ABSTRACT
The theory of real numbers gives us a consistent and complete framework for handling the concept of quantity. Empiricists, therefore, take exception to the application of the theory of real numbers to the world of experience, and deny that time can be infinitely divisible or that there can be mathematical instants of time. It is a problem, not only about time, but about every sort of measurement, and the theory of knowledge generally. The disadvantages of doing the former are, first, that such a theory will be very clumsy and, secondly, that the 'noticeably' of 'not noticeably greater than' is indefinite: it varies from occasion to occasion; in particular, it changes with each new refinement of measuring technique. Our inability to discriminate we ascribe entirely to ourselves and our own imperfect organs, and not to any inherent indivisibility of what we are failing to divide.
