In what sense can something be at the same time one and many? The problem is familiar since Plato (for example, Republic 524e). In recent times, Whitehead and Russell, in Principia Mathematica, have been struck by the difficulty of the problem: ‘If there is such an object as a class, it must be in some sense one object, yet it is only of classes that many can be predicated. Hence, if we admit classes as objects, we must suppose that the same object can be both one and many, which seems impossible.' It is, however, in Frege's great work, The Foundations of Arithmetic (henceforth, Grundlagen), that many see the final resolution of the old question: how can something be at the same time one and many?

The lead question of Kant's first Critique, indeed his whole Critical Philosophy is ‘How is Metaphysics as a Science Possible?’ Neo-Kantian and recent Anglophone interpretations of Kant's epistemology have concentrated on the ‘Transcendental Analytic’ of the first Critique, and have taken Kant's positive and legitimate sense of metaphysics to concern the necessary conditions of our knowledge of mathematics, natural science, and of course, our common sense knowledge of a spatio-temporal world of objects and events. However, in the ‘Canon of Pure Reason’ in the first Critique Kant indicates quite clearly that, although two of the leading sub-questions of metaphysics — ‘What should I so?’ and ‘What may I hope?’ — cannot be answered on theoretical grounds, they may be answered on practical grounds (A804-05=B832-33). Those practical grounds are elaborated and supplemented (mainly) in the latter two Critiques and the Religion. In each case, however, a definite and positive answer to a metaphysical question involves giving ‘objective reality’ to a concept, e.g., the concepts of freedom or immortality. ‘Objective reality’ involves possible reference to an object, where ‘possible reference’ involves more than merely describing a logical possibility.

The theory that practical reasoning is wholly instrumental says that the only practical function of reason is to tell agents the means to their ends, while their ends are fixed by something other than reason itself. In this essay I argue that Hume has an instrumentalist theory of practical reasoning. This thesis may sound as unexciting as the contention that Kant is a rationalist about morality. For who would have thought otherwise? After all, isn't the ‘instrumentalist’ line in contemporary discussions of this topic descended directly from Hume himself? Contrast the following recent comment from Robert Audi's book on practical reasoning, holding the standard line, with the comment from Christine Korsgaard following it: