Inductive Reasoning no Exception.—It may be supposed that the inductive method of reasoning is an exception to this rule, inasmuch as we proceed, in that case, not from the general to the particular, but the reverse. Whatever may be true of deduction, is not induction essentially a synthetic process? So it might, at first, appear. I have observed, for example, that several animals of a particular species, sheep, for instance, chew the cud. Having observed this in several instances, I presently conclude that the same is true of the whole class to which these several individuals belong, in other words, that all sheep are ruminant. Extending my observation further, I find other species of animals likewise chewing the cud. I observe, moreover, that every animal, possessing this characteristic, is distinguished by the circumstance of having horns and cloven hoofs; I find, so far as my observation goes, the two things always associated, and hence am led, on observing the one, immediately to infer the other. The proposition that was at the outset particular, now becomes general, viz., all animals that have horns and cloven hoofs are ruminant. Is the conclusion at which I thus arrive, involved in the premiss with which I start? Is the fact that all horned and cloven-footed animals are ruminant, implied and contained in the fact that some horned and cloven-footed animals, that is, so many as I have observed, are so?
Even here the Evidence of the Conclusion lies in the Premiss.—A little reflection will convince us that these questions are to be answered in the affirmative. If the conclusion be itself correct and true, then it is a truth involved in the previous proposition; for whatever evidence I have of the truth of my conclusion, that all animals of this sort are ruminant, is manifestly derived from, and therefore contained in, the fact that such as I have observed are so. I have no other evidence in the case supposed. If this evidence is insufficient, then the conclusion is not established. If it be sufficient, then the conclusion which it establishes, is derived from and involved in it.
The argument fully and scientifically stated, runs thus:
A, B, C, animals observed, are ruminant. But A, B, C, represent the class Z to which they belong.
Therefore, class Z is ruminant.
Admitting now the correctness of my observation in respect to A, B, C, that they are ruminant, the argument turns entirely upon the second proposition that A, B, C, represent the class Z, so that what is true of them in this respect, is true of the whole class. If A, B, C, do represent the class Z, then to say that A, B, C, are ruminant, is to say that Z is so. The one is contained in the other. If they do not, then the conclusion is itself groundless, and there is no occasion to inquire in what it is contained, or whether it is contained in any thing. It is no longer a valid argument and therefore cannot be brought in evidence that some reasoning is not analytic.
What sort of Propositions constitute Reasoning.—It is hardly necessary to state that not any and every series of propositions constitute reasoning. The propositions must be consecutive, following in a certain order, and not only so, but must be in such a manner connected with and related to each other, that the truth of the final proposition shall be manifest from the propositions which precede. To affirm that snow is white, that gold is more valuable than silver, and that virtue is the only sure road to happiness, is to state a series of propositions, each one of which is true, but which have no such relation to each other as to constitute an argument. The truth of the last proposition does not follow from the truth of the preceding ones.
§ II.—Relation of Judgment and Reasoning.
Judgment Synthetic, Reasoning Analytic.—The relation of judgment and reasoning to each other becomes evident from what has been said of the nature of the reasoning process. Judgment is essentially synthetic. Reasoning, essentially analytic. The former combines, affirms one thing to be true of another; the latter divides, declares one truth to be contained in another. All reasoning involves judgment, but all judgment is not reasoning. The several propositions that constitute a chain of reasoning, are so many distinct judgments. Reasoning is the evolution or derivation of one of these judgments, viz., the conclusion, from another, viz., the premiss. It is the process by which we arrive at some of our judgments.