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The purpose of this treatise is to discover a method by which we shall be able to syllogize about every proposed problem from probabilities, ​and when we ourselves sustain the argument we may assert nothing repugnant. First, then, we must declare what a ​syllogism is and what are its differences, in order that the dialectic syllogism may be apprehended, for we investigate this in the proposed treatise.

A syllogism then is a discourse in which, certain things being laid down, something different from the posita happens from necessity through the things laid down. Demonstration indeed is when a syllogism consists of things true and primary, or of such a kind as assume the principle of the knowledge concerning them through certain things primary and true; but the dialectic syllogism is that which is collected from probabilities. Things true and primary indeed are those which obtain belief, not through others, but through themselves, as there is no necessity to investigate the "why" in scientific principles, but each principle itself ought to be credible by itself. Probabilities however are those which appear to all, or to most men, or to the wise, and to these either to all or to the greater number, or to such as are especially renowned and illustrious. Moreover a contentious syllogism is one which is constructed from apparent, but not real probabilities, and which appears to consist of probabilities, or of apparent probabilities. For not every thing which appears ​probable is so, since none of those which are called probable has entirely the superficial image (of probability), as happens to be the case about the principles of contentious arguments, since immediately, and for the most part, the nature of the false in them is evident even to those who have small perception. Let then the first of the syllogisms called contentious, be also called a syllogism, but let the other be a contentious syllogism, yet not a syllogism (simply), since it appears indeed to draw an inference, but does not collect one.

Besides all the above-named syllogisms, there are paralogisms, which consist of things peculiar to certain sciences, as happens to be the case in geometry, and those (sciences) allied to it. For this mode seems to differ from the syllogisms enumerated, since he who describes falsely, neither syllogizes from the true and primary, nor from the probable, for he does not fall into definition, since he neither assumes things which appear to all men, nor those which appear to the greater number, nor to the wise, and to these neither to all, nor to the greater part, nor to the most famous; but he makes a syllogism from assumptions, appropriate indeed to science, yet not from the true, as either by describing semicircles not as they ought to be, or by drawing certain lines not as they ought to be drawn, he produces a paralogism.

Let then the species of syllogisms, to comprehend them summarily, be those which I have stated, and in a word, to sum up all that have been spoken of, and those which shall be mentioned hereafter, let our definition be so far given, because we do not propose to deliver an accurate description of any of these, but wish merely to run through them briefly, thinking it quite sufficient according to the proposed method, in some way or other to be able to know each of them.