| OCR Text |
Show Rationality and the Structure of the Self, Volume II: A Kantian Conception 149 (Irr) says that no one prefers an alternative to itself. I take this criterion, too, to be implied by the very meaning of preference. Note its formal similarity to the axiom of nonself-contradiction (4.II') and to Chapter II.4.1's (HC). (Irr) is, in fact, what nonself-contradiction - i.e. horizontal consistency - comes to for noncomparative preferences. Together with (Asy), it imposes analogous restrictions on pairwise comparisons, since if (1) Pw(x.~x), then by substitution on (Asy), (2) Pw(x.~x) ~Pw(x.~x), which implies (3) Pw(x.~x).~Pw(x.~x), in which case self-contradiction abounds (upon which more below, Section 11). (T3) Pw(x.~y).Pw(y.~z).Pw(x.~z) (Transitivity) Recall that we earlier made use of (T3) in Section 6.2.2 above, where we showed its logical equivalence to the acyclicity axiom. (T3) says that if, for example, Bertram prefers veggies to rice and rice to beans, then he prefers veggies to beans. (T3) is the time-independent, logically consistent rule applied by a chooser who is able both to form and apply the concept of some one thing's ranking superiority consistently over a series of pairwise comparisons (condition (2. a) of being a conscious and intentional chooser), and also to remember the relation of the two alternatives she is presently ranking to the third she is not (condition (2. b)). For when she prefers y to z at t2, she remembers having preferred x to y at t1. That is, she remembers at t2, while ranking y and z, that there is also an x such that she prefers x to y, as she is ranking that very same y over z. This is what Kant would call "reproduction of the manifold in imagination." But it is also what lies behind Savage's observation that I find on contemplating the three alleged [cyclical] preferences side by side that at least one among them is not a preference at all, at any rate not any more.20 That is, a cyclical "preference" depends on a failure to properly conceptualize one's selection behavior as the expression of a genuine preference, and a 20 Ibid., 21. © Adrian Piper Research Archive Foundation Berlin |
