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Show Rationality and the Structure of the Self, Volume II: A Kantian Conception 107 historical inception and regardless of its other innovations has persistently concealed its own intensionality. Section 2 makes the case that the way to solve this problem is to rethink and revise the notation. Section 3 derives some criteria a successful decision-theoretic notation would have to meet. Section 4 critically evaluates one possible proposal for revising the notation, and rejects it on the grounds that it fails these criteria. It does, however, suggest additional criteria that also need to be met. I suggest that these require a variable term calculus that integrates the decision-theoretic concept of preference into the language of classical predicate logic. Section 5 introduces some basic notational revisions that define the proposed variable term calculus; demonstrates their fidelity to central conventions of both truth-functional and predicate logic on the one hand, and traditional decision-theoretic notation on the other; and gives some examples of how to navigate with these revisions. The most extended of these examples is the reduction of Luce and Raiffa's indifference relation to my notion of Epicurean indifference. Section 6 then applies the calculus to the analysis of two alternative views. First it compares my analysis of indifference to Mark Kaplan's account of rational indecision. Second, it outlines the rudiments of an "occasional" truth-functional analysis for subsentential constituents, and applies that analysis to the Jeffrey-Bolker representation theorem with respect to the thesis - itself a refinement of Ramsey's reasoning - that indifference is an equivalence relation fully adequate to the extensional work such a relation must do. Section 7 introduces four of my five suggested formal criteria a logically consistent series of pairwise comparisons must meet. Here I demonstrate how, using the conventions of predicate logic rather than traditional decision-theoretic notation, we can dispense with talk about "imposing axioms" that - as I showed in Section 1 - gets us into trouble in the first place. Section 8 introduces some further notational revisions necessary in order to formulate the fifth criterion, i.e. ordinality, in terms of the variable term calculus; and introduces and discusses that criterion. Section 9 contrasts the notion of subsentential predication developed in Section 8 with De Jongh and Liu's structurally similar analysis of strict preference in terms of constraint-predicates derived from optimality theory. Section 10 embeds the resulting, logically consistent conception of genuine preference within the comprehensive rationality constraints on coherent experience in general - i.e. horizontal and vertical consistency - which I introduced in the preceding chapter. Section 11 then applies the resulting Kantian model to the problem described in Section 1, and demonstrates that this model solves it. Since a noncyclical preference ordering is nonvacuous, this alternative, more comprehensive Kantian model of rationality avoids the vacuity of the unreconstructed utility-maximizing model, by demonstrating in what precise and formal sense a cyclical preference ordering is logically self-contradictory. © Adrian Piper Research Archive Foundation Berlin |
