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Show Chapter IV. The Utility-Maximizing Model of Rationality: Formal Interpretations 126 Unlike most formal decision theory, which basically ignores the 1 traditional Boolean connectives, Jeffrey-Bolker expected utility theory does not. It uses them to construct preference alternatives comprising strings of weighted and probabilistically defined propositions and complex gambles among them. But it leaves undisturbed the conventional connectives imported from mathematics (">," "≥," "=,") for ordering those complex preferences themselves. This leaves moot the question whether or not strictly logical interrelationships among them also obtain. So it may seem that in general, the canonical notation and axiomatic formulation of decision theory place it outside the purview and constraints of classical logic. However, the mere fact that formal decision theory in its canonical symbolization does not recognize the constraints of classical logic would not seem sufficient grounds for inferring that those constraints do not apply. Similarly, the fact that we cannot seem to symbolize logically the inconsistency involved in a cyclical ranking does not suffice to infer that no logical inconsistency is present. The question whether or not a cyclical ranking violates the law of noncontradiction is not in theory unanswerable. In Section 3, I merely raise this issue for discussion, by showing some of the commonsense ways in which a cyclical ranking certainly does seem logically inconsistent, even though the canonical notation of formal decision theory does not allow us to express this. I defer to Volume II, Chapter III a full and detailed treatment of this topic, including some suggestions as to how this notation might be modified so as to reveal its subordination, not only philosophically but also formally, to the requirements of logical consistency. Sections 4 and 5 argue that thus relativizing the Humean model renders it, like the maximin principle, contingent with respect to the requirements of rational action more generally understood. Only after reaching this conclusion do I address the metaethical status of the utility-maximizing model of rationality. Most of this chapter looks at the explanatory reach of this theory without regard to its metaethical status as normative or descriptive within any particular discussion. The question whether a theory is explanatory or not can be answered independently of the question whether it has a normative or a descriptive metaethical status. The metaethical status of any principle is fully exhausted by specifying the relation between two descriptive versions of it: that which describes actual behavior and that which describes ideal behavior. 1 See Richard C. Jeffrey, The Logic of Decision, Second Edition (Chicago: University of Chicago Press, 1983), especially Chapter 9; Ethan D. Bolker, "A Simultaneous Axiomatization of Utility and Subjective Probability," Philosophy of Science 34 (1967), 333-340; and Bolker, "An Existence Theorem for the Logic of Decision," Philosophy of Science 67 (2000), S14-S17. I discuss the role of the indifference relation in the JeffreyBolker representation theorem in Volume II, Chapter III.7. © Adrian Piper Research Archive Foundation Berlin |
