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Philosophy 

철학 - 지혜의 탐구

2 ANCIENT AND MEDIEVAL SCHOOLS

 

2.5 Platonism   

 

 

 

Since Plato refused to write any formal exposition of his own metaphysic, our knowledge of its final shape has to be derived from the statements of Aristotle, which are confirmed by scanty remains of the earliest Platonists preserved in the Neoplatonist commentaries on Aristotle. These statements can, unfortunately, only be interpreted conjecturally.

 

2.5.1 ARISTOTLE'S ACCOUNT OF PLATONISM

According to Aristotle (Metaphysics i, 987 b 18-25) Plato's doctrine of forms was, in its general character, not different from Pythagoreanism, the forms being actually called numbers. The two points on which Aristotle regards Plato as disagreeing with the Pythagoreans are (1) that, whereas the Pythagoreans said that numbers have as their constituents the unlimited and the limit, Plato taught that the forms have as constituents the one and the great and small; and (2) that, whereas the Pythagoreans had said that things are numbers, Plato intercalated between his forms (or numbers) and sensible things an intermediate class of mathematicals. It is curious that in connection with the former difference Aristotle dwells mainly on the substitution of the "duality of the great and small" for the "unlimited," not on the much more significant point that the one, which the Pythagoreans regarded as the simplest complex of unlimited and limit, is treated by Plato as itself the element of limit. He further adds that the "great and small" is, in his own technical terminology, the matter, the one, the formal constituent, in a number. (see also  idea)

If we could be sure how much of the polemic against number-forms in Metaphysics xiii-xiv is aimed directly at Plato, we might add considerably to this bald statement of his doctrine, but unluckily it is certain that much of the polemic is concerned with the teaching of Speusippus and Xenocrates. It is not safe, therefore, to ascribe to Plato statements other than those with which Aristotle explicitly credits him. We have then to interpret, if we can, two main statements: (1) the statement that the forms are numbers; and (2) the statement that the constituents of a number are the great and small and the one.

Light is thrown on the first statement if we recall the corpuscular physics of the Timaeus and the mixture of the Philebus. In the Timaeus, in particular, the behaviour of bodies is explained by the geometrical structure of their corpuscles, and the corpuscles themselves are analyzed into complexes built up out of two types of elementary triangle, which are the simplest elements of the narrative of Timaeus. Now a triangle, being determined in everything but absolute magnitude by the numbers that express the ratio of its sides, may be regarded as a triplet of numbers. If we remember then, that the triangles determine the character of bodies and are themselves determined by numbers, we may see why the ultimate forms on which the character of nature depends should be said to be numbers and also what is meant by the mathematicals intermediate between the forms and sensible things. According to Aristotle, these mathematicals differ from forms because they are many, whereas the form is one, from sensible things in being unchanging. This is exactly how the geometer's figure differs at once from the type it embodies and from a visible thing. There is, for example, only one type of triangle whose sides have the ratios 3:4:5, but there may be as many pure instances of the type as there are triplets of numbers exhibiting these ratios; and again, the geometrical triangles that are such pure instances of the type, unlike sensible three-sided figures, embody the type exactly and unchangingly. A mathematical physicist may thus readily be led to what seems to be Plato's view that the relations of numbers are the key to the whole mystery of nature, as is actually said in the Epinomis (990 e).

We can now, perhaps, see the motive for the further departure from Pythagoreanism. It is clear that the Pythagorean parallelism between geometry and arithmetic rested upon the thought that the point is to spatial magnitude what the number 1 is to number. Numbers were thought of as collections of units, and volumes, in like fashion, as collections of points; that is, the point was conceived as a minimum volume. As the criticisms of Zeno showed, this conception was fatal to the specially Pythagorean science of geometry itself, since it makes it impossible to assert the continuity of spatial magnitude. (This, no doubt, is why Plato, as Aristotle tells us, rejected the notion of a point as a fiction.)

There is also a difficulty about the notion of a number as a collection of units, which must have been forced on Plato's attention by the interest in irrationals that is shown by repeated allusions in the dialogues, as well as by the later anecdotes that represent him as busied with the problem of doubling the cube or finding two mean proportionals. Irrational square and cube roots cannot possibly be reached by any process of forming collections of units, and yet it is a problem in mathematics to determine them, and their determination is required for physics (Epinomis 990 c-991 b).

This is sufficient to explain why it is necessary to regard the numbers that are the physicist's determinants as themselves determinations of a continuum (a great and small) by a limit and why at the same time the one can no longer be regarded as a blend of unlimited and limit but must be itself the factor of limit. (If it were the first result of the blending, it would reappear in all the further blends; all numbers would be collections of one and there would be no place for the irrationals.) There is no doubt that Plato's thought proceeded on these general lines. Aristotle tells us that he said that numbers are not really addable (Metaphysics xiii, 1083 a 34), that is, that the integer series is not really made by successive additions of 1; and the Epinomis is emphatic on the point that, contrary to the accepted opinion, surds are just as much numbers as integers. The underlying thought is that numbers are to be thought of as generated in a way that will permit the inclusion of rationals and irrationals in the same series. In point of fact there are logical difficulties that make it impossible to solve the problem precisely on these lines. It is true that mathematics requires a sound logical theory of irrational numbers and, again, that an integer is not a collection of units; it is not true that rational integers and real numbers form a single series.

