ably this: that science (or philosophy) consists wholly of universal and necessary propositions, a limited number of which are self-evident and form a sufficient body of premises for the deduction of the rest. The principal division between rationalists is upon the question of the nature of the self-evident first principles. For Hobbes (as a nominalist), these could be only arbitrary definitions of terms to be employed. For the great mass of continental rationalists, they are significant truths which are cognized by a special faculty of reason called 'intuition.' For Leibniz, they are again definitions; not of mere terms, however, but of concepts. All, again, are agreed in declaring that observations of matter of fact are invariably particular and contingent; and furthermore that whereas universal propositions are conditional in their import,1 particular propositions are categorical and, as such, existential-i. e., imply the existence of their subjects. Accordingly, the whole realm of truth is divided into two distinct provinces, that of reason and that of sense-perception, the former consisting of necessary implications, the latter of observed facts.

All rationalists are further agreed upon certain metaphysical conclusions. If science is deductive, the world must be such as to be knowable by means of deductive science. If knowledge is to fall into series of logically consecutive propositions, the world itself must be similarly ordered. As Spinoza puts it, the order of thoughts and the order of things are the same. In other words, the relation of premise to conclusion in the system of scientific doctrine must everywhere exactly correspond to a relation of cause and effect in the system of objective reality. From the methodological standpoint, this means that all explanation or proof of anything must be in terms of its causes-knowledge of its effects throws no light upon its nature at all.2 The intuitionalists (or rationalists proper, as we may call them) proceed to a

Thus Hobbes maintains that political science (like geometry) is altogether independent of the question, whether any such thing as a state (or a straight line) has ever existed in the world or not.

2The reasoning from effects to causes, which Hobbes includes in his definition of philosophy, is only an apparent exception; for such reasoning, he finds, is never conclusive.

further inference, in which it may be difficult for us to follow them; namely, that the relations just described as everywhere parallel are in fact identical. The necessity with which the cause produces its effect means that a mind possessed of complete knowledge of the former must be able to predict the latter, that is to say, deduce it from the cause as premise. Thus the fundamental nature of the circle, conceived as produced by a rotating line, is the cause of all its other properties-for example, of the fact that every radius is perpendicular to the tangent at its extremity. From this extreme form of the doctrine, Hobbes is saved by his nominalism; while Leibniz is distinguished by his ‘principle of sufficient reason,' according to which the determination of an effect involves not only logical necessity but the selection of the best out of an infinite number of logically possible alternatives.

The keystone of continental rationalism is the doctrine of substance. While the provinces of reason and sense-perception are wholly distinct, a certain connection arises from the obvious. consideration, that when a fact is attested by perception a number of consequences may logically follow from it. Indeed, every observed fact, no matter how irrelevant it may appear from the standpoint of pure science, is known by the law of causality to be absolutely determined by, and thus deducible from, a series of previous facts. Unless, then, some one or more facts could be conceived as eternally necessary on their own account, and thus as serving to support all other facts, the whole chain of facts, taken in its entirety, must be thought of as hanging in mid-airwhich appeared to be inconceivable. Such necessary fact or facts could, however, be attested by no act of perception; the only adequate witness is reason itself. The entity whose existence is implied in any such eternal fact is called a substance; and those philosophers who believe in the existence of but a single substance call it God. In the nominalistic theory this entity is an unknowable, to which, however, the name of God is also given. Those, too, who accept the existence of a plurality of substances,

regard one of these as supreme, the others being substantial only in a secondary sense, as dependent for their existence on the supreme substance, or God, alone. Thus the existence of God has a unique place in the rationalistic scheme of things. It belongs, in a way, to both kinds of truth. It is a fact evident to reason, and the necessary presupposition of all other facts.

