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Show Rationality and the Structure of the Self, Volume II: A Kantian Conception 85 errand. Those of us who go to the store infrequently may think of it instead as an entertaining diversion; others may not think of going to the store as instantiating, as a matter of conceptual necessity, any concept, not even that of an action. Because we each may have different perspectives on such matters, the definitions just offered of higher and lower orders of comprehensiveness must be relativized to an agent's perspective. Whatever the sum total of concepts that constitute my perspective at a particular moment, the holistic regress implies that the law of noncontradiction must be satisfied simultaneously by all of them. Otherwise there would be some thing or property I could neither identify with nor differentiate from anything else. In that case I could neither identify any of those other things with it, nor differentiate any of those other things from it. And then I could make none of them rationally intelligible. This is to say that I must conceive all the things and properties that are simultaneously rationally intelligible to me as logically consistent with one another; i.e. that (A) S observes the law of noncontradiction, in that the members of S are internally and mutually consistent in their application. (A) makes the requirement of nonself-contradiction stated in (15) a special case of the familiar law of noncontradiction more generally. (A) says that we can understand particular things or states of affairs only if the concepts by which we recognize them are neither internally nor mutually contradictory. In standard notation modified as suggested above, (A) would run roughly as follows: For any agent's set S of concepts of things and properties c1, c2, c3, ... cn , and rationally intelligible things or properties t1, t2, …tn assigned to individual variables a1, …an, b1, … bn, …, (HC) (~∃x)(x.~x), i.e. we must conceive any such ci as self-identical, i.e. nonself-contradictory. Call this the requirement of horizontal consistency. For now, some readers may wish to read the expression enclosed in the second set of parentheses in (HC) as predicating ".~x" of x. But I discuss (HC)'s notational peculiarities at greater length in Chapter III.5, 7 and 9, below. 4.2. Vertical Consistency Next consider the regressiveness of the holistic regress, i.e. its implication that we cannot have concepts of the kind of thing some thing or property is, without being able to invoke further concepts of the higher-order properties that in turn identify that kind. This means that if I recognize some thing or property as a certain kind of thing, I also must be able to conceive it as of the © Adrian Piper Research Archive Foundation Berlin |
