1. Cf. Mackenzie, Introduction to Social Philosophy, p. 58. Also Bagehot, Economic Studies, no. 1: "The Presuppositions of English Political Economy."
2. There are three types or schools of mathematical economic theory, connected with the names of Cournot, Jevons, and Walras respectively. Dr. Vilfredo Pareto, of the University of Lausanne (successor of Walras), is now the most prominent exponent of the mathematical method. Among "literary" pure theorists, Wicksteed, Schumpeter, and Pantaleoni stand out.
3. Logic, book VI, chaps. IX and X.
4. The relations between deduction and induction are intimate, and a rigid separation or contrast between the two methods is misleading. A more careful study of the fundamentals of scientific method will be undertaken hereafter (chapter VII). We shall see that there is ultimately no such fact as deduction as commonly understood, that inference is from particulars to particular, and that generalization is always tentative and a mere labor-saving device. The fact is, however, that we can study facts intelligently and fruitfully only in the light of hypotheses, while hypotheses have value more or less in proportion to the amount of antecedent concrete knowledge of fact on which they are based. The actual procedure of science thus consists of making and testing hypotheses. The first hypotheses in any field are usually the impressions of "common sense"; i.e., of that superficial knowledge forced upon intelligence by direct contact with the world. Study, in the light of any hypothesis, corrects or refutes the guiding generalization and suggests new points of view, to be criticized and tested in the same way, and so the organization of the material proceeds. The importance of generalization arises from the fact that as our minds are built, it is nearly fruitless to attempt to observe phenomena unless we approach them with questions to be answered. This is what a hypothesis really is, a question. Superficial observation suggests questions which study answers. If and so long as it answers a question affirmatively and the answer is not contradicted by the test of practical application or casual observation, we have a law of nature, a truth about our environment which enables us to react intelligently to it in our conduct.
There is, then, little if any use for induction in the Baconian sense of an exhaustive collection and collation of facts, though in some cases this may be necessary and fruitful. On the other hand, there is equally little use for deduction taken as doing more than suggesting hypotheses, subject to verification. It is to be noted, however, that our common-sense generalizations have a very high degree of certainty in some fields, giving us, in regard to the external world, for instance, the "axioms" of mathematics. Even more important in the present connection is the r鬺e of common sense or intuition in the study of human phenomena. Observation and intuition are, indeed, hardly distinguishable operations in much of the field of human behavior. Our knowledge of ourselves is based on introspective observation, but is so direct that it may be called intuitive. Its extension to our fellow human beings is also based upon the interpretation of the communicative signs of speech, gesture, facial expression, etc., far more than upon direct observation of behavior, and this process of interpretation is highly instinctive and subconscious in character. Many of the fundamental laws of economics are therefore properly "intuitive" to begin with, though of course always subject to correction by induction in the ordinary sense of observation and statistical treatment of data.
These brief statements must not be thought of as dealing with philosophical problems. The writer is, like Mill, an empiricist, holding that all general truths or axioms are ultimately inductions from experience. By induction as a method is meant deliberate, scientific induction, the planned study of instances for the purpose of ascertaining their "law." And deduction means reaching new truth by the application of general laws to particular cases. In the present view both of these processes are regarded as suggestive merely, exhaustive induction and conclusive deduction being alike impossible.
5. The reader will recall Comte's arrangement of the sciences in the order of generality of the principles they establish. Mathematics, the properties of space and of quantity in the abstract, is applicable to all phenomena—and tells us correspondingly little about any of them. The laws of matter, of living matter, etc., are less general and more concretely real. The same principles are applicable within any grand division of knowledge.
6. Cf. Mill's Essays on Unsettled Questions, no. 5, which really leaves little to be said on the subject. Also Cairnes, on the Character and Logical Method of Political Economy, and the discussions of methodology of the English economists generally. The conception of the "economic man" was one way of emphasizing the abstract and simplified character of the premises of the science. Keynes's Scope and Logical Method of Political Economy is as ably clear and conclusive discussion of this whole subject.
7. It is necessary to admit that in fact only a pitifully small fraction of the race have any particular theoretical sense in the mechanical field either. Certainly a vast majority of literate adults with elementary experience with machinery have no real comprehension of the most fundamental principles of the transformation and equivalence of forces. As far as their own insight is concerned, they could easily be taken in with crude perpetual motion schemes, and an astonishing proportion are willing to back their own judgment in such matters against what they know to be the unanimous verdict of the scientific world. The recurrent discussion of such projects in our National Congress are familiar. A certain mechanical "handiness" is probably all that is to be found in any but the rare scientific minds, and these handy men are precisely the ones who seem most likely to waste their lives and means over palpably absurd enterprises. A large proportion even of competent engineers have neither comprehension nor appreciation of physical theory.
8. The static state idea is further developed along rigidly theoretical lines by Professor Schumpeter in Austria.
9. We shall attempt to show that it does not represent, as Professor Clark contends, the assumptions implicit in the classical economic theory. (See chapter II.)
10. Cf. Dewey's definition of reason as the method of social diagnosis and prognosis.
11. We need not here more than mention the obvious fact that the theoretical method is applicable to monopoly as well as competition and has dealt with both. It has been, of course, a theoretically "ideal" monopoly also—the real assumption being an exceptional instance of perfect monopoly in a general system of perfect competition. The contrast between theory and reality and the significance of the former is of the same sort in both cases, and we shall also discuss the meaning of perfect monopoly in the proper connection. (Chapter VI.)
12. It will be perceived that the word "profit" is here used in the sense of "pure profit, a distributive share different from the returns to the productive services of land, labor, and capital.