Alexander of Aphrodisias

(fl. second-third century a.d.)

philosophy.

Alexander was a Peripatetic philosopher of the second-third century among whose masters were Herminus, Sosigenes, and Aristocles. His fame rests mainly on his interpretation of Aristotle’s doctrines, the scholarly qualities of which earned him the sobriquet of “the interpreter” (δἐξηγητής). Of his works other than commentaries, four have survived in Greek manuscripts; On the Soul; On Fate; a writing going under the title On Mixture; and another, in four books, going under the title Natural Questions, of which the fourth book, however, deals mainly with ethical problems. Additional material is likely to be found in Arabic and Armenian.

Of these, the second part of On the Soul and the Natural Questions are collections of short pieces (some twenty–five in On the Soul, sixty–nine in the Questions) dealing with a great variety of topics and representing different literary forms. It is rather certain that these collections were not arranged or edited by Alexander, and that some pieces are inauthentic. But few of the problems thus posed have yet been sufficiently explored; the following presentation of Alexander’s doctrines will be based indiscriminately on texts handed down to us under his name.

Of his commentaries on Aristotle, those on Analytica priora I, Topics, Meteorologica, and On Sense and Sensibilia survive in their entirety. Of the commentary on Metaphysics under his name, only the part dealing with Metaphysics A–Λ is genuine; the rest, usually referred to as a work by Pseudo-Alexander (his identity is not known), is not his, although it does contain some genuine passages. Of other commentaries, only fragments in the form of quotations in other commentators on Aristotle survive. Of his interpretations of Aristotle (either in formal commentaries or in other writings), two are particularly famous. Whereas Aristotle made Plato’s ideas immanent in the sensible individuals but insisted that only this “ideal” (i.e., universal) aspect of sensibles can be known, so that with regard to us the individual (object of sensation) is prior to the universal–although the universal is actually prior to the individual–Alexander went one step further and declared that only individuals actually exist, the universals existing only as products of our mental (noetic) activity (υοειυ), which abstracts them from the individuals (or the individual existing only in one exemplar e.g., the phoenix). Therefore, the universals exist only as long as they are perceived. Alexander calls them υοητά(usually translated “intelligibles,” in which case (υοειυ) would best be translated “to intelligize” we could then translated the noun υους, the agent of intelligizing, as “intelligence“: one of the Latin translations of υους is mens, to which, unfortunately, only the adjective “mental” corresponds in English).

But in addition to these intelligibles (corresponding to Plato’s transcendent ideas made immanent by Aristotle) existing only as the results of our mental acts, Alexander admits the existence of intelligibles existing outside the realm of the sensible. Roughly, they correspond to Aristotle’s “pure” forms, of which the best–known example is his supreme deity, the Unmoved Mover. These “higher” intelligibles (κυρίωςυοητά) have one thing in common with the lower ones: they exist only as objects of mental (noetic) acts, but the υους (intelligence) that intelligizes (“perceives”) them is not our human intelligence. Rather, it is a (or the) divine intellect, one of whose marks is that its activity is eternal and incessant, so that these “higher” intelligibles also exist eternally and incessantly. They are “caused” by the highest intelligible, in the description of whose causality Alexander anticipates some Neoplatonic categories. The mental act perceiving them does not “abstract” them form matter, for they are not embodied.

