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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.

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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 Large portions are tedious and out of date, while other sections are first-rate philosophy and surprisingly modern.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

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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 reject.

Prior Analytics and Posterior Analytics are Aristotle’s mature account of the formal theory of the syllogism and of what is today called “scientific method.”

Topics concerns itself with the dialectical syllogism; that is, with questions that are matters of “opinion” (in the Platonic sense). The work is an early one, and probably its contents are largely commonplaces from the Academy regarding questions that can profitably be debated. Aristotle offers commonsense advice about how to attack or defend the various views an educated Greek of fourth century Athens might expect to encounter. The work is rather tedious for the modern reader. Its significance lies in the seriousness with which Aristotle treats the problems the Sophists offered to settle cheaply. It is also a reminder of the often forgotten fact that philosophy, for the Greek, was a conversational business. To philosophize, for the Greek, was to talk, not to reflect in private. Such a conception of philosophy as this undoubtedly led Aristotle to focus attention on the syllogism as the instrument of logical argument, since the syllogism is most effective and convincing in debate.

On Sophistical Refutations, although an early work, has been held in high regard by philosophers in all periods. It is concerned with what are today called “material fallacies.” The fundamental distinction Aristotle draws between fallacies resulting from language and fallacies of relevance is still a common approach to the discussion of fallacies. Many of the fallacies he identified are still included in logic books and called by the names he gave them; for example, amphiboly and accent.

Scholarship has shown that so-called traditional logic, although attributed to Aristotle, is actually a synthesis made in late antiquity of some Aristotelian doctrine together with elements from an independent Stoic logic. Stoic logic is now largely lost, but it did play into the rather crude misunderstanding of Aristotle that came to be known as traditional logic. Aristotle is the discoverer of the logic of propositional functions, the branch of logic in which the range of values for the variables is terms. The Stoics discovered the logic of truth functions, or the propositional calculus, the branch of logic in which the range of values for the variables is propositions. The categorical syllogism is Aristotle’s discovery; hypothetical syllogism is a discovery made by the Stoics. The extent of Aristotle’s influence, however, is indicated by the name “hypothetical syllogism,” which has been given to a Stoic inference form that is not syllogistic at all. The barrier traditional logic raises often prevents both a proper recognition of the Stoic achievement and a sound historical approach to and appreciation of Aristotle’s syllogistic.

Categories

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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. Examination of the words “predicable of” and “present in” (a subject) reveals insufficient support for a substratum view. The remarks Aristotle makes immediately following the distinction between primary and secondary substance show that by “predicable of,” he means the relation between a genus or species and one of its members (for example, the species man is “predicable of” the substance Socrates), while “present in” refers to the relation between a substance and one of its attributes (for example, the attribute rational is “present in” the substance Socrates).

Before dispensing with this question, however, it is important to note a remark that Aristotle makes shortly following the section discussed above. He states that primary substances are most properly called substances as a result of the fact that they are the “entities which underlie everything else,” and that everything else is predicated of or present in them. In another place, he states that primary substances are called primary because they “underlie and are the subjects of” everything else. Now although “underlies” immediately suggests “substratum,” it is important to bear in mind that the substratum doctrine was not fully developed until the medieval period, long after Aristotle’s death. One should beware of anachronism and avoid attributing to Aristotle a view that was not current until after his time. If nothing is attributed to him that cannot be supported by the statements he makes in Categories, it is clear that he does not there hold such a view. For the words “present in” and “predicable of” do not by themselves entail a substratum view, and “underlie and are the subjects of” are words that show that Aristotle treats “underlie” as equivalent in meaning to “are subjects.” It would therefore seem wiser to recognize that there is not sufficient evidence to support the view that Categories sets forth a substratum view. What Aristotle had in mind when he spoke about primary substances was simply individual living things without the metaphysical and epistemological frills that decorate the substratum doctrine.

Prior Analytics

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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

The form known as Barbara is also usually attributed to Aristotle. However, neither of these is to be found in Aristotle. He did write about something that resembles these traditional forms, but it was quite different theoretically. Compare the traditional form Barbara with Aristotle’s form:Barbara: All M is P. All S is M. Therefore, all S is P Aristotle’s form: If all B is A, and all C is B then all C is A.

