neither to sense nor understanding, and if he draw the right conclusion, he will syllogize indeed, but not produce a scientific demonstration; but if [he draw] not the right conclusion, he will not syllogize at all.
Now demonstration differs from analysis. For each one of the points demonstrated, is demonstrated by means of points that are demonstrated; those having been previously demonstrated by others; till we get back to those which are self-evident, or to those evident to sense and to understanding; which is called Analysis. But demonstration is, when the point in question reaches us through all the intermediate steps. The man, then, who practises demonstration, ought to give great attention to the truth, while he disregards the terms of the premisses, whether you call them axioms, or premisses, or assumptions. Similarly, also, special attention must be paid to what suppositions a conclusion is based on; while he may be quite careless as to whether one choose to term it a conclusive or syllogistic proposition.
For I assert that these two things must be attended to by the man who would demonstrate—to assume true premisses, and to draw from them the legitimate conclusion, which some also call "the inference," as being what is inferred from the premisses.
Now in each proposition respecting a question, there must be different premisses, related, however, to the proposition laid down; and what is advanced must be reduced to definition. And this definition must be admitted by all. But when premisses irrelevant to the proposition to be established are assumed, it is impossible to arrive at any right result; the entire proposition—which is also called the question of its nature—being ignored.
In all questions, then, there is something which is previously known,—that which being self-evident is believed without demonstration; which must be made the starting point in their investigation, and the criterion of apparent results.