Connected with this piece of noetics is another, with the help of which Alexander interprets a most difficult aspect of Aristotle’s psychology in his On the Soul, Book III, chapters 4 and 5. According to Alexander, Aristotle teaches the existence of human intelligence (Alexander calls it passive, or potential, or material intelligence), which is different for different individuals and is part of everybody’s soul, and of another intelligence, which is identical with the Supreme Deity, called active intelligence (it is this intelligence that incessantly and eternally perceives itself by perceiving the “higher” intelligibles). This intelligence-Deity is unique; it “enters” man from without (i.e., it is not connected in any way with his body); it is active also in the sense of activating the human intelligence, thus enabling this intelligence to perceive intelligibles of both the lower and the higher order. Human intelligence thus activated (we could also say “transformed,” and Alexander almost says “divinized”) in different aspects of its activity is called by Alexander intelligence “in action.” or “acquired as habit,” or “acquired as disponible skill” (έυεργείαι έπίκτος, κάθ′ ε̈ξιυ). The most conspicuous result of this theory is the denial of any kind of personal immortality. Man’s soul perishes with his body; his intelligence, qua transformed by the active intelligence, survives by being reabsorbed into that unique, impersonal, divine intelligence. It is remarkable that Pseudo-Alexander describes the experience of “transformation,” after which human intelligence becomes capable of perceiving the “higher” intelligibles, as a mystical (ineffable) experience. The assertion or the denial of the correctness of Alexander’s interpretation of Aristotle and, even more, the correctness of the doctrine (denial of personal immortality) became one of the great controversies of the Middle Ages and early modern times.

Only a few other doctrines of Alexander can be mentioned here.

(1) In Aristotle’s writings all change is ultimately reduced to locomotion, and prime locomotion is attributed to the celestial bodies (fixed stars and planets, and their spheres). Three explanations are given of the cause of this locomotion. One is that all celestial bodies are moved by being attracted to their Unmoved Mover as lovers are attracted by the objects of their love; the second is that they consist of an element, the ether, which by nature moves eternally, incessantly, and circularly; the third is that they are animated and moved by their souls. Alexander tried to reconcile these three explanations. Ether is animated and the soul is its nature. This soul desires to imitate the Unmoved Mover, which it does by eternally circling him.

(2) Alexander undertakes to prove that man’s will is free (or, as the Greek has it, that there are things in our power, έϕ’ ήμῖυ). One of his main arguments is that nature distinguished man from other animals by endowing him with the faculty of deliberation, which mediates between stimuli (ϕαυτασίαι) and actions, whereas animals simply react to stimuli. And since nature does nothing in vain, the exercise of this deliberative faculty results in reasonable assent to (or dissent form) stimuli, which proves that we are free to choose.

(3) Another theory explaining the freedom of will is based on the assertion that whereas the realm of the eternal and immutable is, if we may say so, full of being, the realm of the changeable (of becoming and perishing) is permeated by nonbeing. In fact, this nonbeing is responsible for such things as chance and freedom of the will; there is no cause of these phenomena.

(4) Connected with the free–will theory is Alexander’s treatment of the problem of fate or destiny (είμαρμέυη) i.e., the doctrine of an unbroken causal chain. The fact of human freedom proves this doctrine wrong. The meaning of the word “fate” should be taken to indicate that everything acts according to its own, individual, nongeneric nature (ϕύσις); in fact, “fate” and “nature” coincide without abridgment of man’s freedom.

(5) Alexander discusses the problem of providence. He denies that the divine provides in a direct way (προηγουμέυως), i.e., the way a shepherd provides for his flock; such providence, says Alexander, would amount to saying that the divine (superior) exists for the sake of or profits from the inferior. He also denies that the effects of divine providence are merely accidental (κατά συμβεβηκός), but he does insist that there are other manners of divine providence, and promises to prove that contrary to what others have asserted, Aristotle recognizes providence. Alexander himself at least tentatively identifies the sum total of effects emanating from the everlasting circular movement of the celestial bodies with providence, its main effect being the generic immortality of perishable individuals of which the world of becoming consists.

(6) Alexander asserts the existence of natural justice. His main proof is that nature created man to live in community; that there can be no community without justice; that therefore justice is natural (ϕύσει)

(7) The object of man’s fundamental desire (πὸπρω̃του οἰκει̃ου)is pleasure (the apparent good) rather than, e.g., self-preservation.

(8) Moral perfection (άρετή) does not guarantee a happy life, as can be seen from the fact that a morally perfect man is justified in committing suicide for good reasons (ε̕ύλσγος έξαγωγή), which he would never do if his life were a happy one.