The Platonic number theory was inspired by thoughts that have since borne fruit abundantly but was itself premature. We learn partly from Aristotle, partly from notices preserved by his commentators, that, in the derivation of the integer series, the even numbers were supposed to be generated by the dyad that doubles whatever it lays hold of, the odd numbers in some way by the one that limits or equalizes, but the interpretation of these statements is, at best, conjectural. In the statement about the dyad there seems to be some confusion between the number 2 and the indeterminate dyad, another name for the continuum also called the great and small, and it is not clear whether this confusion was inherent in the theory itself or has been caused by Aristotle's misapprehension.

Nor, again, is it at all certain exactly what is meant by the operation of equalizing ascribed to the one. It would be improper here to propound conjectures that our space will not allow us to discuss. A collection and examination of the available evidence is given by L. Robin in his Théorie platonicienne des idées et des nombres d'après Aristote (1908), and an admirable exposition of the significance of the problem of the irrational for Plato's philosophy by G. Milhaud in Les Philosophes-géomètres de la Grèce, Platon et ses prédécesseurs, new ed. (1934). For a conjectural interpretation see A.E. Taylor, "Forms and Numbers," in Mind, new series, vol. 35 and 36 (1926, 1927).

 

2.5.2 THE ACADEMY AFTER PLATO: THE RISE OF NEOPLATONISM

Plato's Academy continued to exist as a corporate body down to AD 529, when the emperor Justinian, in his zeal for Christian orthodoxy, closed the schools of Athens and appropriated their emoluments. Plato's greatest scholar, Aristotle, had finally gone his own way and organized a school of his own in the Lyceum, claiming that he was preserving the essential spirit of Platonism while rejecting the difficult doctrine of the forms. The place of official head of the Academy was filled first by Speusippus, Plato's nephew (c. 347-339 BC), then by Xenocrates (c. 339-314 BC). Under Arcesilaus (c. 276-241 BC) the Academy began its long-continued polemic against the sensationalist dogmatism of the Stoics, which accounts both for the tradition of later antiquity that dates the rise of a New (some said Middle) and purely skeptical Academy from Arcesilaus and for the 18th-century associations of the phrase "academic philosophy." (see also  Stoicism)

In the 1st century BC the most interesting episode in the history of the school is the quarrel between its president, Philo of Larissa, and his scholar Antiochus of Ascalon, of which Cicero's Academica is the literary record. Antiochus, who had embraced Stoic tenets, alleged that Plato had really held views indistinguishable from those of Zeno of Citium and that Arcesilaus had corrupted the doctrine of the Academy in a skeptical sense. Philo denied this. The gradual rapprochement between Stoicism and the Academy is illustrated from the other side by the work of Stoic scholars such as Panaetius of Rhodes and Poseidonius of Apamea, who commented on Platonic dialogues and modified the doctrines of their school in a Platonic sense.

The history of the Academy after Philo is obscure, but since the late 1st century AD we meet with a popular literary Platonism of which the writings of Plutarch are the best example. This popular Platonism insists on the value of religion, in opposition to Epicureanism, and on the freedom of the will and the reality of human initiative, in opposition to the Stoic determinism; a further characteristic feature, wholly incompatible with the genuine doctrine of Plato, is the notion that matter is inherently evil and the source of moral evil.

Genuine Platonism was revived in the 3rd century AD, in Rome, and independently of the Academy, by Plotinus. His Neoplatonism represents a real effort to do justice to the whole thought of Plato. Two aspects of Plato's thought, however, in the changed conditions inevitably fell into the background: the mathematical physics, and the politics. The 3rd century AD had no understanding for the former, and the Roman Empire under a succession of military chiefs no place for the latter. The doctrine of Plotinus is Platonism seen through the personal temperament of a saintly mystic and with the Symposium and the teaching of the Republic about the form of good always in the foreground. Plotinus lived in an atmosphere too pure for sectarian polemic, but in the hands of his successors Neoplatonism was developed in conscious opposition to Christianity. Porphyry, his disciple and biographer, was the most formidable of the anti-Christian controversialists; in the next century, "Platonists" were among the allies and counsellors of the emperor Julian in his attempts to invent a Hellenic counterpart to Christianity.

Early in the 5th century, Neoplatonism flourished for a short time in Alexandria (which disgraced itself by the murder of Hypatia in 415) and captured the Athenian Academy itself, where its last great representative was the acute Proclus (AD 410-485). The latest members of the Academy, under Justinian, occupied themselves chiefly with learned commentaries on Aristotle, of which those of Simplicius are the most valuable. The doctrine of the school itself ends with Damascius in mystical agnosticism.

