Even in cases where the inquiry is not of this nature, hypothesis is of use in the suggestion of future investigations, and, as such, is frequently indispensable.
View of Mr. Mill.—Nearly every thing which is now theory, was once hypothesis, says Mill. "The process of tracing regularity in any complicated, and, at first sight, confused set of appearances, is necessarily tentative: we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena we learn what corrections to make in our assumption. The simplest supposition which accords with any of the most obvious facts, is the best to begin with, because its consequences are the most easily traced. This rude hypothesis is then rudely corrected, and the operation repeated, until the deductive results are at last made to tally with the phenomena. Let any one watch the manner in which he himself unravels any complicated mass of evidence; let him observe how, for instance, he elicits the true history of any occurrence from the involved statements of one or of many witnesses. He will find that he does not take all the items of evidence into his mind at once, and attempt to weave them together; the human faculties are not equal to such an undertaking; he extemporizes, from a few of the particulars, a first rude theory of the mode in which the facts took place, and then looks at the other statements, one by one, to try whether they can be reconciled with the provisional theory, or what corrections or additions it requires to make it square with them. In this way, which, as M. Comte remarks, has some resemblance to the methods of approximation of mathematicians, we arrive by means of hypothesis at conclusions not hypothetical."
§ V.—Different Forms of Reasoning.
It remains to treat briefly of the different forms of reasoning, as founded in the laws of thought.
How far these Forms fall within the Province of Psychology.—As there are different kinds or modes of reasoning, according to the difference of the subject-matter or material about which our reasoning is employed, so there are certain general forms into which all reasoning may be cast, and which, according to the laws of thought, it naturally assumes. To treat specifically of these forms, their nature, use, and value, is the business of logic; but, in so far as they depend upon the laws of thought, and are merely modes of mental activity as exercised in reasoning, they are to be considered, in connection with other phenomena of the mind, by the psychologist. Briefly to describe these forms, and then to consider their value, is all that I now propose. I begin with the proposition, as the starting point in every process of reasoning.
I. Analysis of the Proposition.
What constitutes a Proposition.—All reasoning deals with propositions, which are judgments expressed. Every proposition involves two distinct conceptions, and expresses the relation between them; affirms the agreement or disagreement of the one with the other. As when I say, Snow is white, the conception of snow is before my mind, and also of whiteness; I perceive that the latter element enters into my notion of snow, and constitutes one of the qualities of the substance so called; I affirm the relation of the two, accordingly, and this gives the proposition enunciated. Every proposition then consists of these several parts, a word or words expressing some conception, a word or words expressing some other conception, a word or words expressing the relation of the two. The words which designate these two conceptions are called the terms of the proposition, and, according to the above analysis, there are, in every proposition, always two terms. That term or conception of which something is affirmed, is called the subject, that which is affirmed of the same, the predicate, and the word which expresses the relation of the two, the copula. In the above proposition, snow is the subject, white, the predicate, and is, the copula.
Quality and Quantity.—Propositions are distinguished as to quality and quantity. The former has reference to the affirmative or negative character of the proposition, the latter to its comprehensiveness. Every proposition is either affirmative or negative, which is called its quality. As to quantity, every proposition is either universal, affirming something of the whole of the subject—as, All men are mortal; or else particular, affirming something of only a part of the subject—as, Some tyrants are miserable.
Four kinds of categorical Propositions.—We have, then, four kinds of categorical propositions, viz., universal affirmative, universal negative, particular affirmative, particular negative. That is, with the same subject and predicate, it is always possible to state four distinct propositions; as, every A is B, no A is B, some A is B, some A is not B. For the sake of convenience, logicians designate these different kinds of propositions severally by the letters A, E, I, O. Propositions that thus differ in quantity and quality are said to be opposed to each other. Of these, the two universals, A and E, are called contraries; the two particulars, I and O, sub-contraries; the universal affirmative, and the particular affirmative, A and I, also the universal negative and the particular negative, E and O, are respectively subalterns; while the universal affirmative and the particular negative, A and O, as also the universal negative and particular affirmative, E and I, are contradictories.
Rules of Opposition.—The following rules will be found universally applicable to propositions as opposed to each other. If the universal is true, so is the particular. If the particular is false, so is the universal. Contraries are never both true, but may be both false. Sub-contraries are never both false, but may be both true. Contradictories are never both true, or both false, but always one is true, the other false. The truth of these maxims will be evident on applying them to any proposition and its opposites, as for example, to the affirmation, Every man is mortal.