In his theory of knowledge Aristotle begins by brushing aside the Platonic view. Science requires no such "Ideas," transcending sense-experience, as Plato had spoken of; they are, in fact, no more than "poetic metaphors." What is required for science is not that there should be a "one over and above the many" (that is, such pure concepts, unrealised in the world of actual perception, as Plato had spoken of), but only that it should be possible to predicate one term universally of many others. This, by itself, means that the "universal" is looked on as a mere residue of the characteristics found in each member of a group, got by abstraction, _i.e._ by leaving out of view the characteristics which are peculiar to some of the group and retaining only those which are common to all. If Aristotle had held consistently to this point of view, his theory of knowledge would have been a purely empirical one. He would have had to say that, since all the objects of knowledge are particular facts given in sense-perception, the universal laws of science are a mere convenient way of describing the observed uniformities in the behaviour of sensible things. But, since it is obvious that in pure mathematics we are not concerned with the actual relations between sensible data or the actual ways in which they behave, but with so-called "pure cases" or ideals to which the perceived world only approximately conforms, he would also have had to say that the propositions of mathematics are not strictly true. In modern times consistent empiricists have said this, but it is not a position possible to one who had passed twenty years in association with the mathematicians of the Academy, and Aristotle’s theory only begins in naturalism to end in Platonism. We may condense its most striking positions into the following statement. By science we mean _proved_ knowledge. And proved knowledge is always "mediated"; it is the knowledge of _conclusions_ from premisses. A truth that is scientifically known does not stand alone. The "proof" is simply the pointing out of the connection between the truth we call the conclusion, and other truths which we call the premisses of our demonstration. Science points out the _reason why_ of things, and this is what is meant by the Aristotelian principle that to have science is to know things through their _causes_ or _reasons why_. In an ordered digest of scientific truths, the proper arrangement is to begin with the simplest and most widely extended principles and to reason down, through successive inferences, to the most complex propositions, the _reason why_ of which can only be exhibited by long chains of deductions. This is the order of logical dependence, and is described by Aristotle as reasoning _from_ what is "more knowable in its own nature,"[#] the simple, to what is usually "more familiar to _us_," because less removed from the infinite wealth of sense-perception, the complex. In _discovery_ we have usually to reverse the process and argue from "the familiar to us," highly complex facts, to "the more knowable in its own nature," the simpler principles implied in the facts.