Logic, Inductive and Deductive

by William Minto

The best way of preventing confusion now is to retain the established titles, recognise that the doctrines behind each have a radically different aim or end, and supply the interpretation of this end from history. What they have in common may be described as the prevention of error, the organisation of reason against error. I have shown that owing to the bent impressed upon it by the circumstances of its origin, the errors chiefly safeguarded by the Aristotelian logic were the errors of inconsistency. The other branch of Logic, commonly called Induction, was really a separate evolution, having its origin in a different practical need. The history of this I will trace separately after we have seen our way through the Aristotelian tradition and its accretions. The Experimental Methods are no less manifestly the germ, the evolutionary centre or starting-point, of the new Logic than the Syllogism is of the old, and the main errors safeguarded are errors of fact and inference from fact.

At this stage it will be enough to indicate briefly the broad relations between Deductive Logic and Inductive Logic.

Inductive Logic, as we now understand it—the Logic of Observation and Explanation—was first formulated and articulated to a System of Logic by J. S. Mill. It was he that added this wing to the old building. But the need of it was clearly expressed as early as the thirteenth century. Roger Bacon, the Franciscan friar (1214-1292), and not his more illustrious namesake Francis, Lord Verulam, was the real founder of Inductive Logic. It is remarkable that the same century saw Syllogistic Logic advanced to its most complete development in the system of Petrus Hispanus, a Portuguese scholar who under the title of John XXI. filled the Papal Chair for eight months in 1276-7.

A casual remark of Roger Bacon's in the course of his advocacy of Experimental Science in the Opus Majus draws a clear line between the two branches of Logic. "There are," he says, "two ways of knowing, by Argument and by Experience. Argument concludes a question, but it does not make us feel certain, unless the truth be also found in experience."

On this basis the old Logic may be clearly distinguished from the new, taking as the general aim of Logic the protection of the mind against the errors to which it is liable in the acquisition of knowledge.

All knowledge, broadly speaking, comes either from Authority, i.e., by argument from accepted premisses, or from Experience. If it comes from Authority it comes through the medium of words: if it comes from Experience it comes through the senses. In taking in knowledge through words we are liable to certain errors; and in taking in knowledge through the senses we are liable to certain errors. To protect against the one is the main end of "Deductive" Logic: to protect against the other is the main end of "Inductive" Logic. As a matter of fact the pith of treatises on Deduction and Induction is directed to those ends respectively, the old meanings of Deduction and Induction as formal processes (to be explained afterwards) being virtually ignored.

There is thus no antagonism whatever between the two branches of Logic. They are directed to different ends. The one is supplementary to the other. The one cannot supersede the other.

Aristotelian Logic can never become superfluous as long as men are apt to be led astray by words. Its ultimate business is to safeguard in the interpretation of the tradition of language. The mere syllogistic, the bare forms of equivalent or consistent expression, have a very limited utility, as we shall see. But by cogent sequence syllogism leads to proposition, and proposition to term, and term to a close study of the relations between words and thoughts and things.

[Footnote 1:] We know for certain—and it is one of the evidences of the importance attached to this trivial-looking pastime—that two of the great teacher's logical treatises, the Topics and the Sophistical Refutations, were written especially for the guidance of Questioners and Respondents. The one instructs the disputant how to qualify himself methodically for discussion before an ordinary audience, when the admissions extracted from the respondent are matters of common belief, the questioner's skill being directed to make it appear that the respondent's position is inconsistent with these. The other is a systematic exposure of sophistical tricks, mostly verbal quibbles, whereby a delusive appearance of victory in debate may be obtained. But in the concluding chapter of the Elenchi, where Aristotle claims not only that his method is superior to the empirical methods of rival teachers, but that it is entirely original, it is the Syllogism upon which he lays stress as his peculiar and chief invention. The Syllogism, the pure forms of which are expounded in his Prior Analytics, is really the centre of Aristotle's logical system, whether the propositions to which it is applied are matters of scientific truth as in the Posterior Analytics, or matters of common opinion as in the Topics. The treatise on Interpretation, i.e., the interpretation of the Respondent's "Yes" and "No," is preliminary to the Syllogism, the reasoning of the admissions together. Even in the half-grammatical half-logical treatise on the Categories, the author always keeps an eye on the Syllogistic analysis.