Chapter I: Whether a Demonstrative Science existsEdit
- Previous knowledge is required for all scientific studies or methods of instruction. Examples from Mathematics, Dialectic and Rhetoric. Previous knowledge as variously expressed in theses concerning either the existence of a thing or the meaning of the word denoting it. Learning consists in the conversion of universal into particular knowledge.
All communications of knowledge from teacher to pupil by way of reasoning pre-suppose some pre-existing knowledge. The truth of this statement may be seen from a complete enumeration of instances:—it is thus that the mathematical sciences are attained and every art also. The same is the case with dialectical arguments whether proceeding by means of the syllogism or of induction, for the former kind makes such assumptions as people who understand the meaning admit, the latter uses the recognized clearness of the particular as an indication of the universal, so that both convey their information by means of things already known. So too orators produce conviction in a like manner, using either Example, which is equivalent to induction, or Enthymeme, which corresponds to syllogism.
Pre-existing knowledge of two kinds is required: one must either assume beforehand that something exists, or one must understand what the word means, while sometimes both sorts of knowledge are required. As an example of the first case we may take the necessity for previously knowing the proposition ‘everything must be either affirmed or denied.’ Of the second case an instance would be the knowledge of the meaning conveyed by the word ‘triangle’; of the combination of both kinds, the knowledge both of what ‘Unit’ means, and of the fact that ‘Unit’ exists. The distinction is necessary, since the grounds of certainty differ in the two cases.
Some facts become known as a result of previously acquired knowledge, while others are learned at the moment of perceiving the object. This latter happens in the case of all things comprised under a universal, with which one is already acquainted. It is known to the pupil, before perceiving any particular triangle, that the interior angles of every triangle are equal to two right angles; but it is only at the moment of sense-perception that he learns that this figure inscribed in the semi-circle is a triangle.
In some cases knowledge is only acquired in this latter way, and the particular is not learned by means of a middle term: that is to say, in the cases where we touch the concrete particular, that is in the case of things which are not predicable of any subject. We ought to admit that, even before arriving at particulars, and so obtaining a syllogism, we do, from one point of view perhaps, possess knowledge, although from another we do not. For how, it may be asked, when he did not know whether the thing existed at all or not, could he have known absolutely that it contains two right angles? The answer is that he knows it from a particular point of view, in that he knows the universal, but he does not know it absolutely. On any other view we shall have the dilemma of the Meno—a man will either learn nothing at all or only what he knows before. This difficulty must not be solved as some try to do. The question is asked, ‘Do you or do you not know every dyad to be even?’ On receiving an affirmative reply they bring forward some dyad of the existence of which the other was ignorant, and so could not have known it to be even. The solution suggested is to say that one does not know every dyad to be even, but only that which one knows to be a dyad. On the other hand one knows that of which one possesses or has received a demonstration, and no demonstration concerns merely (e.g.) every triangle, or number, one may happen to know, but every possible triangle or number. No demonstrative proposition is taken as referring to ‘any number you may know of,’ or ‘any straight line you may know of,’ but to the entire subject. Nothing, however, I should suppose, precludes our knowing already what we learn from one point of view and not knowing it from another. The absurdity would consist not in having some sort of knowledge of what one learns, but in having knowledge of it in a certain respect—I mean in the very same respect and manner in which one learns it.