(9) Nobody can possess one moral perfection (άρετή), such as courage, without possessing all others.

(10) Alexander devotes a comparatively large amount of space to the problem of vision and related problems.

(11) Alexander refutes in great detail the Stoic doctrine of total interpenetration of bodies (κραᾰσις δι’οὅλου), which he feels is the foundation of the main tenets of the whole Stoic system.

(12) The magnet attracts because iron desires it, just as other things, although inanimate, desire that which nature has destined for them.

In any history of the problem of squaring the circle, Alexander is likely to be mentioned as he commented on all passages in which Aristotle criticized the methods used for this purpose by Hippocrates of Chios, Bryson, and Antiphon, always briefly to the point of obscurity. It seems that Alexander, probably misled by Aristotle, falsely assumed that Hippocrates did not distinguish lunules formed on quadrants (sides of a square inscribed in a circle) from sextants (sides of a hexagon inscribed in a circle), and also assumed that Antiphon violated the principle that a curve and a straight line can have only a point in common, which probably implies that Antiphon asserted the existence of atomic lengths of which both curves and straight lines would consist. On this basis Alexander rejected Hippocrates’ and Antiphon’s methods of squaring the circle.

BIBLIOGRAPHY

1. Original Works. All commentaries mentioned in the text are available in the collection Commentaria in Aristotelem Graeca, 23 vols. (Berlin, 1882–1909), Vols, II and III in 2 parts each. All his other writings preserved in Greek are in Supplementum Aristotelicum, II, pts. 1 and 2 (Berlin, 1887–1892). The content of a writing on providence, translated from Greek into Arabic, has been translated into French in P. Thillet, “Un traité inconnu d’Alexandre d’Aphrodise sur la Providence dans une version arabe inédite,” in Actes du Premier Congrès International de Philosophie Médiévale (Louvain–Paris, 1960), pp. 313–324, See also A. Dietrich, “Die arabische Version einer unbekannten Schrift des Alexander von Aphrodisias über die differentia specifica,” in Nachrichten der Akademie der Wissenschaften in Göttingen, 1 (1964), 90–148; E.G. Schmidt, “Alexander von Aphrodisias in einem altarmenischen Kategrien–Kommentar,” in Philologus, 110 (1966), 277286; J.van Ess, “Über einige neue Fragmente des Alexander on Aphrodisias und des Proklos in arabischer “Übersetzung,” in Der Islam, 42 (1966), 148–168. Translations of Alexander’s works include On Destiny, A. FitzGerald. ed. and trans. (London, 1931); and Commentary on Book IV of Aristotle’s Meteorologica, V.C.B. Coutant, trans. (New York, 1936).

II. Secondary Literature. A brief but comprehensive presentation is E. Zeller, Die Philosophic der Griechen, 5th ed., III, pt. I (Leipzig, 1923; repr. 1963), 817–830. Still briefer are A. Tognolo, “Alessandro di Aphrodisia” and “Alessandrismo”, in Enciclopedia filosofica, I (VeniceRome, 1957), 136–139; and F. Ueberweg and K. Praechter, Die Philosophie des Altertums, 12th ed. (Berlin, 1926; repr. Basel, 1953). Special problems are discussed in I. Bruns, “Studien zu Alexander von Aphrodisias,” in Rheinisches Museum, 44 (1889), 613–630; 45 (1890), 138–145, 223–235; and Preface to his ed. of the Natural Questions in Supplementum Aristotelicum (see above), pp. v–xiv; E. Freudenthal, “Die durch Averroes erhaltenen Fragmente Alexanders zur Metaphysik des Aristoteles,” in Abhandlungen der Berliner Akademie com Jahre 1884 (Berlin, 1885); P. Merlan, “Ein Simplikios-Zitat bei Ps. Alexandros and ein Plotinos-Zitat bei Simplikios,” in Rheinisches Museum, 84 (1935), 154–160; Philologische Wochenschrift. 58 (1938), 65–69; and Monopsychism, Mysticism, Metaconsciousness (The Hague, 1963), Index, under “Alexander” and “Pseudo-Alexander” P. Moraux, Alexandre d’Aphrodise, exégéte de la noètique d’Aristote (Paris, 1942); and J. Zahlfleisch, “Die Polemik Alexandres von Aphrodisias gegen die verschiedenen Theorien des Sehens,” in Archiv für Geshichte der Philosophie, 8 (1895), 373–386, 489–509; 9 (1896), 149–162. Additional literature is listed in Ueberweg and Praechter (see above).

