PLATO

(b. Athens [?], 427 B.C.; d. Athens, 348/347 B.C.)

theory of knowledge; advocacy, in theory and practice, of education based on mathematics; organization of research.

Plato’s enthusiasm for mathematics, astronomy, and musical theory appears everywhere in his writings, and he also displays a far from superficial knowledge of the medicine and physiology of his day. In ancient times competent judges held that he had promoted the advance of mathematics, especially geometry, in his lifetime.¹ Theodore of Cyrene and Archytas of Tarentum were his friends, and Eudoxus of Cnidus, Theaetetus, and Menaechmus his colleagues or pupils. His critics assert that his theory of knowledge rules out any empirical science and that, owing to his idealism, he had a radically false idea of the procedure and value of the mathematics that he admired. Even so, it can be said that the Academy, founded by him at Athens at a date not exactly known (380 B.C.?), became a center where specialists—not all of them sympathizers with his philosophy and epistemology—could meet and profit by discussion with him and with one another.

Our object here must be to trace Plato’s intellectual development and, incidentally, to submit part of the material upon which an estimate of his services or disservices to science must be based. It must be considered how far he is likely to have carried out in his school the project, sketched in the Republic, of a mathematical training preparatory for and subordinate to dialectic, and whether, in the writings believed to belong to the last twenty years of his life, he took note of recent scientific discoveries or was influenced by them in matters belonging to philosophy.

As for sources of information, the account of Plato’s life and doctrine by Diogenes Laertius (probably early third century A.D.) is based on previous authorities of unequal value. He reports some evidently reliable statements by men who were in a position to know the facts and who were neither fanatical devotees nor detractors, and he has preserved the text of Plato’s will. Aristotle gives us a few details, and Cicero a few more.

The Epistles, ascribed to Plato and printed in the Herrmann and Burnet editions of the Greek text of his works, would, if genuine, furnish us with a personal account of his conduct at important crises in his life; and, what is more, they would tell far more about his ideals of education and the work of the Academy than can be gathered from the dialogues. Unfortunately, opinion regarding authenticity of the Epistles is so divided that caution is essential. In the ensuing account, where reference is made to this source, the fact has been indicated.

Plato’s writings have been preserved entire. But the double fact that they are dialogues and that the scene is usually laid in the past leads to difficulties of interpretation which are sufficiently obvious. Moreover, nothing definite is known about either the manner of their first publication or their relative order, still less the dates. Some hypothesis about the latter is a presupposition of fruitful discussion of Plato’s development.

A statistical study of the style of Plato’s works, in which the pioneer was the Reverend Lewis Campbell (1869), has led to results which have met with wide approval: many scholars hold that Parmenides and Theaetetus were written later than the Republic, and that a group of dialogues having close stylistic affinity to one another and to the Laws (which is plainly a work of old age) came still later. This is credible from a philosophical point of view, and its correctness is assumed here; but such a method can only yield a probable result.

Several members of Plato’s family are mentioned, or appear as characters, in his dialogues. He himself was the son of Ariston² and Perictione, and was born either at Athens or Aegina, where his father may have gone as a settler when the Athenians occupied the island. Nothing reliable is known of his father’s ancestors, but those on his mother’s side were men of distinction. Perictione was descended from Dropides, a close friend (some say brother) of Solon, the famous poet-statesman of the sixth century B.C. She was a cousin of Critias, son of Callaeschrus, an intellectual daring in both speculative thought and action. It was Critias who in 404 B.C. led the extremists among the Thirty Tyrants and put to death the moderate Theramenes. He became guardian of Perictione’s brother Charmides and drew him into public affairs. Both perished in the battle which put an end to the Thirty’s six months of power.

Plato was one of four children. His brothers Adeimantus and Glaucon take a leading part in the Republic, where they are depicted with admiration and a clear impression of their personality is left. They appear once more briefly in the Parmenides, and Xenophon presents Socrates proving to Glaucon the folly of his trying to address the Assembly when he is not yet twenty.³ The brothers were considerably older than Plato, and his sister Potone (mother of Speusippus, who followed him as head of the Academy) was doubtless born in the interval.

Plato’s father, Ariston, appears to have died young. Perictione then married Pyrilampes, son of Antiphon, who had been prominent in state affairs as a close associate of Pericles; he was probably her uncle. Another son, called Antiphon after his grandfather, was born; this half brother of Plato’s has a part in the Parmenides. Most of these persons are mentioned either in Charmides (155–158), or in Timaeus (20E), or at the opening of Parmenides.⁴

Plato’s social position was such that he might well have aspired to an active part in public affairs, but it could not have been easy for him to decide what role to assume. Some scholars take it for granted that the example and writings of Critias left a deep impression upon him; others point out that it was only in the concluding phase of the Athenian struggle against the Peloponnesians that Plato’s maternal relatives emerged as reactionary extremists, and that in his stepfather’s home he would have been imbued with liberal opinions and respect for the memory of Pericles.

