Aristotle has just finished his conclusion of Book 1 of the Topics. He claimed he would continue his discussion of dialectic reasoning by talking about how to use the various tools of argument. This begins Book 2 of the Topics.
Of problems some are universal, others particular. Universal problems are such as Every pleasure is good and No pleasure is good- particular problems are such as Some pleasure is good and Some pleasure is not good. The methods of establishing and overthrowing a view universally are common to both kinds of problems- for when we have proved that a predicate belongs in every case, we shall also have proved that it belongs in some cases. Likewise, also, if we prove that it does not belong in any case, we shall also have proved that it does not belong in every case. First, then, we must speak of the methods of overthrowing a view universally, because such are common to both universal and particular problems, and because people more usually introduce theses asserting a predicate than denying it, while those who argue with them overthrow it.
Some problems are universal and some are particular. Universal problems have the form Every A is B or No A is B. For example, Every pleasure is good and no pleasure is good are both universal problems. Particular problems have the form Some A is B or Some A is not B. For example, Some pleasures are good and Some pleasures are not good. The methods of proving and disproving universal problems also work on particular problems. If we have proven that all As are Bs, then we have also proven that some As are Bs. If we have proven that no As are Bs, then we have also proven that some As are not Bs. The first set of rules Aristotle discusses will be about how to prove or disprove universal claims. There are two reasons for doing this. First, these rules will help with both universal and particular problems. Second, most people usually argue for the truth of something universal. Those who argue against it are also making a universal claim.
Modern logic does not agree with these claims. Aristotle has reasons for the logical moves he makes. These reasons come from his metaphysics. Since modern logicians separate logic from metaphysics, they cannot make use of Aristotles reasons. Modern logicians often claim that universal statements do not claim that anything exists, while all particular statements do. Aristotle and Aristotelians disagree. They claim that both universal and particular claims can either be about things that exist or things that do not exist.
Next, Aristotle talks about naming objects based on accidental characteristics.