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Show Rationality and the Structure of the Self, Volume II: A Kantian Conception 115 then it may be the case that (9".9) S prefers F to H, and (9".10) S is indifferent between F and H. This implication of (9") seems intuitively self-contradictory. Hence (9) cannot be presumed to hold, even of an ideally rational chooser under conditions of full information. The prima facie plausibility of (9) - and the derivation (6) - (14) - depends on concealing their intensionality by repackaging what is in fact an intentional operator - the preference operator - as a quasi-logical connective of mathematical ancestry. But we have just seen that in decision theory, neither ">" nor "≥" are genuine relational connectives, whether logical or quasi-logical, because they do not connect extensional terms. They are rather symbolic expressions of intentional operators that denote certain of a subject's intentional attitudes - namely, preference and weak preference respectively - toward pairs of intentional objects - namely preference alternatives. So if a rule of transitivity of preference is going to hold in decision theoretic formalizations, the intensional conditions under which it does hold need to be spelled out. I believe these conditions can be spelled out, consistently with showing the sense in which (1) is logically self-contradictory, and so the sense in which classical logic provides the "reality test" that authorizes the decision-theoretic rejection of cyclical preference as logically contradictory. I address this task in Section 11, below. Of course that (1) can be shown to be logically selfcontradictory does not imply the logical impossibility of cyclical selection behavior, any more than it would the logical impossibility of self-contradictory speech behavior. What it does imply is that choice behavior is just as much subject to the consistency requirements of classical logic as speech behavior, in both normative and descriptive systems; and so that the utility-maximizing model of rationality is similarly subject to a more inclusive, Kantian model of rationality that places classical logic at its base. 2. Savage's Concept of a Simple Ordering Reconsidered I argued in Volume I, Chapter IV.2.3 that Savage's concept of a simple ordering was insufficient to ensure transitivity of preference through three sequential pairwise comparisons, because his "logic-like" rule of transitivity (T), Section 1 above, is neither among nor implied by the laws of logic. I contended that if something like (T) were a logical axiom, it would assert something close to a conceptual truth about what it means to prefer F to G and G to H. Under these circumstances, to violate (T), as does the cyclical ordering (C), Section 1 above, would be to have no genuine preferences among F, G and H at all. Savage seconds that observation: © Adrian Piper Research Archive Foundation Berlin |
