Context (World Philosophers and Their Works)
The six treatises that make up Aristotle’s Organon are the first writings on logic as an independent discipline to appear in Western civilization. The title has been used to refer to the collection since at least the sixth century, but there is no evidence that Aristotle himself referred to the treatises by this name. Aristotle’s word for what today is called formal logic was “analytics.” Traditionally, the treatises have been ordered as follows: Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations. This order is based on the contents: Categories treats of terms, On Interpretation treats of propositions, Prior Analytics treats of syllogisms. The remaining three treat of kinds of argument; Posterior Analytics of apodictic (necessary) syllogisms, Topics of dialectical (debatable) syllogisms, and On Sophistical Refutations of unsound arguments (informal fallacies). However, Aristotle did not write the treatises in this order, and there is no evidence to support the rather common misconception that Aristotle regarded them (except for the Prior and Posterior Analytics) as successive chapters in a systematic treatise on logic. The Categories, Topics, and On Sophistical Refutations are early works, On Interpretation was probably written some time later, and the two Analytics were written last. The Categories is perhaps as much a work on metaphysics as it is on logic; it has considerable historical significance, but its logical content is rather meager.
There is a wealth of material discussed in the six works, but it is of very uneven importance. Large portions are tedious and out of date, while other sections are first-rate philosophy and surprisingly modern. What follows is a very brief summary of the contents of each treatise, with a somewhat more detailed account of the Categories and the two Analytics.
The Six Treatises (World Philosophers and Their Works)
The Greek word kategoria, from which the word “category” is derived, ordinarily is used simply to mean “predicate.” Categories is concerned with the ten ultimate kinds of predicates people can use in communicating with one another. There are references to the categories throughout the Aristotelian corpus, but at various places in his writings, Aristotle departs from the list given in Categories. Those listed in Categories are substance, quality, quantity, relation, action, affection, place, time, position, and state. Aristotle specifies what he means by each category and points out its peculiar characteristics. This work has had considerable historical importance.
On Interpretation opens with some grammatical distinctions. Nouns, verbs, sentences, and various kinds of propositions are characterized, and the relations between various propositional forms are traced. The traditional square of opposition has its roots in On Interpretation. The four traditional A, E, I, and O forms of propositions are discussed, although the matter of the distribution of predicate terms is not raised. (A: All S is P; E: No S is P; I: Some S is P; O: Some S is not P.) It is one of the more controversial treatises because it is the source of the view (which has plagued philosophers as gifted as Gottfried Wilhelm Leibniz) that all propositions must finally be resolved into subject-predicate propositions, a view that modern logicians...
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Categories (World Philosophers and Their Works)
The ten ultimate predicates Aristotle lists in Categories may be separated into two divisions, substance and the remaining nine. Substance is by far the most important; it is presupposed by all the others—they are really all characteristics or properties of substances. Within the broad category of substance, Aristotle distinguishes primary and secondary substance. Philosophers have often held that Aristotle’s primary substance was the substratum of later metaphysics. Aristotle says that it is neither “predicable of” nor “present in” a subject, and he lists as examples the individual person or the individual horse. Secondary substances are the species of which primary substances are members; “person” and “horse,” for example, are illustrations of secondary substances. One might get closer to Aristotle’s doctrine if one recognizes that practically everything he meant by substances could be included if one talked merely about that which is symbolized by whatever word may stand as the subject of a proposition.
However, it would be going beyond the doctrine of Categories to charge Aristotle with a substratum view of primary substance. Actually, Aristotle seems to mean by primary substance merely the commonsense notion of a living individual thing. After all, the term “thing” is metaphysically vague and its mere occurrence in a passage is not sufficient ground for inferring that Aristotle held a substratum doctrine....
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Prior Analytics (World Philosophers and Their Works)
Considerable interest has developed in Aristotle’s syllogistic as it is presented in Prior Analytics. Viewed on its own merits, apart from the additions and revisions of “traditional logic,” the doctrine of Prior Analytics is seen to be surprisingly modern and innocent of many of the charges often made against it. It lacks the refinement of contemporary functional calculi, but it nevertheless is a surprisingly sophisticated formal, axiomatic system, needing but little to make it a completely acceptable logical calculus.
A modern logical calculus includes four elements:1. A set of terms that are undefined (within the calculus) or “primitive” and that serve as a basis for defining all other terms in the system. Examples of such primitive terms in a logical calculus are “not” and “if . . . then . . . ” and the notion of a variable. 2. Formation rules that specify which expressions are to be included as well-formed and which expressions are inappropriate or not well-formed. For example, everyone recognizes implicitly that “The instructor is tardy” is a sensible English sentence and that “The stone sang a solo” is inappropriate or not well-formed. The formation rules explicitly state the conditions well-formed expressions must meet. 3. Certain axioms or postulates from which the theorems of the system are derived. Euclid’s axiom that the shortest distance between two points is a straight line is an example—taken from geometry rather than logic, of course—of an unproved axiom. 4. A set of rules specifying how the theorems are to be derived from the axioms.
Aristotle does not call his primitive terms by that name, but he uses “not” and “and” and “if . . . then . . .” as primitives, taking it for granted that the reader can also use them, and offering no definitions for them. In the case of variables, however, he has clearly and self-consciously arrived at the modern point of view. Throughout Prior Analytics, he uses letters of the alphabet in stating his syllogistic forms, and only after stating them formally does he give examples of terms that can be substituted for the variables. For example, he discusses syllogistic forms of the first figure using the letters A, B, and C, and then often lists terms that can be taken as values for these variables, terms such as “horse,” “man,” and “animal.”
Prior Analytics does not include any specific formation rules because Aristotle presupposed that he and his readers were able to recognize well-formed expressions and to rule out inappropriate expressions. He did not recognize the theoretical importance of such rules. Nor did he include explicitly stated inference rules for passing from axioms to theorems. However, a great number of proofs appear in the course of the treatise, and the proof techniques that are appropriate for deriving the theorems from the axioms are given names. Thus Aristotle illustrated the rules of proof, even though he did not lay them down as a modern logician would. The axioms are the valid moods of figure one, and the theorems are the valid moods of the other figures. The proof techniques are the techniques of “reduction,” and Aristotle makes it clear that all valid moods in the second and third figures can be derived from figure one either by “conversion” (later called “direct reduction” by logicians) or by reductio per impossible (later called “indirect reduction” by logicians).
The axiomatic character of Prior Analytics is what is most often overlooked by contemporary logicians and scholars. Aristotle is usually credited with the well-known syllogism:All men are mortal. Socrates is a man. Therefore, Socrates is mortal...
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Bibliography (World Philosophers and Their Works)
Ackrill, J. L. Essays on Plato and Aristotle. New York: Oxford University Press, 1997. This work contains important and insightful reflections on two of the most influential thinkers in Western philosophy.
Adler, Mortimer J. Aristotle for Everybody: Difficult Thought Made Easy. New York: Scribner’s 1997. A reliable interpreter provides an account that introduces Aristotle’s thought in accessible fashion.
Bar On, Bat-Ami, ed. Engendering Origins: Critical Feminist Readings in Plato and Aristotle. Albany: State University of New York Press, 1994. Feminist...
(The entire section is 683 words.)