Aphorism XIX.
The inductive act of thought by which several Facts are colligated into one Proposition, may be expressed by saying: The several Facts are exactly expressed as one Fact, if, and only if, we adopt the Conceptions and the Assertion of the Proposition.
Aphorism XX.
The One Fact, thus inductively obtained from several Facts, may be combined with other Facts, and colligated with them by a new act of Induction. This process may be 98 indefinitely repeated: and these successive processes are the Steps of Induction, or of Generalization, from the lowest to the highest.
Aphorism XXI.
The relation of the successive Steps of Induction may be exhibited by means of an Inductive Table, in which the several Facts are indicated, and tied together by a Bracket, and the Inductive Inference placed on the other side of the Bracket; and this arrangement repeated, so as to form a genealogical Table of each Induction, from the lowest to the highest.
Aphorism XXII.
The Logic of Induction is the Criterion of Truth inferred from Facts, as the Logic of Deduction is the Criterion of Truth deduced from necessary Principles. The Inductive Table enables us to apply such a Criterion; for we can determine whether each Induction is verified and justified by the Facts which its Bracket includes; and if each induction in particular be sound, the highest, which merely combines them all, must necessarily be sound also.
Aphorism XXIII.
The distinction of Fact and Theory is only relative. Events and phenomena, considered as Particulars which may be colligated by Induction, are Facts; considered as Generalities already obtained by colligation of other Facts, they are Theories. The same event or phenomenon is a Fact or a Theory, according as it is considered as standing on one side or the other of the Inductive Bracket.