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Show Chapter IV. The Utility-Maximizing Model of Rationality: Formal Interpretations 146 17 determinate cut-offs between truth and falsity - is indeterminate. Although 18 Schiffer would disagree, we in fact often say that such concepts - for example, baldness or wealth - hold true to different degrees; that propositions containing them are more or less true. But the concept of aggregate value - like the concepts of weight, probability or degree itself, and unlike the concepts of baldness or wealth - already is precisely that sort of formal quantitative and gradient concept of degree to which the principle of bivalence typically yields in propositions containing vague concepts. Yet in order successfully to apply that concept of degree itself in (a) and (b), the principle of bivalence must be invoked: it either is or is not true that whether G in (2) has aggregate value or not is a matter of degree. If we answer that ^whether G in (2) has aggregate value or not is a matter of degree^ is itself a matter of degree, the unavoidable reply is that it either is or is not true that ^^whether G in (2) has aggregate value or not is a matter of degree^ is itself a matter of degree^ and so on. (a) and (b) demonstrate that even concepts of degrees of shading admit of degrees of shading; and so that abandoning bivalence exacerbates rather than dissolves the sorites paradox, by generating an infinite regress of concepts of degrees of shading. A resolution to the question of whether G in (2) has aggregate value or not requires some means of differentiating between having and not having a particular degree of aggregate value. This is the principle of bivalence. To this question, Allais would answer affirmatively for all probability assignments to G excluding (3). Von Neumann-Morgenstern would beg to differ; and perhaps might marshal a large sample of experimental subjects to settle the matter statistically by voting. But if whether any preference alternative has aggregate value is, as (a) and (b) imply, a matter of degree, which itself is a matter of degree, etc., then no such means of differentiating between having and not having aggregate value can be found. Then whether any preference alternative has aggregate value or not is indeterminate; and the above argument applies to the concept of indeterminacy as well. Either it, too, is subject to the principle of bivalence; or else it is vague and so generates an infinite regress of degrees of indeterminacy. 17 Schiffer argues that the paradox can be generated for any vague concept whatsoever (ibid., 178, n.1). 18 See Schiffer's critique of degree-theoretic notions of truth at ibid., 191-194. © Adrian Piper Research Archive Foundation Berlin |