Barbara is an inference rule. It justifies asserting the conclusion on the basis of the two premises. There are three propositional forms in Barbara, together with the special word or symbol “therefore,” the sign or mark of an inference. Aristotle’s form, however, has only one proposition, and no word “therefore.” It is a propositional form, not a rule of inference. Aristotle’s form is really an axiom, one of four that correspond to the four valid moods of the first figure in the same way that the two forms above correspond. As axioms, then, in Aristotle’s axiomatic syllogistic, there are propositions corresponding to the four valid moods of figure one. As theorems, derived by reduction, there are the valid moods of figures two and three.

There is one additional point that should be made about Aristotle’s axioms, however. Contemporary logicians do not try to establish the truth of their axioms; they merely assume them and deduce their consequences. Aristotle tried to justify his axioms by appealing to the dictum de omni et nullo; this was his definition of the first figure. Aristotle regarded the dictum as self-evidently true, and he said that the first figure, which it defined, was the “perfect” figure.

The dictum as the definition of the first figure leads to the last point about the doctrine of Prior Analytics. Aristotle, as is commonly known, recognized only the first three figures. He has sometimes been charged with error here, but, as he defined the figures, there are only three. The basis for his division is the width of the middle term. If the middle term is predicated of both the major and the minor, the syllogism is second figure. If the major and the minor are both predicated of the middle, the syllogism is third figure. If the middle is predicated of one extreme, while the other extreme is predicated of the middle term, the syllogism is first figure. These exhaust the possibilities, of course, and the last definition includes both the traditional first and fourth figures. In fact, Aristotle did recognize and list the valid moods of the fourth figure, even though he (somewhat uncomfortably) treated them as strange first figure moods.

In Posterior Analytics, Aristotle’s account of scientific method, the philosopher stresses two features of scientific knowledge: its factual character and its necessary character. To know something, for Aristotle, meant knowing that an event occurred, and it meant knowing the cause of the event; this is the factual character. In addition, scientific propositions “cannot” be false; they are not merely contingently true; this is the necessary character of such knowledge. For Aristotle, then, science consists of a series of propositions that are logically systematic, have factual reference, and are necessarily true.

What gives the collection of propositions logical order is, of course, the syllogism. Scientific propositions are syllogistically demonstrated conclusions from true premises. However, the premises must also have been demonstrated; otherwise the conclusion is merely consistent, not necessarily true. However, it is obvious that not all premises can be syllogistically demonstrated. Ultimately the regress of demonstrations must come to an end. At this point, one has reached premises that must be justified in another manner. Aristotle offers a justification for such first premises, and this justification is the most fascinating part of Posterior Analytics.

Aristotle lists six characteristics of ultimate premises. Ultimate premises1. must be true propositions about things that exist (matters of fact) 2. they must be primary, by which Aristotle means logically indemonstrable 3. they must be immediate; that is, they must be self-evident 4. they must be better known than the conclusions that follow from them 5. they must be prior to the conclusions in a logical sense 6. they must state the causes of the events referred to by the conclusions

Aristotle mentions two methods of establishing such ultimate premises, induction and intuition. The induction he is speaking about in Posterior Analytics, however, is perfect induction, and so the question ultimately turns on the account of intuition.

At the very end of Posterior Analytics, Aristotle describes intuition as a process involving the following steps:1. sense perception 2. retention of the sense percept in the soul following the removal of the external stimulus 3. memory 4. experience as the product of repeated memories 5. abstraction of the universal—”the one in the many”—from experience

Here it is revealed, however, that the justification of first premises has led to the problem of the role played by the active intellect, a matter that is more fully—though not completely satisfactorily—dealt with in Aristotle’s psychology, his treatise De anima (second Athenian period, 335-323 b.c.e.; On the Soul, 1812).

This brief survey should make it clear that Aristotle’s claim to the title Father of Logic is a just one. He marked out many of the problems of logic and offered solutions that in many cases retain their fascination and pertinence. Of course, he made mistakes and his system of logic is incomplete by modern standards. However, he closes Organon with the comment that there was nothing written on the subject before him. He then asks to be excused for his mistakes but thanked for the light he has shed on the matter. Surely Western civilization is deeply in debt to Aristotle for his contributions to logic.

