hn is a set of mutually exclusive and exhaustive hypotheses, and p(E) > 0, it ought to be that pE (Hi ) =

  • Providing all agents share the same prior, as Douven assumes, that is equivalent to applying the Bayesian rule to the extracted evidence and has the same advantages when assessed for accuracy

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Summary

B Richard Pettigrew

As I noted above, Bayes’ Rule says that my posterior confidence in each hypothesis from should be obtained by asking how likely the evidence is given that hypothesis, weighting that by how likely I thought the hypothesis was prior to receiving the evidence, and normalizing the resulting credences. The explanationist updating rule we just described is a particular case of the following rule, which Bas van Fraassen (1989, Chapter 6) sketched in his early discussion of the tension between inference to the best explanation and Bayesianism, and which Igor Douven (2013, 2021) has made precise and explored in great detail: Explanationist’s Rule (general) If H1, . His goal is to reject the dominance of Bayesianism, rather than to establish the dominance of explanationism He allows that Bayes’ Rule may be the right way to go in certain situations, but sees no reason to think that’s always the case. I conclude that the dominance of Bayes’ Rule should continue

Pragmatic arguments for Bayes’ Rule
Lewis’ sure loss argument for Bayes’ Rule
Avoiding the sure loss
The expected pragmatic utility argument for Bayes’ Rule
Getting to the truth faster
Accuracy arguments for Bayes’ Rule
Updating in a social setting
Choosing your intellectual trajectory
Conclusion
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