The superiority of the Deductive Method, both in its mode of advancing to the discovery of new truth and in the precision, clearness, and certainty which accompany its findings, must now easily become apparent. Whether we regard Induction and Deduction as correlative Processes belonging to one Method, each of which has been disproportionately in vogue at different epochs, or as distinctive Methods, having each their own Deductive and Inductive Processes, in either aspect, Induction is only a preparative labor, leading in the more important work of the application of the Law or Principle derived. It is only, indeed, for the purpose of discovering this Law that Observation, Classification, and Induction are undertaken. It has been the triumphant boast of the Inductive Method, that it guarded, by means of these preliminary steps, in the most careful manner, against error in establishing its Laws. To the extent of its capacity it has done so. But we have already seen, that deriving its Principles, as it was obliged to, from less than _all_ the Facts which appertained to the Principles, these must inevitably have been lacking in some particulars; it being impossible to make the whole out of less than all its parts.
The Inductive Method has obtained an importance greatly exaggerated, for the reason that it has been brought into comparison, for the most part, with the Anticipative or Hypothetical, the bastard Deductive Method only, and its superiority over this exhibited in the most detailed manner, while the right application of the Deductive Method, except in Mathematics, has not been considered possible. The reason of this can be made obvious.
The immense superiority of _Mathematical_ Reasoning, as _Demonstration_ is often called, over all other kinds, is universally known and recognized. For in this mode of reasoning there is no room for doubt or uncertainty. It starts from Principles of whose truth there can be no doubt, because it is impossible for _the human mind to apprehend them in more than one way_, and proceeds by steps, every one of which can likewise be apprehended in only one way. Hence all men arrive _inevitably_ at the same conclusion at the close of the chain of reasoning. It is, therefore, a Method of proof which sets out from a precise, definite, universally established Law or Principle which really contains the conclusion in itself, and which can be developed to the end through a series of necessary and irresistible convincements; while in the Inductive Method we are obliged to start from this or that admitted Fact or Truth assumed after Observation, Classification, and Induction, which may have been rigorously performed, but which, nevertheless, could not, in the nature of the case, prove the Fact or Truth with complete certainty, and which is not, perhaps, universally admitted, and proceed by merely probable inferences drawn from various, diverse, and often uncertain relations, until we reach a conclusion. Such reasoning may be sufficient to incline the mind to a particular conclusion, as against those which tend to any other conclusion, but they are never quite sufficient, as in Demonstrative or _true_ Deductive reasoning, to _necessitate_ the conclusion, and render any other impossible.