Virtually all presentations of Aristotle’s noetics deal with Alexander; a recent example is L. Barbotin, La théorie aristotelicienne de l’intellect d’aprés Théophraste (Louvain, 1954). Other recent literature includes O. Becker, “Formallogisches and Mathematisches in griechischen philosophischen Texten,” in Philologus, 100 (1956), 108–112; R. Hackforth, “Notes on Some Passages of Alexander Aphrodisiensis De fato,” in Classical Quarterly, 40 (1946), 37–44; F. P. Hager, “Die Aristotelesinterpretation des Alexander von Aphrodisias und die Aristoteleskritik Plotins bezüglich der Lehre vom Geist,” in Archiv für Geschichte der Philosophie, 46 (1964), 174–187; P. Henry, “Une comparaison chez Aristote, Alexandre et Plotin,” in Les sources de Plotin (Geneva, 1960), PP. 429–444; H. Langerbeck, “Zu Alexander von Aphrodisias’ De fato,” in Hermes, 64 (1936), 473–474; S. Luria, “Die Infinitesimaltheorie der antiken Atomisten,” in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B; Studien2 (1932), 106–185; P. Moraux, “Alexander von Aphrodisias Quaestiones 2, 3,” in Hermes, 95 (1967), 159–169; R. A. Pack, “A Passage in Alexander of Aphrodisias Relating to the Theory of Tragedy,” in American Journal of Philology, 58 (1937), 418–436; S. Pines, “Omne quod movetur necesse est ab aliquo moveri: A Refutation of Galen by Alexander of Aphrodisias and the Theory of Motion,” in Isis, 52 (1961), 21–54; J. M. Rist, “On Tracking Alexander of Aphrodisias,” in Archiv für Geschichte der Philosophie, 48 (1996), 82–90.

Philip Merlan

LOGIC In general usage, the process of reasoning and sound judgement, often taken to be the outcome of adequate education, an aspect of common sense, or both: a logical decision. In philosophy, the study and development of close reasoning, especially inference, traditionally the concern of logicians and mathematicians and currently important for computer programmers, computational linguists, and researchers into artificial intelligence. There are several kinds of logic, such as formal logic and symbolic logic, of philosophical systems that acknowledge its influence, such as logical positivism, and of techniques considered to incorporate logic, such as logic arrays and logic circuits in electronic technology.

Classical logic

The term logikḗ was coined by the Greek philosopher Alexander of Aphrodisias in the 3c, but systems of organized thinking had already developed well before this in Greece, India, and China. Western culture has inherited the Greek tradition mainly through Rome and the Arab world. In this tradition, logic is closely linked with grammar and rhetoric, and discussion of one often leads to discussion of the others. For the Greeks, both reasoning and language were encompassed in the word lógos, which they contrasted with mûthos, a term that encompassed words, speech, stories, poems, fictions, and fables. Plato (5c BC) in The Republic represented Socrates as wishing to exclude poetry from the proper education of the young, and after some 2,500 years, this viewpoint still carries weight: logic, science, and reason are commonly set on one side and poetry, art, and myth on the other. To make his case, however, Plato used many devices from poetry and rhetoric: he so structured his dialogues that Socrates always won, often with the help of poetic analogies such as the Simile of the Cave. His pupil Aristotle laid the foundations of logic proper, as the study of inference from propositions arranged as formal arguments.