No one can say with certainty what the complexion of his views was at the age of twenty-four, except that he was obviously no friend to egalitarianism and full democracy. The story which he tells, or is made to tell, in Epistle VII seems probable. His friends and relatives among the Thirty at once called upon him to join them, but instead he determined to wait and see what they would do. They soon made the former regime seem highly desirable by comparison. Socrates was commanded to help in the arrest of a man who was to be put to death illegally under a general sentence, so that he would either be involved in their impious actions or refuse and thus expose himself to punishment. When the Thirty were overthrown, Plato again thought of public affairs—but with less eagerness than before. The democratic leaders restored to power showed moderation at a time when ruthless acts of revenge might have been expected. Nevertheless Socrates was brought to trial on the pretext of impiety and found guilty. As Plato grew older and the politicians, laws, and customs of the day displeased him more and more, he was thrown back on a theorist’s study of ways of reform.⁵

None of this is inconsistent with what is otherwise known. Socrates’ disobedience to the illegal command of the Thirty was a fact widely spoken of. Plato would probably have been impressed to an equal degree by Socrates’ courageous independence in such matters and by his faith in argument (argument with himself when he could not find a respondent). He became conspicuous among Socrates’ habitual companions, as distinct from the occasional listeners to his conversation. With Adeimantus he heard Socrates’ provocative defense in court against the charge of impiety;⁶ when a majority had found him guilty, Plato was one of those who induced Socrates to offer to pay a substantial fine, for which he would be a guarantor.⁷

Owing to illness, Plato was absent from the last meeting of Socrates’ with his friends.⁸ After the tragedy, he retried, with other Socratics, to Megara, the home of Euclid.⁹ The attack on Socrates was personal, and perhaps the prosecutors did not desire his death. His Athenian friends can hardly have been in danger. But there are some hints in the Phaedo that he advised those present, among whom were the Megarians Euclid and Terpsion, to pursue the search for truth in common and not lose heart when plausible reasoning led them nowhere; rather, they must make it their business to master the “art of argument,” log?n techu?.¹⁰

Probably his wish was piously carried out by his followers, and a few years elapsed before the different direction of their interests became clear. As a metaphysician Euclid was a follower of Parmenides, and accepted the Socratic thesis that there is a single human excellence, not a plurality of “virtues.” His thought had no religious coloring, nor was he an educational reformer. His younger disciples turned in earnest fee the hoped-for logon techne, and not without result; they prepared the way for the propositional logic of the Stoic school.¹¹ This might be supposed to go together with an interest in the sciences, but this is not recorded of the Megarians. Plato, on the other hand, began to turn in that direction; his first dialogues and the Apology must have been written during the years 399–388 B.C. He felt it his duty to defend the memory of Socrates, especially since controversy about his aims had been revived by hostile publications. As the chance of political action remained remote, he gradually developed the idea of a training of the young not in rhetoric but in mathematics—and in Socratic interrogation only after the mathematical foundation had been laid. Part of his diagnosis of the ills of Athens was that young men had bewildered themselves and others by engaging too soon in philosophical controversy; these ideas probably found little sympathy among the Megarians. How long he remained among them is not recorded, but he was liable to Athenian military service, probably as a cavalryman. A statement has indeed come down to us ¹² that he went on expeditions to Tanagra (in Boeotia) and Corinth. This is credible in itself, and in the latter case the reference could be to an engagement in 394 B.C. outside Corinth, in which the Spartans and their allies defeated the Athenians and Thebans. But neither does it seem inconsistent with Plato’s regarding Megara for a time as his home. About 390 he resolved to visit the West, where Archytas of Tarentum survived as a maintainer of the Pythagorean system of education and was also active in research.

Plato’s views at the time of departure on his journey to the West are well seen in the Gorgias. It is his first major constructive effort as a moralist, but there is as yet no positive doctrine of knowledge and reality. When Callicles spurns conventional justice, as a means of defrauding the strong and energetic of what naturally belongs to them, and declares that temperance is not a virtue (why should a clear-sighted man choose to curb his own desires?), Socrates confidently develops an answering thesis: the supervision of the soul must be supposed comparable in its operation to the arts, which impose form and design (eidos, taxis) and preserve the natural subordination of one part of a subject to another (kosmos). Human good does not consist in the ceaseless satisfaction of desires, irrespective of their quality (if it did, man would stand apart from the general world order), and self-discipline is the basis of happiness. But the statesmen of Athens, the dramatists and musicians, the teachers and learners of rhetorical persuasion, have all alike failed to understand this and have flattered rather than guided the public.