 

2.5.3 INFLUENCE OF PLATONISM ON CHRISTIAN THOUGHT

Traces of Plato are probably to be detected in the Alexandrian Wisdom of Solomon; the thought of the Alexandrian Jewish philosopher and theologian Philo, in the 1st century AD, is at least as much Platonic as Stoic. There are, perhaps, no certain marks of Platonic influence in the New Testament, but the earliest apologists (Justin, Athenagoras) appealed to the witness of Plato against the puerilities and indecencies of mythology. In the 3rd century Clement of Alexandria and after him Origen made Platonism the metaphysical foundation of what was intended to be a definitely Christian philosophy. The church could not, in the end, conciliate Platonist eschatology with the dogmas of the resurrection of the flesh and the Last Judgment, but in a less extreme form the platonizing tendency was continued in the next century by the Cappadocians, notably St. Gregory of Nyssa, and passed from them to St. Ambrose of Milan. The main sources of the Platonism that dominated the philosophy of Western Christian theologians through the earlier Middle Ages, were, however, Augustine, the greatest thinker among the western Fathers, who had been profoundly influenced by Plotinus read in a Latin version before his conversion to Christianity; and Boethius, whose wholly Platonist vindication of the ways of Providence in his De Consolatione Philosophiae was the favourite serious book of the Middle Ages. (see also  Christian Platonism)

A further powerful influence was exerted by the writings of the Pseudo- Dionysius the Areopagite. These works are, in fact, an imperfectly Christianized version of the speculations of Proclus and cannot date before the end of the 5th century AD at the earliest, but they enjoyed an immense authority based on their attribution to an immediate convert of St. Paul. After their translation into Latin in the 9th century by John Scotus Erigena, they became popular in the West.

Apart from this theological influence, Plato dominated the thought of the earlier Renaissance that dates from the time of Charlemagne in another way. Since the West possessed the philosophical writings of Cicero, with the Neoplatonic comment of Macrobius on the Somnium Scipionis, as well as the Latin translation of the first two-thirds of the Timaeus by Chalcidius, with his commentary on the text, and versions, also, at least of the Phaedo and of the Meno, whereas nothing was known of the works of Aristotle except Latin versions of some of the logical treatises, the Middle Ages, between Charlemagne and the beginning of the 13th century, when the recovery of Aristotle's physics and metaphysics from Moors, Persians, and Jews began, was much better informed about Plato than about Aristotle; in particular, in the various encyclopaedias of this period, it is the Timaeus that forms the regular background.

The 13th century saw a change. Aristotle came to displace Plato as the philosopher, partly in consequence of the immediately perceived value of his strictly scientific works as a storehouse of well-digested natural facts, partly from the brilliant success of the enterprise carried through by St. Thomas Aquinas, the reconstruction of philosophical theology on an Aristotelian basis. Plato is, however, by no means supplanted in the Thomist system; the impress of Augustine on Western thought has been far too deep for that. Augustine's " exemplarism," that is, the doctrine of forms in the version, ultimately derived from Philo of Alexandria, which makes the forms creative thoughts of God, is an integral part of the Thomist metaphysics, though it is now denied that the exemplars are themselves cognizable by the human intellect, which has to collect its forms, as best it can, from the data of sense. (see also  Thomism)

Directly or through Augustine, the influence of Plato, not only on strictly philosophic thought but also on popular ethics and religion, has repeatedly come to the front in ages of general spiritual requickening and shows no signs of being on the wane.

Two revivals in particular are famous. The first is that of the 16th century, marked by the Latin translation of Marsilio Ficino and the foundation of Lorenzo de' Medici's fantastic Florentine Academy. What was revived then was not so much the spirit of Plato as that of the least sober of the Neoplatonists; the influence of the revival was felt more in literature than in philosophy or morals, but in literature its importance may be measured by the mere mention of such names as Michelangelo, Sir Philip Sidney, and Edmund Spenser. (see also  Platonic Academy)

In the 17th century, Plato, seen chiefly through the medium of Plotinus, supplied the inspiration of a group of noble thinkers who were vindicating a more inward morality and religion against the unspiritual secularism and Erastianism of Hobbes: namely the so-called Cambridge Platonists, Benjamin Whichcote, Henry More, Ralph Cudworth, and John Smith. In the 20th century, on the one hand A.N. Whitehead tried to work out a philosophy of the sciences that confessedly connected itself with the ideas of the Timaeus; and on the other the rise of totalitarian governments produced a number of publications confronting Plato with the theories (Communist, Fascist, etc.) inherent in their policies. Neo-Kantianism, Existentialism, and analytical philosophy produced their own interpretations of Plato. ( A.E.Ta./Pp.M.)

 
   


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