On the Philosophy of Discovery, Chapters Historical and Critical

by William Whewell

But without insisting upon the name, are we to suppose that the Dichotomous Method of the Sophistes Dialogue, (I may add of the Politicus, for the method is the same in this Dialogue also,) is the method of division of a subject according to its natural members, of which Plato speaks in the Phædrus?

If the Sophistes be the work of Plato, the answer is difficult either way. If this method be Plato's Dialectic, how came he to omit to say so there? how came he even to seem to deny it? But on the other hand, if this dichotomous division be a different process from the division called Dialectic in the Phædrus, had Plato two methods of division of a subject? and yet has he never spoken of them as two, or marked their distinction?

This difficulty would be removed if we were to adopt the opinion, to which others, on other grounds, have been led, that the Sophistes, though of Plato's time, is not Plato's work. The grounds of this opinion are,—that the doctrines of the Sophistes are not Platonic: (the doctrine of Ideas is strongly impugned and weakly defended:) Socrates is not the principal speaker, but an Eleatic stranger: and there is, in the Dialogue, none of the dramatic character which we generally have in Plato. The Dialogue seems to be the work of some Eleatic opponent of Plato, rather than his.

(Rep. B. VII.) But we can have no doubt that the Phædrus contains Plato's real view of the nature of Dialectic, as to its form; let us see how this agrees with the view of Dialectic, as to its matter and object, given in the seventh Book of the Republic.

According to Plato, Real Existences are the objects of the exact sciences (as number and figure, of Arithmetic and Geometry). The things which are the objects of sense transitory phenomena, which have no reality, because no permanence. Dialectic deals with Realities in a more general manner. This doctrine is everywhere inculcated by Plato, and particularly in this part of the Republic. He does not tell us how we are to obtain a view of the higher realities, which are the objects of Dialectic: only he here assumes that it will result from the education which he enjoins. He says (§ 13) that the Dialectic Process (ἡ διαλεκτικὴ μέθοδος) alone leads to true science: it makes no assumptions, but goes to First Principles, that its doctrines may be firmly grounded: and thus it purges the eye of the soul, which was immersed in barbaric mud, and turns it upward; using for this purpose the aid of the sciences which have been mentioned. But when Glaucon inquires about the details of this Dialectic, Socrates says he will not then answer the inquiry. We may venture to say, that it does not appear that he had any answer ready.

Let us consider for a moment what is said about a philosophy rendering a reason for the First Principles of each Science, which the Science itself cannot do. That there is room for such a branch of philosophy in some sciences, we easily see. Geometry, for instance, proceeds from Axioms, Definitions and Postulates; but by the very nature of these terms, does not prove these First Principles. These—the Axioms, Definitions and Postulates,—are, I conceive, what Plato here calls the Hypotheses upon which Geometry proceeds, and for which it is not the business of Geometry to render a reason. According to him, it is the business of "Dialectic" to give a just account of these "Hypotheses." What then is Dialectic?

(Aristotle.) It is, I think, well worthy of remark, that Aristotle, giving an account in many respects different from that of Plato, of the nature of Dialectic, is still led in the same manner to consider Dialectic as the branch of philosophy which renders a reason for First Principles. In the Topics, we have a distinction drawn between reasoning demonstrative, and reasoning dialectical: and the distinction is this:—(Top. I. 1) that demonstration is by syllogisms from true first principles, or from true deductions from such principles; and that the Dialectical Syllogism is that which syllogizes from probable propositions (ἠξ ἠνδόξων). And he adds that probable propositions are those which are accepted by all, or by the greatest part, or by the wise. In the next chapter, he speaks of the uses of Dialectic, which, he says, are three, mental discipline, debates, and philosophical science. And he adds (Top. I. 2, 6) that it is also useful with reference to the First Principles in each Science: for from the appropriate Principles of each science we cannot deduce anything concerning First Principles, since these principles are the beginning of reasoning. But from the probable principles in each province of science we must reason concerning First Principles: and this is either the peculiar office of Dialectic, or the office most appropriate to it; for it is a process of investigation, and must lead to the Principles of all methods.

That a demonstrative science, as such, does not explain the origin of its own First Principles, is undoubtedly true. Geometry does not undertake to give a reason for the Axioms, Definitions, and Postulates. This has been attempted, both in ancient and in modern times, by the Metaphysicians. But the Metaphysics employed on such subjects has not commonly been called Dialectic. The term has certainly been usually employed rather as describing a Method, than as determining the subject of investigation. Of the Faculty which apprehends First Principles, both according to Plato and to Aristotle, I will hereafter say a few words.

The object of the dichotomous process pursued in the Sophistes, and its result in each case, is a Definition. Definition also was one of the main features of the inquiries pursued by Socrates, Induction being the other; and indeed in many cases Induction was a series of steps which ended in Definition. And Aristotle also taught a peculiar method, the object and result of which was the construction of Definitions:—namely his Categories. This method is one of division, but very different from the divisions of the Sophistes. His method begins by dividing the whole subject of possible inquiry into ten heads or Categories—Substance, Quantity, Quality, Relation, Place, Time, Position, Habit, Action, Passion. These again are subdivided: thus Quality is Habit or Disposition, Power, Affection, Form. And we have an example of the application of this method to the construction of a Definition in the Ethics; where he determines Virtue to be a Habit with certain additional limitations.

Thus the Induction of Socrates, the Dichotomy of the Eleatics, the Categories of Aristotle, may all be considered as methods by which we proceed to the construction of Definitions. If, by any method, Plato could proceed to the construction of a Definition, or rather of an Idea, of the Absolute Realities on which First Principles depend, such a method would correspond with the notion of Dialectic in the Republic. And if it was a method of division like the Eleatic or Aristotelic, it would correspond with the notion of Dialectic in the Phædrus.