Part I: Lesson

We will begin our study of logic by defining the three basic notions used to characterize declarative sentences, their parts, and the relations between them. These are terms, propositions, and syllogisms. We will nuance and refine each of these further in future modules. For now, we look at terms.

“Forms of speech are either simple or composite. Examples of the latter are such expression as ‘the man runs,’ ‘the man wins;’ of the former ‘man,’ ‘ox,’ ‘runs,’ ‘wins.’”

Aristotle, Categories (W.D. Ross, 1952)

Here are some examples of terms:

Terms: man, ox, runs, wins, yellow, that funny comedian, the book on that shelf, etc.

Grammatically, terms fall into three classes: nouns, verbs, and adjectives. “Man” and “ox” are nouns; “runs” and “wins” are forms of the verbs “to run” and “to win”; “yellow” and “funny” are adjectives.

Combinations of terms are used in order to predicate something of a subject. For example, when you say “The ox runs,” you predicate “runs” of the ox; we say that “The ox” is the subject, and “runs” is the predicate. When you say “The man is funny,” you predicate “funny” of the man; we say that “The man” is the subject, and “runs” is the predicate.

When you predicate something of a subject, you form a proposition; the proposition is either true or false. For example: “the ox runs” is either true or false.  But can a term, by itself, be true or false? Let’s see what Aristotle has to say: 

“No one of these terms, in and of itself, involves an affirmation; it is by the combination of such terms that positive or negative statements arise. For every assertion must, as is admitted, be either true or false, whereas expressions which are not in any way composite, such as ‘man,’ ‘white,’ ‘runs,’ ‘wins,’ cannot be either true or false.”-Aristotle, Categories (W.D. Ross, 1952)

Here, Aristotle argues that while assertions must be either true or false, terms are neither. For instance, take the assertion, “Africa is large.” This is an assertion which is either true or false. On the other hand, let’s take the term, “Africa.” The term “Africa” cannot be either true or false. It is simply a word that refers to something. It refers to a continent south of Europe and south-west of Asia. It is not saying whether or not such a continent exists, or whether or not such a continent is anything. “Africa” is simply a term. 

Later, we will look at the copula. The copula is the word that relates the predicate and the subject. It generally takes the form of “is,” “are,” “was,” or “were.” It is not considered a term. For instance, in the assertion “All men are mortal,” “All men” and “mortal” are terms, while “are” is the copula, so it is not a term.  

A helpful distinction can be made between two types of terms:

• Categorematic Terms: Terms that refer to a category of thing(s) in the world; terms that have determinate meaning without surrounding terms (as in a proposition).
• Syncategorematic Terms: Terms that do not refer to a category of thing(s) in the world; terms that require surrounding terms in a proposition for a determinate meaning. 

For example, terms like “dog,” “humans,” “happiness,” “Aristotle,” “that computer,” and “the gentleman running to catch the bus” are all categorematic terms. On the other hand, terms such as “and”, “or”, “every”, “of”, and “on” as they stand by themselves are syncategorematic. There’s an intuitive difference between the two types just by giving examples, but the technical difference can be described in terms of categories. What is a category?

A category is roughly a collection of things that have some sort of relevant common property. For instance, all of the particular chairs in existence are members of the category “chairs”. All of these chairs have a relevant common property: they all have the property of being a chair. This is why “chairs” is a categorematic term – it refers to the category of objects that are a certain thing. Here’s a diagram to visualize the category “states.”

The largest circle represents the category “states”, where anything inside the circle is a member of the category “states”. Although there is not enough room to have smaller circles for all of the states, a perfect diagram would have all states in existence inside the category “states”. 

Finally, it is worth noting that some categories, unlike “chairs” or “states”, have only one member. For instance, the category “Aristotle” has only one member: Aristotle himself! Since Aristotle is the only thing that is Aristotle, he is the only member in the category “Aristotle.” The same holds for the category “that chair” or the category “The United States of America”.

For Aristotle, there are many categories in the world, and we use terms to refer to them. Now we can clearly say that categorematic terms are those that refer to categories. On the other hand, syncategorematic terms do not refer to categories. There is no category “of”, “on”, or “an”. This distinction is extremely important, as categorematic terms will be emphasized in logic. However, some syncategorematic terms will also be important, especially terms like “and” and “or,” by which we connect sentences, as well as terms like “all” and “some” – but we postpone discussion of these syncategorematic terms.

It is also important to note that some terms seem to be composed of many terms. Take, for instance, the categorematic term “the ugly computer on top of the table”. This is a categorematic term, since it designates a category of things in the world (namely, a category which has only one member: the actual ugly computer on top of the table). However, it also contains the terms “the”, “ugly”, “computer”, etc. For the sake of this course, you will only need to deal with tasks relating to the larger term, rather than the more complicated task of dealing with smaller terms within the larger term.

From here on out in this lesson sheet, when we simply refer to “terms”, we are referring to categorematic terms, as they are of highest importance in logic.