Aristotle has finished the introduction to Topics and continues onwards in Book 1. He claimed that he will now explain what deduction is and how many kinds there are. He does that now.
Now a deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them. It is a demonstration, when the premisses from which the deduction starts are true and primitive, or are such that our knowledge of them has originally come through premisses which are primitive and true- and it is a dialectical deduction, if it reasons from reputable opinions. Things are true and primitive which are convincing on the strength not of anything else but of themselves- for in regard to the first principles of science it is improper to ask any further for the why and wherefore of them- each of the first principles should command belief in and by itself. On the other hand, those opinions are reputable which are accepted by everyone or by the majority or by the wise i.e. by all, or by the majority, or by the most notable and reputable of them. Again, a deduction is contentious if it starts from opinions that seem to be reputable, but are not really such, or again if it merely seems to reason from opinions that are or seem to be reputable. For not every opinion that seems to be reputable actually is reputable. For none of the opinions which we call reputable show their character entirely on the surface, as happens in the case of the principles of contentious arguments- for the nature of the falsity in these is obvious immediately, and for the most part even to persons with little power of comprehension. So then, of the contentious deductions mentioned, the former really deserves to be called deduction, but the other should be called contentious deduction, but not deduction, since it appears to deduce, but does not really do so.
Aristotle defines deduction as a particular kind of reasoning. We start with some sort of opinion. That opinion cannot do anything but lead to another opinion. That kind of reasoning is deduction. He says that there are two kinds of deduction. One is demonstration, the other is dialectic. Demonstration begins starts with something that is true and primitive, while dialectic begins with common opinions that may or may not be true. Primitive opinions are ones that you do not believe based on other opinions, and even asking for a reason to believe them makes no sense. There are three kinds of common opinions: everyone believes them, majority opinion and expert opinion.
The previous division between demonstration and dialectic covers all of the forms of deduction. But there are forms of thought that look like deductive arguments. Such forms of thought Aristotle calls contentious and we call fallacies. Forms of thought that look dialectic but do not start with any of the three kinds of opinions are fallacies. Sometimes it is not obvious and we can be fooled. Sometimes people who are not good at reasoning will miss these fallacies when others will see them. In all cases, fallacies are not deductive arguments.
Now that Aristotle has laid out the various kinds of deduction, he is going to discuss a possible exception to his argument.