Abstract
There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD (Probability-Difference), PR (Probability-Ratio), LD (Likelihood-Difference), and LR (Likelihood-Ratio). He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and LR. The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation.
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Notes
All references to Zalabardo are to Zalabardo (2009).
LR, like PR, yields the (prima facie) implausible result that the degree to which E confirms H is greater than, in fact, much greater than, the degree to which E* confirms H*: LR(H, E) ≈ 10101000 > > 9801 = LR(H*, E*).
If Joyce is right, then this is true of any (Bayesian) confirmation measure. He writes: “All Bayesians agree that the degree to which [E] counts as evidence for … [H] [i.e., the degree to which E confirms H] for a given person is a matter of the extent to which learning [E] would increase … her confidence in [H]” (1999, p. 205).
Similarly, PD and PR are naturally understood as measuring degree of disconfirmation in terms of degree of decrease in probability.
For example: p(E ∧ E * ∧ H ∧ H *) = 8/161; p(E ∧ ¬ E * ∧ H ∧ ¬ H *) = 15139/16100; p(E ∧ ¬ E * ∧ ¬ H ∧ ¬ H *) = 1/20000000; p(¬ E ∧ E * ∧ ¬ H ∧ ¬ H *) = 153/16100000; p(¬ E ∧ ¬ E * ∧ ¬ H ∧ ¬ H *) = 32169239/3220000000.
I owe this idea to Roush (2005, Ch. 5). But I develop the idea somewhat differently than Roush does.
p(E | H) = 1 while p(E | ¬H) = 0 iff p(¬E | ¬H) = 1 while p(¬E | H) = 0. So E fully discriminates between H and ¬H iff ¬E fully discriminates between ¬H and H.
If LR is to be understood as measuring degree of confirmation in terms of partial discrimination, then, presumably, the same is true of LD. It might be that standard objections to LD need to be rethought.
References
Hájek, A., & Joyce, J. (2008). Confirmation. In S. Psillos & M. Curd (Eds.), The Routledge companion to philosophy of science (pp. 115–128). London: Routledge.
Joyce, J. (1999). The foundations of causal decision theory. Cambridge: Cambridge University Press.
Roche, W. (2014). A note on confirmation and Matthew properties. Logic & Philosophy of Science, XII, 91–101.
Roche, W., & Shogenji, T. (2014). Dwindling confirmation. Philosophy of Science, 81, 114–137.
Roush, S. (2005). Tracking truth: Knowledge, evidence, and science. Oxford: Oxford University Press.
Schlesinger, G. (1995). Measuring degrees of confirmation. Analysis, 55, 208–212.
Zalabardo, J. (2009). An argument for the likelihood-ratio measure of confirmation. Analysis, 69, 630–635.
Acknowledgments
I wish to thank an anonymous reviewer for a helpful suggestion and Tomoji Shogenji for extremely helpful comments on prior versions of the paper.
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Roche, W. Confirmation, increase in probability, and partial discrimination: A reply to Zalabardo. Euro Jnl Phil Sci 6, 1–7 (2016). https://doi.org/10.1007/s13194-015-0115-z
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DOI: https://doi.org/10.1007/s13194-015-0115-z