Abstract
To prepare this work’s subsequent discussions of morally instrumental and morally teleological discourse, Chap. 3 addresses the issue of theory choice. It surveys four views of how to choose a theory: probabilism, falsificationism, decision theory, and virtue epistemology. The chapter argues that each of these approaches has serious debilities, but those of decision theory are less debilitating than the rest. It therefore proposes a decision-theoretic approach to theory choice of any kind—moral and non-moral alike. However, attempts to apply decision theory to real-world problems confront a well-known difficulty: the exceptionally heavy information load the theory imposes on users. Bayesian decision theorists take the probability and utility functions that underlie expected utilities to determine sharp numeric values. Real-life decisions, however, must usually be made without nearly as much information. To ameliorate this difficulty, the chapter introduces a version of comparative decision theory. Because this form of decision theory requires no more than a bare minimum of comparative values for plausibilities and utilities, it can be widely applied. The chapter concludes with a consideration of three decision-theoretically foundational issues: transitivity, independence, and suspension of judgment.
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- 1.
Theory choice and theory acceptance are distinct but intimately related acts. Whereas theory choice is selecting a theory for a cognitive purpose such as explanation or prediction, theory acceptance can be defined as the belief that a theory is true or as the mental state expressed by asserting a theory (cf. Maher 1993, p. 130, 133). One often chooses a theory because one accepts it. But since one might choose a theory for one purpose yet choose a rival for another, it is possible to choose a theory without accepting it either in the sense of believing that it is true or in the sense of being disposed to assert it.
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Early work on interval probability functions includes Kyburg (1961), Good (1962), and Levi (1974, with further references on p. 407). Advocates of this approach include Good’s less extreme Bayesians (1965, p. 10), today’s robust Bayesians who take each probability to lie within an interval of values (Berger 1984; 1985).
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As noted, the topics of theory choice and theory acceptance are intimately related. An acceptance rule based on high probability is discussed in Festa (1999, § 3).
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John L. Pollock argues that decision theory is properly applied to plans, that is, groups of acts (2006, Chap. 10).
- 10.
Generality figures only in the Quine -Ullian and Lycan lists, though Kuhn ’s broad scope and van Fraassen ’s great scope may come to the same thing. Both Kuhn and van Fraassen include consistency. Quine-Ullian and Lycan concur on conservatism. Van Fraassen and Lycan both mention explanatory power, though Lycan adds that explanatory power “is just a wider, more global simplicity” (1998, § 1).
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High probability appears to be neither necessary nor sufficient for the related act of rational acceptance (Maher 1993, pp. 133–139, 163–180).
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It is symptomatic that Popper concedes that after all he may need a “whiff” of induction : “there may be a ‘whiff’ of inductivism here. It enters with the vague realist assumption that reality, though unknown, is in some respects similar to what science tells us or, in other words, with the assumption that science can progress towards greater verisimilitude” (1974, pp. 1192–1193). This is hardly surprising given that even mathematics cannot get by without non-deductive reasoning (Franklin 1987).
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Expectation can be defined for the infinite case by replacing summation with integration. See, for example, Pollock (2006, pp. 16–17).
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I have adapted Chu and Halpern ’s set-theoretic statement to the propositional idiom.
- 17.
The example is adapted from Fishburn (1986, p. 339).
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This example is discussed in Levi (1986, pp. 1–2).
- 19.
Paul Samuelson ’s observation on Savage ’s theory (along with Ramsey ’s and de Finetti ’s) is still worth noting: “it is important to realize that this is a purely ordinal theory and the same facts can be completely described without using privileged numerical indicators of utility or probability” (1952, p. 670 n. 1).
- 20.
‘||’, which was defined in Sect. 3.3.2.6 for incomparable plausibilities, utilities, and plausibilistic expectations, is used analogously here. A product such as uP can be thought of as the plausibilistic expectation of an act relative to a single state.
- 21.
An analogous distinction can be drawn for probability. “Whether or not a given sentence is accepted depends not so much on its total probability taken in isolation, but on that probability as compared to the probabilities of the alternative hypotheses being considered” (Levi 1967, p. 98).
- 22.
Maher takes independence to be a requirement of rationality “when the preferences are relevant to a sufficiently important decision problem, and where there are no rewards attached to violating… independence” (1993, p. 12, 63–83).
- 23.
An alternative approach is explored by Ted Lockhart , who relies on ordinal probability rankings, second-order probabilities, integration to calculate average values, and the principle of indifference to address moral questions (2000, pp. 62–66, 71–72).
- 24.
The option of suspending judgment is discussed further in Sect. 3.6.3.
- 25.
Thanks to David Schrader for bringing this case to my attention.
- 26.
“In nonquantitative cases the principle to maximize utility may not apply because options’ utilities may not exist. The absence of crucial probabilities and utilities may prevent computing them according to principles of expected utility analysis” (Weirich 2004, p. 59).
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- 28.
This issue is addressed in a different context in Welch (2013, p. 327).
- 29.
Distinctions among cognitive, partly cognitive, and noncognitive decisions are introduced in Sect. 3.3.2.3.
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Welch, J. (2014). Comparative Decision Theory. In: Moral Strata. Theory and Decision Library A:, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-08013-0_3
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