Thus, the class of the Exact Sciences consists only of the formal Logic, and pure Mathematics. These two are distinct from all other sciences, because their logical method of procedure is wholly Deductive. Deduction is the process of the mind, by which we pass from a general truth to a particular case under it, that is to say, from more to less inclusive propositions. Stuart Mill argues at much length in his book on Logic, that even the axioms of pure Mathematics are originally gained by Induction, while others claim that the truth of these axioms is perceived intuitively, but no matter how this point is decided, the construction process of the Pure Mathematics is from the General to the Particular. So it is also with the Aristotelian logic, whose Major Premise, whether only supposed to be true or intuitively perceived or inductively proved is always General in its terms. This is the form of Aristotle's Syllogism:—All sinners deserve to be punished; John is a sinner; and therefore, John deserves punishment.

Physical Sciences are those concerned with the classifications and laws of action belonging to material substances. There are a great circle of these, of which Astronomy, Botany, and Chemistry, may serve as examples. They have been mostly developed since the time, and in accordance with the methods, of Lord Bacon; who, in strong reaction against the Deductive logic of Aristotle, exalted Induction or the mode of generalizing from particulars, as the true way of building up Sciences; and, as the subject-matter of each of the physical sciences is well open to observation and experiment, to Induction and Deduction, and to corrective verifications, both inductive and deductive, the new method proved remarkably pregnant and successful. Each of these sciences has a distinct Class of objects or phenomena to which its attention is directed; the class is circumscribed by the scientific Conception and Definition; its devotees as a rule are skilled in using the Baconian tools; and consequently, its conclusions receive the confidence and control the action of men. All of the Physical Sciences are constantly enlarging "the body of exact definitions and sound principles" connected with their several classes "of facts or phenomena."

Moral Sciences are those concerned with the classifications and laws of action belonging to beings having Thoughts and Desires and Will. The most developed of these sciences at present are Metaphysics, Ethics, and Economics. Each of these is concerned with a single class of phenomena, which may be exactly conceived of and defined, and is open to the logical processes by which alone Sciences can be built up. But Induction cannot march up with quite so sure a stride, nor Deduction descend with so large degrees of certainty, in relation to persons endowed with free-will, as in relation to physical substances held firm in the grip of unvaried law. Still, the doubt always attaches far more to the actions of an individual than to the actions of the masses of men. It is much easier to know human nature in general, than one man in particular, because many Inductions guided by observation and History make it almost certain how masses of men will act under a given set of conditions, while any one may act in a contrary way. Deduction, accordingly, cannot hold quite the same place in the Moral Sciences so far as individuals are concerned, as it holds in the Physical and Exact Sciences; but this lack is perhaps more than made up by other advantages. Experience in the moral sciences corresponds to Experiments in the physical sciences. Then there is the great advantage of Introspection; since each man has within himself the means of interpreting and testing the inductions of Metaphysics, Ethics, and Economics. Then also there is the great resource of Feigned Cases, which, provided only they be cases possible to occur, open up to Reasoning a new means of proving and correcting. Besides these, which it enjoys in common with them, Economics, as we shall soon see, possesses one other great advantage over and above the rest of the Moral Sciences.

Since, then, Political Economy deals primarily with Persons, and only quite secondarily with Things, it is, under the definition and on every ground, a "moral science"; yet it must not be confounded in the least with what is sometimes called the science of Morals, or Ethics. There is one word that marks and circumscribes the field of Ethics, and that word is Ought; there is one word also that marks and circumscribes the field of Economics, and that word is Value. Now, the idea of obligation, on which ethical science is founded, and the idea of gainful exchange, on which economical science is founded, are totally distinct ideas. The imperatives of ethical obligation rest upon the consciences of men, and Duty is to be done at all hazards; guilt is incurred if it be neglected; while pecuniary gains and losses, however large, do not, or at least ought not, weigh a feather against an intuition of Right and Wrong. Economics, on the other hand, does not aspire to place its feet upon this lofty ethical ground; no man is ever under any moral obligation to make a trade; he properly makes it or not, according to his present sense of its gainfulness to himself; and so economic science finds a solid and adequate footing upon the expedient and the useful. Ethics appeals only to an enlightened conscience, and certain conduct is approved because it is Right, and for no other reason; Economics appeals only to an enlightened self-interest, and exchanges are made because they are mutually Advantageous, and for no other reason; each of the two Sciences, therefore, has a basis and sphere of its own, and the grounds of the two are not only independent, but also incommensurable.

We will now apply seriatim to Political Economy the four fundamental conditions belonging to all recognized Sciences, and so determine for ourselves whether it be not a strict science, and thus worthy in its leading propositions of all acceptation.