Bibliography

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Additional Reading

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 perspectives are brought to bear on Aristotle’s philosophy in significant ways.

Barnes, Jonathan. Aristotle. New York: Oxford University Press, 1982. A reliable study designed for readers who want an introduction to Aristotle’s thought.

Barnes, Jonathan, ed. The Cambridge Companion to Aristotle. New York: Cambridge University Press, 1995. An excellent guide to Aristotle’s thought, which features significant essays on major aspects of his work.

Broadie, Sarah. Ethics with Aristotle. New York: Oxford University Press, 1991. This carefully done book concentrates on Aristotle’s ethical theory and its implications.

Brumbaugh, Robert S. The Philosophers of Greece. Albany: State University of New York Press, 1981. An introductory study that discusses Aristotle’s philosophy within the larger context of the Greek world.

Cooper, John M. Reason and Human Good in Aristotle. Cambridge, Mass.: Harvard University Press, 1975. Cooper’s book is a study of the “theoretical backbone” of Aristotle’s moral philosophy—his theories of practical reasoning and of human happiness.

Copleston, Frederick. A History of Philosophy: Greece and Rome. Garden City, N.Y.: Doubleday, 1962. A leading scholar of Western philosophy discusses Aristotle’s life as well as his logic, metaphysics, ethics, politics, and aesthetics.

Edel, Abraham. Aristotle and His Philosophy. New Brunswick, N.J.: Transaction Books, 1996. A careful and helpful study by a veteran interpreter of Western thought.

Ferguson, John. Aristotle. Boston: Twayne, 1972. Assisting the general reader in the study of Aristotle’s works, this book discusses Aristotle’s life and his views about nature and psychology and also offers perspectives on Aristotle’s lasting influence.

Hughes, Gerard J. Aristotle on Ethics. New York: Routledge, 2001. A fresh introduction to the philosopher, refining the translation of Arstotle’s terms with a sensitivity to context.

Husain, Martha. Ontology and the Art of Tragedy: An Approach to Aristotle’s Poetics. Albany: State University of New York, 2001. An examination of the Poetics using Metaphysics as a touchstone. Husain demonstrates the relationship between the works and how the latter illuminates the former.

Jones, W. T. A History of Western Philosophy: The Classical Mind. New York: Harcourt, Brace and World, 1969. Combines historical interpretation of Aristotle’s far-reaching thought with relevant readings from Aristotle’s writings.

Kenny, Anthony. Aristotle on the Perfect Life. New York: Cambridge University Press, 1980. This work focuses on Aristotle’s views about human nature, ethics, and politics.

Lear, Jonathan. Aristotle and Logical Theory. New York: Cambridge University Press, 1980. A detailed study of Aristotle’s views on logic and their continuing significance for understanding human reasoning.

McLeisch, Kenneth. Aristotle. New York: Routledge, 1999. An excellent biographical introduction to the thoughts of the philosopher, clearly presented and requiring no special background. Bibliography.

Mulgan, R. G. Aristotle’s Political Theory: An Introduction for Students of Political Theory. Oxford: Clarendon Press, 1977. Seeks to bring the major themes and arguments in Aristotle’s political theory into sharper focus than they appear in the Politics itself.

Randall, John Herman, Jr. Aristotle. New York: Columbia University Press, 1960. An older but reliable survey of Aristotle’s philosophy.

Robinson, Timothy A. Aristotle in Outline. Indianapolis, Ind.: Hackett, 1995. Accessible to beginning students, this clearly written survey covers Aristotle’s full range of thought.

Rorty, Amélie Oksenberg, ed. Essays on Aristotle’s ‘Ethics.’ Berkeley: University of California Press, 1981. An important collection of essays that concentrates on various facets of Aristotle’s influential moral philosophy.

Smith, Thomas W. Revaluing “Ethics”: Aristotle’s Dialectical Pedagogy. Albany: State University of New York, 2001. Smith argues for a reading of Ethics, not as a moral guidebook, but as a pedagogy—course work—for developing a questioning mind.

Strathern, Paul. Aristotle in Ninety Minutes. Chicago: Ivan Dee, 1996. A brief, easily accessible, introductory overview of Aristotle’s philosophy.

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