Sentence Forms

The traditional, categorical logic which ReasonLines illustrates is sometimes called "term logic" because its variables are "terms" such as A, nonA, B, nonB, etc. (This contrasts with "propositional logic" whose variables are entire propositions.) But it is also called "categorical logic" because the terms can be used to refer to sets, classes, or categories of real things. Two terms are linked together as "subject" and "predicate" by a "copula," and "quantified" to yield the four basic sentence forms of the logic. According to its composition, each sentence form has a quantity (i.e., each is either universal or particular) and a quality (i.e., each is either affirmative or negative), as follows:

The terms can be replaced by nouns, or noun phrases, that indicate "categories" of things to provide "content" for the forms in order to make meaningful sentences. For example, for a universal affirmative sentence, A might simply be replaced by "poodles" and B by "dogs" to get

or one or both could be replaced by complex phrases that denote a specific category, such as

and the same holds for the terms of the other types of sentences.

Moreover, for every term, A, B, etc., there is a "complementary term," nonA, nonB, etc., and accordingly for any class that a term indicates there is a "complementary class" composed of all the things not indicated by that original term. To be consistent we will let all the terms, A, nonA, B, nonB, etc., stand for plural as well as singular nouns, and also let the copula always be "are (not)" rather than "is (not)."

It is important to note that the logic is not concerned with whether these statements are true or false in fact. Rather, the logic is concerned with the form rather than with the "content" of the sentences, and the forms, viz.,

are neither true nor false. Rather, they only become true or false when content is substituted for A (nonA) and B (nonB) so as to render them complete sentences.