Quantity and Number
Quantity is the fi rst category that Aristotle lists after substance. More than any other category, it has an extraordinary epistemological clarity. “2 + 2 = 4” is the paradigm of objective and irrefutable knowledge, and “2 million + 2 million = 4 million” is not far behind in certainty, despite its distance from immediate perception. Indeed, certainties about quantity extend to the infi nite-for example, we know that the counting numbers do not run out. Nor does this certainty come at the expense of application to reality. If we put two rabbits and two rabbits in a box and later fi nd fi ve rabbits in there, it is our absolute certainty that 2 + 2 = 4 that allows us to infer that the rabbits must have bred. Continuous quantities are no less open to perfection of knowledge: The quantity π, the ratio of the circumference of any circle to its diameter, is calculable to any degree of precision that computers can cope with (currently claimed to be ten trillion decimal places). 1 The mathematics of quantity delivers certainty about reality, to the envy of other disciplines, including philosophy.