Non-Bayesian Accounts of Evidence: Howson’s Counterexample Countered

ABSTRACT

There is a debate in Bayesian confirmation theory between subjective and non-subjective accounts of evidence. Colin Howson has provided a counterexample to our non-subjective account of evidence: the counterexample refers to a case in which there is strong evidence for a hypothesis, but the hypothesis is highly implausible. In this article, we contend that, by supposing that strong evidence for a hypothesis makes the hypothesis more believable, Howson conflates the distinction between confirmation and evidence. We demonstrate that Howson’s counterexample fails for a different pair of hypotheses.

Acknowledgements

The authors would like to thank John G. Bennett and the editor and an anonymous referee of this journal for their helpful comments regarding the contents of the paper.

Notes

1 Bandyopadhyay and Brittan (2006, 2010) introduced a similar distinction earlier. Then they called it the belief/evidence distinction, following Royall (1997).

2 Several other Bayesian measures are available to provide an account of confirmation. However, we have opted for this one. We have criticised the subjective measure used by Christensen and Joyce to address a Bayesian account of confirmation and evidence in Bandyopadhyay, Brittan, and Taper (2016), 63–72.

3 This account can be extended to comparing multiple hypotheses by making multiple pairwise comparisons.

4 See Lele (2004, 203) for the proof. It is worth noting the comments of a referee on a similar claim in another paper of ours:

if in the end we hope for an account of evidence in which evidence gives us reason to believe, it is totally unclear why efficiency in the sense described would be taken as a sign of a meritorious measure of evidence.

One of the principal aims of this paper is to disabuse its readers of what we call the ‘true-model’ assumption, that evidence gives us reasons to believe that a hypothesis is true. In our view, evidence provides information about a hypothesis on the basis of which we can make reliable inferences and not necessarily reasons to believe that it is true (in section 4, we argue with the help of a tuberculosis example how this is possible). Since evidence is a way of identifying and assessing such information, efficiency in the sense indicated is indeed a meritorious property of it.

5 The assumption that hypotheses are simple is not a defining characteristic of any particular school of statistics, as both Royall (1997), who accepts the likelihood approach, and Mayo (1996), who holds an error-statistical approach, have also taken this assumption for granted. However, we have generalised our account of confirmation to address the model selection problem (Bandyopadhyay, Boik, and Basu 1996; Bandyopadhyay 2007).

6 Statisticians prefer to use ‘models’ to ‘hypotheses’ in this connection. We stick to the philosophers’ usage.

7 Royall (1997) has provided an intuitive justification for the choice of number of 8 as a cut-off point for strong evidence. Royall has mentioned that this benchmark value (i.e. 8) or any value in that neighbourhood is widely shared by statisticians of different stripes. See Taper (2004) for more on this issue. In fact, the value 8 is close to the 0.05 of classical statistics.

8 This frequency-based prior for tuberculosis still holds for the US population.