Traditional Logic CS 3234: Logic and Formal Systems

Our first deductive system expresses relationships between classes of things. Each class is represented by a noun naming the class, or by an adjective that describes a property that distinguishes the members of the class from nonmembers. These nouns or adjectives denoting classes of things are called categorical terms, or simply terms. For example, the term animals refers to the class of things that contains all animals. As another example, the term brave refers to the class of persons that we consider brave. Note that we are not very concerned with the difficulty to deliberate the attribute of bravery in individual cases. In logic, we do not spend much time arguing whether a particular person, say Socrates, is brave or not. Instead, we assume that it is always possible to univocally attest the given attribute to a given person or not. Categorical terms constitute the basic unit of meaning in our first deductive system, which is therefore called term logic (sometimes also categorical logic). In the history of philosophy, term logic plays a prominent role, because many arguments that appear in everyday discourse (and also in political statements, philosophical treatises, etc) can be analysed and verified using term logic. In fact, term logic has been investigated extensively by the Greek philosopher Aristotle (384–322 BCE) already, whose treatise Prior Analytics is considered the earliest study in formal logic and was widely accepted as the definitive approach to deductive reasoning until the 19century. To understand the concerns of term logic, consider the following argument.