Grammar and logic

Because logic and GRAMMAR developed together they have overlapping terminologies: both use the term sentence, and deductive logic consists of a logic of propositions (also called sentential logic) and a logic of predicates (also called a logic of noun expressions). Logicians, grammarians, and rhetoricians are all interested in such matters as AMBIGUITY, FALLACY, paradox, syntax, and SEMANTICS, and in such modalities as necessity, possibility, and contingency; linguists who are concerned with grammar, computation, and artificial intelligence take as much interest in logic as in natural language. Logicians and mathematicians have created systems that contain both sets of abstract symbols and the rules necessary for their combination and manipulation in strings. Such symbols, rules, and strings are often idealizations of elements in, or thought to be in, natural language (but isolated from such everyday factors as dialect variation, personal idiosyncrasy, figurative usage, emotional connotation, colloquial idiom, social attitude, and semantic change). When such a system of symbols is adapted to practical ends, however, as in computer technology and artificial intelligence, pure logic becomes applied logic, operating within a real machine intended to do real work in real time.

Although many logicians, grammarians, and linguists have been interested in a universal calculus of language (something that would transcend natural language or allow the dispassionate description of all language), they have built their systems out of the natural languages that they know best: Greek for Aristotle and his disciples, Latin for medieval and Renaissance grammarians, and English for such present-day theorists as Noam Chomsky. Both prescriptive and descriptive grammarians of such Western languages as French and English have been influenced by logic and by the languages in which the principles of logic developed. Because it emerged in large part through the use and analysis of language, it has not been difficult to find quasi-logical patterns in language. Some analysts have been inclined to see logical orderliness either as inherent in language or as a reasonable goal of language planning, especially when a language is in the process of being standardized. Everyday language, however, has a persistent (even frustrating) tendency towards the illogical or non-logical, as for example in the use of double negatives (I didn't do nothing, which does not therefore mean ‘I did something’) and in idiomatic expressions (such as it's raining cats and dogs).

All analysts of language work towards orderliness, but some go further and engage in or recommend making certain aspects of language, such as the spelling of English, more ‘regular’ (that is, more rule-governed and therefore more logically consistent). They may also favour an artificial language such as Esperanto or Basic English that is (apparently) free from the illogic of natural language. Interest in such reforms has often gone hand in hand with particular conceptions of and assumptions about, progress, science, efficiency, education, literacy, and standards. Logic has therefore been used as a tool for both the description of natural language and its prescriptive improvement. In the development of the first grammars of English, the model was Latin and the analytical terms were Greek as used by the describers of Latin. Medieval and Renaissance models for vernacular prose as a vehicle of rational discourse were either Latin prose or vernacular prose written in the Latin style. Theories of sentences and parts of speech were those developed by classical grammarians and logicians, often the same people. The analysis of sentences into subjects and predicates, main and subordinate clauses, and the like, has paralleled the logician's view of propositions as the core of language and of binary division as a powerful conceptual tool.

The limits of logic

In the second half of the 20c, ancient practice has gained fresh impetus through the work of Noam Chomsky. Some features of his work are: (1) The definition of a language as a set of well-formed sentences, indefinite in number. (2) Abstract and diagrammatic analyses of sentences of standard written English. (3) The use of quasi-logical symbols such as S for sentence, NP for noun phrase, and VP for verb phrase, to sustain the analysis of such sentences. (4) Logical transformations performed on strings of symbols so as to produce further strings. (5) The creation of a generative grammar, that is, a set of explicit, formal rules that specify or generate all and only the sentences which constitute a language; in so doing, they are seen as demonstrating the nature of the implicit knowledge of that language possessed by an ideal native speaker-hearer. Such an approach has often been taken to be a break with the past, but is rooted in more than two millennia of logical and grammatical system-building. It remains a matter of debate whether natural language can be handled by linguistic theories that derive in the main from or are closely associated with aspects of formal logic. Natural language is a neural mechanism, apparently the result of genetic and social evolution. While it is sometimes regular, logical, and precise, it is as often irregular, non-logical, and imprecise, and oftener still a mix of the two. It blends intellect with instinct, logic with inspiration, and the standard with the varied. Logic is closely associated with language and with its description and discussion in literate societies. As such, it is an essential tool, but one cannot deduce from this usefulness that it is the sole or even primary means by which natural language can be understood.

