There belongs, accordingly, to methodology a list of problems which we can divide, to be sure only in abstracto, into three separate groups. First, methodology has to analyze the methods which have been technically developed in the different fields of knowledge into the elementary forms of our thinking from which they have been built up. Next to this work of analyzing, there comes a second task which may be called a normative one; for it follows that we must set forth and deduce systematically from their sources the nature of these manifold elements, their resulting connection, and their validity. To these two offices must be added a third that we may call a potiori a synthetic one; for finally we must reconstruct out of the elements of our thinking, as revealed by analysis, the methods belonging to the different fields of knowledge and also determine their different scope and validity.
The beginning of another conception of the office of methodology can be found in those thoughts which have become significant, especially in Leibnitz's fragments and drafts of a calculus ratiocinator or a spécieuse générale. The foregoing discussion has set aside all hope that these beginnings and their recent development may give, of the possibility of constructing the manifold possible methods a priori, that is, before or independent of experience. However, it remains entirely undecided, as it should in this our preliminary account of the office of general methodology, whether or not all methods of our scientific thought will prove to be ultimately but branches of one and the same universal method, a thought contained in the undertakings just referred to. Although modern empiricism, affiliated as it is with natural science, tends to answer this question in the affirmative even more definitely and dogmatically than any type of the older rationalism, still the question is one that can be decided only in the course of methodological research.
The conception of a methodology of scientific thought can be said to be almost as old as scientific thought itself; for it is already contained essentially, though undifferentiated, in the Socratic challenge of knowledge. None the less, the history of methodology, as the history of every other science, went through the course of which Kant has given a classical description. "No one attempts to construct a science unless he can base it on some idea; but in the elaboration of it the schema, nay, even the definition which he gives in the beginning of his science, corresponds very seldom to his idea, which, like a germ, lies hidden in the reason, and all the parts of which are still enveloped and hardly distinguishable even under microscopical observation."[[5]]
We are indebted to the Greek, and especially to the Platonic-Aristotelian philosophy for important contributions to the understanding of the deductive method of mathematical thought. It was precisely this trend of philosophic endeavor which, though furnishing for the most part the foundation of methodological doctrine well on into the seventeenth century, offered no means of differentiating the methods that are authoritative for our knowledge of facts. What Socrates was perhaps the first to call "induction," is essentially different, as regards its source and aim, from the inductive methods that direct our research in natural and mental science. For it is into these two fields that we have to divide the totality of the sciences of facts, the material sciences, let us call them, in opposition to the formal or mathematical sciences,—that is, if we are to do justice to the difference between sense and selfperception, or "outer" and "inner" perception.
Two closely connected forces especially led astray the methodological opinions regarding the material sciences till the end of the eighteenth century, and in part until the beginning of the nineteenth century. We refer, in the first place, to that direction of thought which gives us the right to characterize the Platonic-Aristotelian philosophy as a "concept philosophy;" namely, the circumstance that Aristotelian logic caused the "concept" to be set before the "judgment." In short, we refer to that tendency in thought which directs the attention not to the permanent in the world's occurrences, the uniform connections of events, but rather to the seemingly permanent in the things, their essential attributes or essences. Thus the concept philosophy, as a result of its tendency to hypostasize, finds in the abstract general concepts of things, the ideas, the eternal absolute reality that constitutes the foundation of things and is contained in them beside the accidental and changing properties.[[6]] Here we have at once the second force which inspired the ancient methodology. These ideas, like the fundamentally real, constitute that which ultimately alone acts in all the coming into existence and the going out of existence of the manifold things. In the Aristotelian theory of causation, this thought is made a principle; and we formulate only what is contained in it, when we say that, according to it, the efficient and at the same time final causes can be deduced through mere analysis from the essential content of the effects; that, in fact, the possible effects of every cause can be deduced from the content of its definition. The conceptual determination of the causal relation, and with it in principle the sum total of the methods in the material sciences, becomes a logical, analytical, and deductive one. These sciences remain entirely independent of the particular content of experience as this broadens, and so do also the methods under discussion.
