Page:Logic Taught by Love.djvu/77

Rh of reasoning applied to metaphysical questions, it will occasionally be found that different trains of thought are blended together; that particular but essential parts of the demonstration are given parenthetically, 0r out of the main course of the argument; that the meaning of a premise may be in some degree ambiguous; and, not unfrequently, that arguments, viewed by the strict laws of formal reasoning, are incorrect or inconclusive. The difficulty of determining and distinctly exhibiting the true premises of a demonstration" (in a book which we are studying and analyzing), "may, in such cases, be very considerable. But it is a difficulty which must be overcome by all who would ascertain whether a particular conclusion is proved or not, whatever form they may be prepared or disposed to give to the ulterior process of reasoning. It is a difficulty, therefore, which is not peculiar to the method of "mathematical analysis," though it manifests itself more distinctly in connection with this method than with any other. So intimate, indeed, is this connection, that it is impossible, employing the method of this treatise, to form even a conjecture as to the validity of a conclusion, without a distinct apprehension and exact statement of all the premises upon which it rests. In the more usual course of procedure" (i. e. verbal analysis), "nothing is, however, more common than to examine some of the steps of a train of argument, and thence to form a vague general impression of the scope of the whole, without any such preliminary and thorough analysis of the premises which it involves.

"The necessity of a rigorous determination of the real premises of a demonstration ought not to be