XXII.: In Affirmations some final and ultimate point is reached where the series must cease
Chap. XXIII.: Certain Corollaries
Chap. XXIV.: Whether Universal or Particular Demonstration is superior
Chap. XXV.: That Affirmative is superior to Negative Demonstration
Chap. XXVI.: Direct Demonstration is superior to Reduction per impossible
Chap. XXVII.: What science is more certain and prior, and what less certain and inferior
Chap. XXVIII.: What constitutes one or many Sciences
Chap. XXIX.: Concerning many Demonstrations of the same thing
Chap. XXX.: On fortuitous occurrences
Chap. XXXI.: Sense perception cannot give Demonstrative Science
Chap. XXXII.: On the difference of Principles corresponding to the difference of Syllogisms
Chap. XXXIII.: The distinction between Science and Opinion
Chap. XXXIV.: On Sagacity
Book II.
Chap. I.: On the number and arrangements of Questions
Chap. II.: Every question is concerned with the discovery of a Middle Term
Chap. III.: The distinction between Definition and Demonstration
Chap. IV.: The Essence of a thing cannot be attained by Syllogism
Chap. V.: Knowledge of the Essence cannot be attained by Division
Chap. VI.: The Essence cannot be proved by the Definition of the thing itself or by that of its opposite
Chap. VII.: Whether the Essence can in any way be proved
Chap. VIII.: How the Essence can be proved
Chap. IX.: What Essences can and what cannot be proved
Chap. X.: The nature and forms of Definition
Chap. XI.: The kinds of Causes used in Demonstration
Chap. XII.: On the Causes of events which exist, are in process, have happened, or will happen
Chap. XIII.: On the search for a Definition
Chap. XIV.: On the discovery of Questions for Demonstration
Chap. XV.: How far the same Middle Term is employed for demonstrating different Questions
Chap. XVI.: On inferring the Cause from the Effect
Chap. XVII.: Whether there can be several causes of the same thing
Chap. XVIII.: Which is the prior cause, that which is nearer the particular, or the more universal?
Chap. XIX.: On the attainment of Primary Principles
Chapter I: Whether a Demonstrative Science exists
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
