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.