Abstract
According to the sortal conception of the universe of individuals every individual falls under a highest sortal, or category. It is argued here that on this conception the identity relation is defined between individuals a and b if and only if a and b fall under a common category. Identity must therefore be regarded as a relation of the form \(x=_{Z}y\), with three arguments x, y, and Z, where Z ranges over categories, and where the range of x and y depends on the value of Z. An identity relation of this kind can be made good sense of in Martin-Lof’s type theory. But identity so construed requires a reformulation of Hume’s Principle that makes this principle unfit for explaining the sortal concept of cardinal number. The Neo-Logicist can therefore not appeal to the sortal conception in tackling the Julius Caesar problem, as proposed by Hale and Wright (The reason’s proper study. Oxford University Press, Oxford, pp. 335–396, 2001b).
Published Version
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