The development of rationalism in the seventeenth century was followed by an equally brilliant development of empiricism in the first half of the eighteenth century. Bacon at last came into his own. The movement is commonly regarded as dating from the publication of Locke's Essay concerning Human Understanding in 1690. Against the common view it has been urged with much force that Locke was at least as much a rationalist as an empiricist; and, indeed, his direct debt seems to be far greater to Descartes and Hobbes than to Bacon. His theory of mathematics and ethics is strongly rationalistic. He believes these . sciences are concerned wholly with the relations between ideas in our own minds, and are in need of no confirmation from experience. The ideas of which they treat are arbitrarily put together by us; and the principal caution which we must observe in their manipulation is to define accurately and use consistently the terms by which we choose to denote them. Locke therefore accepts the distinction between intuitive and demonstrative truths on the one hand and inductive probabilities on the other, and maintains that the latter can never through any process of experience be raised to complete certainty. He believes, for example, that the existence of each one of us is intuitively certain to himself, and that the existence of God is demonstrably certain; while the existence of other persons and things can only be morally certain, that is to say, true enough for all practical purposes.

On the other hand, there are two peculiarities in Locke's doctrine which were very important for the future development of empiricism. In the first place, he attacked one of the most central positions of rationalism by maintaining that all our ideas

of substances, whether material or spiritual, finite or infinite, are inadequate—i. e., fail to correspond accurately to their objects. In the second place, his theory of intuition differed from that of the rationalists in a way which brought into prominence a new problem for science. According to the rationalists, the intuitive truth presents itself to reason as a whole,-subject, predicate, and all. According to Locke, the ideas involved in such a truth must, like all other ideas, be originally derived from experience, however they may have since been modified by processes of abstraction and composition; all that intuition gives is the connection between them. Locke was thus led to undertake to show in detail how various ideas and classes of ideasespecially those which had been generally regarded as intuitive— are indeed derived from our outer and inner experience, or, as he puts it, from sensation and reflection. And though his methods of research were primitively crude, he succeeded in endowing modern psychology with a problem of the first importance: the origin of our ideas.

As mathematics was the science of sciences for rationalism, all other sciences being either extensions or special applications of this one; so for empiricism psychology became the science of sciences, central and fundamental, its method being the organon of philosophy. There had been psychology before this, occasionally (as in the early chapters of Hobbes's Leviathan) containing suggestions whose full value has only recently been realized. But for the most part it was a very superficial affair, a formulation of definitions of various mental processes, based on no evidence except undisciplined observation. The elementary distinction between the logical implications of an idea or a passion and its actual structure in consciousness was either unrecognized or neglected. Psychology is of all sciences the least amenable to deductive treatment, the one in which even today it is most necessary to keep one's eye fixed on the phenomena to be described and declare simply and plainly what one finds there. No modern man before Locke had done this, and Locke himself

was incapable of doing it with any consistency. But he made the attempt inevitable to the generation of investigators who followed him.

The development of English empiricism was carried on in two lines which at first appear to be entirely separate. On the one hand, Mandeville, Shaftesbury, Hutcheson, and Butler attempted in various directions and with varying success to apply the empirical study of human nature to ethical problems. On the other hand, George Berkeley in his New Theory of Vision-a work which marks one of the great turning-points in the history of science-formulated with distinctness the method of introspection and applied it with unsurpassed acuteness and judgment; and in his Principles of Human Knowledge first claimed for psychology the highest place among the sciences, subjecting their fundamental conceptions and principles to its final jurisdiction. The two lines of development meet in David Hume.

The form which the system of empiricism took in Hume's hands may be outlined somewhat as follows. All science must begin with human experience and can never get beyond it. The fundamental science is thus the science of human experience as such; and all explanations whatsoever, if carried back with rigor, must lead us at last to psychological considerations. However, no complete solution of any problem—that is to say, no solution in terms that do not themselves constitute new problems-is ever possible. Science must be fundamentally inductive. All our reasonings must start from principles of whose ground we have no inkling, but which we assume to be true simply because they appear to be verified by our detailed observations of matter of fact. The limit of explicability is reached in the elementary sensations and feelings, the fainter ideas which copy them, and the observed laws of the association and mutual relations of the elements. No existence over and above our perceptions is conceivable. The idea of substance is indispensable to common sense, but wholly useless to science-except as it may be identified with a closely conjoined mass of ideas. The belief in an ex