Aristotle’s works on logic are collected in the Organon, which includes the Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations.

On Interpretation provides a method of determining the grammatical structure of a sentence or the logical structure of a proposition. Interpretation may be a means of assigning meaning to sentences and propositions. Aristotle explains how meaning can be assigned to sentences and propositions which are concerned with conditions of possibility, contingency, and necessity.

Aristotle begins by saying that spoken words are symbols of thoughts and that written words are symbols of spoken words (Chapter I). Individual words and isolated expressions are not propositions, if they express thoughts which do not involve truth or falsehood. A sentence must be either true or false if it is to be a logical proposition. Every sentence has meaning, but not every sentence is a proposition (Chapter 4).

Propositions may be simple or compound. A compound proposition is formed by a combination of simple propositions. A simple proposition may be a simple affirmation or a simple denial. An affirmation is a positive assertion about something. A denial is a negative assertion about something. For every affirmation, there is a possible denial. For every denial, there is a possible affirmation.

Positive and negative propositions which have the same subject and predicate are contradictory. A predicate is that which is affirmed or denied concerning the subject of a proposition.

To predicate is to affirm or deny something about the subject of a proposition. In the simple sentence, “Socrates is wise,” the syntactic unit “is wise” is the predicate of the subject “Socrates.”

Contrary propositions are not the same as contradictory propositions. If two propositions are contrary, it is possible for both propositions to be false. For example, the proposition that “every man is just” is contrary to the proposition that “no man is just,” but both propositions may be false if some men are just.

On the other hand, the proposition that “not every man is just” is contradictory to the proposition that “every man is just,” because both propositions cannot simultaneously be true, and both propositions cannot simultaneously be false. If there are two propositions, such that when one is true the other must be false, and when one is false the other must be true, then they are contradictory.

Propositions may be universal, indefinite, or individual in what they affirm or deny. A proposition which is of universal character is a proposition predicated of many subjects. A proposition which is of individual character may be predicated of a particular subject.

With respect to propositions of individual character, if the affirmation is false, the contrary is true. With respect to propositions of universal character, if the affirmation is false, the contradictory is true.

A dialectical question is a request for an answer which is found in one of two contradictory alternatives. The answer to the question requires the admission of a premise, or the admission of a contradictory premise.

When two simple propositions having the same subject are true, it does not follow that the predicates of the propositions can always be combined to form a single predicate.

Predictates of separate propositions having the same subject do not always combine to form a unity. For example, if a man is good, and is also a shoemaker, it does not follow that he is a good shoemaker.

If something is contingent, it is not necessary. If a proposition is contingently true, its truth depends upon the truth of another proposition. If a proposition is necessarily true, it is true in and of itself, and does not depend for its truth upon the truth of another proposition.

Propositions may assert or deny possibility, impossibility, contingency, or necessity. It is impossible for two contradictory propositions to be simultaneously true of the same subject.

The contradiction of a proposition which asserts possibility (such as, “it may be”) is not another proposition which asserts possibility (such as, “it may not be”), but is a proposition which asserts impossibility (such as, “it cannot be”).

Similarly, the contradiction of a proposition asserting necessity (such as, “it is necessary that it should be”) is not another proposition asserting necessity (such as, “it is necessary that it should not be”), but is a proposition asserting lack of necessity (such as, “it is not necessary that it should be”).

A proposition may be the expression of a judgment. An affirmation may be opposed by another affirmation. A denial may be opposed by another denial. Judgments are not contrary because they have contrary subjects, but because they have a contrary effect (Chapter 14).

The contrary of a universal affirmation, such as “every man is good,” is a universal denial, such as “no man is good.” The proposition that “every man is good” is contradictory to the proposition that “not every man is good.”

The problem with which Aristotle is mainly concerned in On Interpretation is how logical propositions may affirm or deny each other. Aristotle shows how a proposition may be opposed by a denial or a contradiction. The negation of a proposition is seen in its contradiction. Negating a proposition means replacing it with a contradictory proposition.

Aristotle. “De Interpretatione (On Interpretation).” Translated by E.M. Edghill. The Basic Works of Aristotle. Edited by Richard McKeon. New York: Random House, (1941), pp. 38-61.