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Show Rationality and the Structure of the Self, Volume II: A Kantian Conception 117 and its negation at one and the same time and in one and the same respect is the requirement of non-contradiction, i.e. (x)~(Fx.~Fx), for classical predicate logic. This is the sentential analogue of Chapter II.4.1's proposed requirement of horizontal consistency for variables (HC) (~∃x)(x.~x), i.e. (x)~(x.~x). The rule that requires consistent application of concepts to particulars in order to exclude self-contradiction applies, a fortiori, to the application of the concept of a genuine preference to the particular choice alternatives offered. The consistent application of this concept over time also presupposes satisfaction of the criterion of vertical consistency developed in Chapter II.4.2. Applying consistently through time the concept of a thing's ranking superiority, and so of some other thing's ranking inferiority, to a series of pairwise comparisons ((a), above) satisfies (B) of Chapter II.4.2, i.e. that any particular ci in S is either (i) an instantiation of some other cj in S; or (ii) instantiated by some other ck in S. That is, suppose S' is that subset of S comprising the choice alternatives available to her at that moment. Then (a) implies that given any choice alternative F in S' that enters into a pairwise comparison with some other choice alternative G in S', F in that comparison instantiates at least one of two other cjs in S', namely the concept of a thing's ranking superiority or of its inferiority; and similarly for any F, G in S'. So S' is minimally coherent. In addition, remembering the relation of the two alternatives the agent is ranking to the third she is not ((b), above) satisfies (C) of Chapter II.4.2; i.e. that for any cognitively available particular thing t, there is a cj in S that t instantiates. That is, if F, G, H, …are choice alternatives in S', then F, G and H are cognitively available things t1, t2, and t3 such that there is at least one cj in S' that each of t1, t2, and t3 instantiate, namely the concept either of a thing's ranking superiority or of its ranking inferiority; i.e. S' is complete. Then for any pairwise comparison among them, an agent who can form and apply these concepts consistently through time can at any moment in time use both of them to locate any one of these choice alternatives relative to the other. She remembers the relation of the two alternatives she is presently ranking to the third she is not. Now if (a) and (b) presuppose satisfaction of Chapter II.4.2's (B) and (C), then we should be able to symbolize (T) as an instantiation of Chapter II.4.2's formalized criterion of vertical consistency, i.e. © Adrian Piper Research Archive Foundation Berlin |
