ABSTRACT

Time, in a different aspect of that Scheme of Things, is indispensable to reason. Mathematics can explore the meaning of what is already implicitly stated, of what is already given. A mathematical model of a society in its economic affairs can treat the members of that society as gaining access steadily or step-by-step to items in a bank of knowledge which the model in some sense specifies. Such a model has no place for novelty. When the analyst or model-constructor is not detached and 'omniscient', but is a participant in the process of discovery of things not deducible from existing knowledge, then no model can encompass the course of the society's history. Mathematics turns its back on fundamental novelty, except when it is itself undergoing fundamental transformation by the invention of concepts not implicit in what has been hitherto recognized as mathematics. Time is a denial of the omnipotence of reason.