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Show Chapter III. The Concept of a Genuine Preference 112 just is intentionally conceptualized behavior of a goal-oriented kind, and so presupposes thought. Practical reasoning just is an application of theoretically rational rules of causal inference to the special-case event of intentionally conceptualized behavior of a goal-oriented kind. Then if decision theory is a formalization of practical reasoning, then it is a special case of the classical logic that formalizes theoretical reasoning. The question is how to show this. Now it might be argued that decision-theoretic formalizations are best compared not with classical logic, but rather with intensional logics of belief, in which it is logically possible for a subject to have logically contradictory beliefs bP and b~P simultaneously. But first, we saw in discussing Ramsey's value axioms in Volume I, Chapter IV.2.1 - 2 that neither orthodox decisiontheoretic notation nor decision-theoretic idiolect recognizes an intensional component to preference rankings. The use of the passive voice, as in "F is preferred to G" conceals any that might be there, and gives the interpretation of decision-theoretic symbols a strong extensional cast. Second, even if intensional logics of belief were the correct comparison, the similarity would break down at the next step. For intensional logics of belief have to acknowledge the logical possibility of contradictory beliefs as admissible within the system in order to preserve the logically consistency of the system itself; whereas both classical and decision-theoretic axiom systems make strong claims to exemplify in what consistent theoretical and practical reasoning respectively consist. Nevertheless, the issue of intensionality first encountered in discussing Ramsey's value axioms is unavoidable. For - as I now argue - the reason we cannot formalize cyclical inconsistency within the constraints of orthodox decision theory is because orthodox decision theory treats as extensional connectives what are in fact intensional operators buried in declarative sentential propositions.2 Here is an argument that purports to derive a straightforward logical inconsistency from the conjunction of (C) and (T). Reading the weak preference relation F ≥ G as "F is preferred or indifferent to G," define a strong preference relation F>G in terms of it such that That orthodox decision theory does, in fact, treat ">," "≥," etc. as extensional connectives is not seriously open to doubt. See, for example, John Von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1990), 18-19, fn. 3 for a treatment of ">" and "<" as having the same notational status as "=". For the straightforward appropriation of such connectives from the mathematical into the decision-theoretic context for purposes of formally defining a simple ordering, see Leonard Savage, The Foundations of Statistics (New York: Dover Publications, Inc., 1971), 18-19; for purposes of formally defining utility-maximization, see R. Duncan Luce and Howard Raiffa, Games and Decisions (New York: John Wiley and Sons, Inc., 1957), 15; and for purposes of formally defining majority decision, see Amartya K. Sen, Collective Choice and Social Welfare (San Francisco: Holden-Day, Inc., 1970), 71. 2 © Adrian Piper Research Archive Foundation Berlin |
