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._ 1. THE subject to which the present chapter refers is described by phrases which are at the present day familiarly used in speaking of the progress of knowledge. We hear very frequent mention of _ascending from particular to general_ propositions, and from these to propositions still more general;--of {99} truths _included_ in other truths of a higher degree of generality;--of different _stages of generalization_;--and of the _highest step_ of the process of discovery, to which all others are subordinate and preparatory. As these expressions, so familiar to our ears, especially since the time of Francis Bacon, denote, very significantly, processes and relations which are of great importance in the formation of science, it is necessary for us to give a clear account of them, illustrated with general exemplifications; and this we shall endeavour to do.