(a) Every science must have to begin with a definite Class of facts, which lie in an easily circumscribable field, and which are not likely to be confounded with other facts of a differing nature. Economy has such a class of facts, that lie in such a field, and that cut themselves off by sharp lines from all other things. Valuables is its class of things. It has nothing to do with any other class of things. Its field is Value, or Sales, or Exchanges. This field is perfectly definite. Sales are never confounded with gifts, and are never confounded with thefts. They have a distinctive character of their own. They have always been in the world, will always be in the world in ever-multiplying volume, and no one ever mistakes their main features for anything else. Anything whatsoever that is salable, or is about to be made so, comes within the view of Economics, and scientifically it cares for nothing else. While it finds its field definite, it also finds it broad. It has no wish to encroach on other sciences, nor will it tolerate any encroachments on its own. Before anything is sold, or is being made ready to sell, it cares nothing what other science employs itself upon that thing; after the thing is sold, Economy loses its interest in it, and other sciences may take it up if they choose. Valuableness is the one quality that constitutes the Class of things with which the Science is conversant, and it claims complete jurisdiction over all things just so far forth as they have this one quality, and no farther. Now there is in the actual world such a Class of things; its exterior boundaries have been exactly ascertained by a long series of Inductions and Deductions, tentative, corrective, and confirmatory; and accordingly, Political Economy has now in full possession the first grand condition of a Science.

(b) This great class of facts, thus reached by logical Generalization and grasped and held by a mental Conception and fixed by an adequate verbal Definition, is remarkably open to all the logical processes of reasoning, by which alone sciences are constructed, and thus possesses in full measure the second grand condition of the Sciences. Not one logical resource is denied to the economists: all the tools of the scientific workshop are at their hands. Let us now catalogue these in their order.

(1) Induction. This is the logical and universal process, by which the mind naturally passes up from a certain number of observed cases, in which a certain quality appears, to a Generalization, which is a conception of the mind followed by a statement in words to the effect, that all possible cases of that kind will exhibit the quality already observed in the few cases. It has as its basis a confidence in the resemblances and uniformities of Nature; it proceeds upon the axiom that Nature throughout is consistent with herself; and this confidence has been ten thousand times justified in the issue, when it is found that Nature preordained the Sciences by causing grand analogies to run through each department of her works, including man and his works. The structure of the human mind corresponds with these objective resemblances; it seizes upon them, and delights in them, and naturally and joyfully infers and concludes that what has been observed of a part may be safely affirmed of the whole of that kind; accordingly, the world over, when certain things are found to be true in a considerable number of cases, the mind leaps over space and time to a whole class, and frames for itself a general rule or principle, which binds all the cases into one bundle, and thereafter confidently affirms what is known to be true of some to be probably true of all. This is inductive Generalization; and the strength and the joy of it is well expressed by Descartes: "I have thought that I could take as a just generalization that which I very clearly and vividly conceived to be true."

Experience in Economics corresponds to Experiment in the Physical Sciences, and furnishes to Induction all the fuel it can ask for to feed its logical furnace and to forge the chains that bind the Cases to the Classes. Personal experience in buying and selling, local experience in buying and selling, and national experience in buying and selling, with all that belongs to these, the records of which are full to overflowing, afford to the inductive inquirer in Economics an inexhaustible supply of material. Instances abound. Particulars may be gathered up one by one on every hand and linked into the inductive chain. If any doubt be felt about the strength of any one of these chains, another one may at once be linked in terms drawn from another field of Experience with a view to test the strength of the first. Most fortunate from this point of view is the United States, because here there are States with substantive powers of control over most matters of trade within their borders, as well as a Nation with sovereign powers of control over some points of trade within the country as a whole. This feature has given birth to commercial experiments as well as commercial experience of all kinds; and Induction rejoices in all these abundant materials for generalization thus furnished free of cost to Science, though unfortunately not free of cost to the People.

(2) Deduction. This is a logical process exactly the reverse of the first, in that it descends from a generalized statement reached by the inductive process to some particular, or subordinate class of particulars, ostensibly covered by the general maxim. Induction examines a number of particulars, and then makes a leap, it may be a long leap, over all intervening particulars, to its Generalization clamping them. The main use of Deduction is to make sure of any one of these overleaped particulars, which may come into importance, and thus confirm the generalization, or correct it. It is not strictly true, what is often alleged against deductive reasoning, that there is nothing new in its result, that the Induction had already passed through that particular in rising to its Generalization, and therefore to descend to any particular link to examine that, is something useless. The exact truth is, that it is useless to examine again deductively the very particulars that were carefully studied inductively, but on the other hand there is always much actually untraversed territory between these already examined particulars and the inductive generalization, and Deduction is often very useful in carrying us down to questionable points in this territory. Even Lord Bacon, who scorned the syllogism, admits this: "Axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active."