A syllogism then is a discourse (cohesion) in which, certain things being laid down, something different from these necessarily comes about through them.
Demonstrative – Dialectical
The syllogism, therefore, is demonstrative, when the premises from which the syllogism consists of are true and primary, or are such that the origin of our knowledge about them has come through premises which are primary and true. On the other hand, the syllogism is dialectical, when it consists of opinions that are generally admitted. Now things that are true and primary are those which are believed in virtue not of anything else but of themselves (for with the principles of the branches of knowledge we must not ask for the “why”, but each principle ought to be credible just by itself); while opinions that are generally admitted are those which are admitted by everyone or by the majority or by the wise, and to these, too, either by all, or by the majority, or by the most renowned and illustrious.
Again, a syllogism is eristical, when it consists of opinions that seem to be generally admitted, but are not such, or even when it seems to be such that consist of opinions which are generally admitted or seem to be generally admitted; for not every opinion that seems to be generally accepted is necessarily generally admitted. For none of the opinions that are called generally admitted becomes visible in mind without a hitch at all, as happens with the principles of sophisms; for in these the nature of the fallacy is obvious immediately, and as a rule even to those who can barely see at a glance.
Let then the first of the eristical syllogisms mentioned above be called syllogism as well, while the other should be called eristical syllogism but not syllogism, since it appears to conclude, but does not really do so.
Moreover, besides all the above-mentioned syllogisms, there are paralogisms that come about through principles peculiar to certain sciences, as happens with geometry and those sciences related to it. For this mode seems to differ from the syllogisms mentioned above, since he who draws a false figure concludes neither from true and primary nor from opinions that are generally admitted. For this kind of syllogism does not fall within the definition, since he who draws a false figure does not assume those which are admitted by everyone or by the majority or by the wise, and to these, too, neither those which are admitted by all, nor by the majority, nor by the most illustrious – but he makes the syllogism through premises which are peculiar to the science, yet not true; for he makes the paralogism either by describing semicircles not as they ought to be, or by drawing certain lines in a way in which they could not be drawn.
Bibliography: Aristotle Topics (100a.25)
Translation – text editing: George Kotsalis