As a consequence, every essential difference between mathematical thought and the science of causes is done away with in favor of a rationalistic construction of the methods of material science. Accordingly, throughout the seventeenth century, the ideal of all scientific method becomes, not the inductive method that founded the new epoch of the science of to-day, but the deductive mathematical method applied to natural scientific research. The flourish of trumpets with which Francis Bacon hailed the onslaught of the inductive methods in the natural science of the time, helped in no way; for he failed to remodel the traditional, Aristotelian-Scholastic conception of cause, and, accordingly, failed to understand both the problem of induction and the meaning of the inductive methods of the day.[[7]] Descartes, Hobbes, Spinoza, and related thinkers develop their mathesis universalis after the pattern of geometrical thinking. Leibnitz tries to adapt his spécieuse générale to the thought of mathematical analysis. The old methodological conviction gains its clear-cut expression in Spinoza's doctrine: "Aliquid efficitur ab aliqua re" means "aliquid sequitur ex ejus definitione."
The logically straight path is seldom the one taken in the course of the history of thought. The new formulation and solution of problems influence us first through their evident significance and consequences, not through the traditional presuppositions upon which they are founded. Thus, in the middle of the seventeenth century, when insight into the precise difference between mental and physical events gave rise to pressing need for its definite formulation, no question arose concerning the dogmatic presupposition of a purely logical (analytisch) relationship between cause and effect; but, on the contrary, this presupposition was then for the first time brought clearly before consciousness. It was necessary to take the roundabout way through occasionalism and the preëstablished harmony, including the latter's retreat to the omnipotence of God, before it was possible to miss the question of the validity of the presupposition that the connection between cause and effect is analytic and rational.
Among the leading thinkers of the period this problem was recognized as the cardinal problem of contemporaneous philosophy. It is further evidence how thoroughly established this problem must have been among the more deeply conceived problems of the time in the middle of the eighteenth century, that Hume and Kant were forced to face it, led on, seemingly independently of each other, and surely from quite different presuppositions and along entirely different ways. The historical evolution of that which from the beginning has seemed to philosophy the solving of her true problem has come to pass in a way not essentially different from that of the historical evolution in all other departments of human knowledge. Thus, in the last third of the seventeenth century, Newton and Leibnitz succeeded in setting forth the elements of the infinitesimal calculus; and, in the fifth decade of the nineteenth century, Robert Mayer, Helmholtz, and perhaps Joule, formulated the law of the conservation of energy. In one essential respect Hume and Kant are agreed in the solution of the new, and hence contemporaneously misunderstood, problem. Both realized that the connection between the various causes and effects is not a rational analytic, but an empirical synthetic one. However, the difference in their presuppositions as well as method caused this common result to make its appearance in very different light and surroundings. In Hume's empiricism the connection between cause and effect appears as the mere empirical result of association; whereas in Kant's rationalism this general relation between cause and effect becomes the fundamental condition of all possible experience, and is, as a consequence, independent of all experience. It rests, as a means of connecting our ideas, upon an inborn uniformity of our thought.
Thus the way was opened for a fundamental separation of the inductive material scientific from the deductive mathematical method. For Hume mathematics becomes the science of the relations of ideas, as opposed to the sciences of facts. For Kant philosophical knowledge is the knowledge of the reason arising from concepts, whereas the mathematical is that arising from the construction of concepts. The former, therefore, studies the particular only in the universal; the latter, the universal in the particular, nay, rather in the individual.
Both solutions of the new problem which in the eighteenth century supplant the old and seemingly self-evident presupposition, appear accordingly embedded in the opposition between the rationalistic and empiristic interpretation of the origin and validity of our knowledge, the same opposition that from antiquity runs through the historical development of philosophy in ever new digressions.