ALEXANDER OF APHRODISIAS

Alexander of Aphrodisias, who was teaching at Athens in 200 CE, was recognized for centuries as the most authoritative exponent of Aristotle. His influence has probably been most far-reaching in the development of the theory of universals because he emphasized certain elements in Aristotle's not always unambiguous account. These were the unqualified priority of the particular substance and the existence of universals only as concepts, or "acts of intellect." The form was what made "this" matter (that is, an identifiable piece) what it was, but it was contingent whether the form was universal in the sense of generic. (Alexander does not notice that a class with only one member, like his case of the sun, is still a class.) What the form is as a subject remains unclear.

More famous is his doctrine about soul and intellect. A human being's intellectual faculty can exist in three conditions, described as three intellects: (1) the "material" intellect (intellectus possibilis ), which is nothing actual but the bare potentiality (so Aristotelian matter) of the body to develop reason—the condition of babies; (2) the intellect (intellectus in habitu ) that is the possession of, in fact, is identical with, concepts, or universals gained from sense experience—the condition of adults; (3) the "active" intellect (intellectus agens ), which is exercising the thoughts that form the intellectus in habitu and is thus equivalent to the intellect as aware of itself.

What is distinctively Alexandrist is the identification he made, or seemingly made, of the "active" intellect both with the intellect that Aristotle said entered the body "from outside" and with the intellect eternally thinking of itself that Aristotle said was God. Intellect was, of course, the highest part or function of the soul, but since only the "active" intellect, as a "separate form," could exist without matter, it followed that there was no individual immortality for human beings. The exact relation of the "active" intellect to the individual soul or intellect is obscure in Alexander. He does not describe an active intellect acting directly like an efficient or even formal cause on a passive intellect but suggests rather the quasi-logical relationship which was fundamental to Neoplatonism and which made the less perfect instance of a kind entail the existence of the perfect. Thus, it is not at all certain that he meant thinking itself to go the way of immortality. In the fifteenth century Italian philosophers known as Alexandristi defended this interpretation of Aristotle's psychology against both Averroes's version and the theologically orthodox version of Themistius and Thomas Aquinas.

In other subjects we see Alexander less original but often attacking Stoic doctrine, notably in his tracts On Fate and On Mixture. But the exact understanding of him is colored always by the difficulty of knowing how far we can trust the writings attributed to him. The commentary on Books E (VI) to N (XIV) of Aristotle's Metaphysics and parts of Book II of his own De Anima are probably not his. The latter includes the section On Intellect which greatly influenced later Greek, Arab, and medieval philosophers. But both may well depend on and be closer to his thought than is allowed by a modern tradition that underestimates Neoplatonizing features of Aristotle as well as of Alexander.

See also Aristotle; Averroes; Neoplatonism; Themistius; Thomas Aquinas, St.; Universals, A Historical Survey.

Bibliography

Alexander's works, including dubious ones, are in Commentaria in Aristotelem Graeca, Vols. I–III, and Supplementum Aristotelicum, Vol. II (Berlin, 1883–1901). P. Moraux, Alexandre a'Aphrodise, exégète de la noétique d'Aristote (Paris, 1942), includes a French translation of On Intellect. See also F. E. Cranz, in Catalogus Translationum et Commentariorum: Mediaeval and Renaissance Latin Translations and Commentaries, Vol. I (Washington, DC: Catholic University of America Press, 1960), pp. 77–135; Ernst Cassirer, Das Erkenntnisproblem, 3rd ed., Part I, "Die Reform der aristotelischen Psychologie" (Berlin: Cassirer, 1922); and J. H. Randall Jr., The School of Padua and the Emergence of Modern Science (Padua, 1961).

A. C. Lloyd (1967)