The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses by _necessary_ sequence;[60] meaning by the term _necessary_ thus much and no more--that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.[61] When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism--the inference from all particular bile-less animals to the whole class bile-less--he assumes that we have ascertained the attribute to belong to _all_ the particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observe _all_ the particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observe _some_ of the particulars, a greater or smaller proportion. Now it is in the transition from these _to_ the totality of particulars, that the real inductive inference consists; not in the transition _from_ the totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:[62]--"You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them." You may say that Induction is _through_ all the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimate _terminus ad quem_. But the Induction must first travel _to_ all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most