The old empiricist view, as typified by Mill, was that the mind had been impressed with all its principles, such as the truths of arithmetic, the axioms of geometry, and the law of causation, by an uncontradicted course of experience, until it generalized facts into ‘laws,’ and was enabled to predict a similar future with certainty.  But this theory had really been exploded in advance by Hume.  Facts do not appear as causally connected, nor, if they did, would this guarantee that they will continue to do so in the future.  The continuum of experience, we may add, is not given as a series of arithmetical units or geometrical equalities, unless we deliberately measure it out in accordance with mathematical principles.  Empiricism thus gives no real account of the scientific rational order of the world.

But does it follow from the failure of empiricism that apriorism is true?  This has always been assumed, and held to dispense rationalist philosophers from giving any direct and positive proof that these principles are a priori truths.  But manifestly their procedure is logically far from cogent.  If a third explanation can be thought of, it will not follow that apriorism is true.  All that follows is that something has to be assumed before experience proves it.  What that something is, and whence it comes, remains an open question.  Moreover, apriorism has not escaped from the empirical doubt about the future.  Even granted that facts now conform to the necessities of our thoughts, why should they so comport themselves for ever?

Let us, therefore, try a compromise, which ignores neither that which we bring to experience (like empiricism), nor that which we gain from experience (like apriorism).  This compromise is effected by the doctrine of postulation.  For though a postulate proceeds from us, and is meant to guide thought in anticipating facts, it yet allows the facts to test and mould it; so that its working modifies, expands, or restricts its demands, and fits it to meet the exigencies of experience, and permits, also, a certain reinterpretation of the previous ‘facts’ in order to conform them to the postulate.

A postulate thus fully meets the demands of apriorism.  It is ‘universal’ in claim, because it is convenient and economical to make a rule carry as far as it will go; and it is ‘necessary,’ because all fresh facts are on principle subjected to it, in the hope that they will support and illustrate it.  Yet a postulate can never be accused of being a mere sophistication, or a bar to the progress of knowledge, because it is always willing to submit to verification in the course of fresh experience, and can always be reconstructed or abandoned, should it cease to edify.  A long and successful course of service raises a postulate to the dignity of an ’axiom’—­i.e., a principle which it is incredible anyone should think worth disputing—­whereas repeated failure in application degrades it to the position of a prejudice—­i.e., an a priori opinion which is always belied by its consequences.