In his use of the varied senses of kosmos (which, according to the context, means world or world order, moral discipline, or adornment). Socrates is here on Pythagorean ground; and ideas are already present which Plato expanded only in his later writings and his oral instruction.¹³ The Gorgias passage is also an emphatic answer to the friends who had sought to draw Plato into Athenian politics.¹⁴

Concerning the journey itself, in Epistle VII Plato says, or is made to say, that he was then forty years old (324A) and that in Italy and Sicily he was appalled by the sensuous indulgence which he found taken for granted there. On crossing to Syracuse he made the acquaintance of Dion, the young brother-in-law of the tyrant Dionysius the Elder, who listened attentively to his discourses and aroused his admiration by his intelligence and preference for a sober life. In the tyrant’s entourage this was viewed as an affectation of singularity and led to Dion’s becoming unpopular.¹⁵

If this evidence is set aside as suspect, the next best source is Cicero.¹⁶ He says that Plato visited Egypt before proceeding to Italy; that he spent a considerable time with Archytas and with Timaeus of Locri; and that the object of the voyage was to gain acquaintance with Pythagorean studies and institutions. To this some reservations must be made. First, it can hardly be true—if Cicero means this that when he boarded the ship Plato was altogether ignorant of mathematics. In his own dialogues there is clear evidence that the sciences were to some extent taught to boys at Athens and that there was an opportunity of learning from specialists in mathematics and astronomy, no less than from those in music, meter, and grammar. About Pythagoreanism also Plato already had some information, judging from the Gorgias passage mentioned above; he could have obtained this (as Wilamowitz suggests) from the Thebans Simmias and Cebes, pupils of Socrates who are said to have met Philolaus.¹⁷

Secondly, it does not seem likely that Timaeus of Locri was still alive at the time of Plato’s journey. In Timaeus 20A he is described as a man of intellectual distinction who has already held high office, and this is at a time certainly previous to 415 B.C. (It is possible that at this time Plato met Philistion of Locri, and derived from him the interest in the physiology of the Sicilian Empedocles, which is visible in both Meno and Phaedo) Cicero’s report may be wrong in some of its detail, but it seems true in spirit. Plato’s purpose in visiting the West was to see for himself how the Pythagoreans conducted their science-based educational system, and he did at this time establish a connection with Archytas.

Plato returned to Athens, after two years’ absence, in 388 B.C. (Ancient biographers related, with some circumstantial detail, that at Syracuse he had exasperated the tyrant Dionysius the Elder by open criticism of his rule and had been handed over as a prisoner to a Spartan envoy. But such insolence is hardly in character for Plato, and probably his voyage home was of a less sensational kind.) He might at this time have visited the Pythagoreans at Phlius, in the Peloponnesus. The setting of the Phaedo suggests personal acquaintance with their leader Echecrates, and Cicero confirms this.¹⁸

Nothing definite is recorded about Plato’s personal life during the ensuing twenty-two years. But the Academy was founded, or gradually grew up, during this time, and he composed further dialogues in Socratic style. The Meno and Euthyplwo, Euthydemus. Phaech, Symposium, and Republic must all be assigned to these years. In them he puts forward the distinctive account of knowledge which has taken shape in his mind; explains his purpose and method in education and shows the continuity of his aims with those of Socrates; and differentiates himself, where necessary, from the Italian Pythagoreans. It is natural to place the Republic at the end of this series, and to regard it as either a prospectus for a proposed school or as a statement to the Athenian public of what was already being carried out among them.

Aristotle gives a clear analysis of the factors which produced Plato’s doctrine of Forms.¹⁹ Plato was acquainted from youth with an Athenian named Cratylus, who declared with Heraclitus that there is no stable substance, or hold for human knowledge, in the sense world. Plato did not deny this then or later but, wishing to take over and continue the Socratic search for universals, in the sphere of morals, which do remain permanent, he necessarily separated the universals from sensible particulars. It was he who termed them Ideas and Forms. In his view particulars (that is, things and states of things, actions and qualities) derive reality from Forms by “participation” and when we name or speak of these particulars, we in effect name Forms.

In the dialogues Plato often starts from a contrast between knowledge and opinion. To live in a state of opinion is to accept assertions, either of fact or of principle, on authority or from mere habit. The opinion may be true and right; but since it is held without a rational ground, it may be driven from the mind by emotion and is less proof against forgetfulness than knowledge is. The holder of it may also be deceived in an unfamiliar instance. Based as it is on habit, an opinion cannot easily be transmitted to another; or, if the transmission takes place, this is not teaching. In terms of the theory of Forms, the holder of knowledge knows the Forms and can relate particular instances to them (although Plato did not successfully explain how this occurs), whereas the contented Holder of opinions moves about among half-real particulars.

In middle life, then, Plato had advanced from his Socratic beginnings toward beliefs, held with assurance, from which many practical consequences flowed. The chief elements were the knowledge-opinion contrast; the belief in a realm of immutable Forms, with which human minds can make intermittent contact and which on such occasions the minds recognize as “their own” or as akin to them;²⁰ given this, the soul, or its intellectual part, is seen to be likewise eternal; and the belief that the Forms, each of which infuses reality into corresponding particulars, in turn derive their existence, intelligibility, and truth from one supreme Form, the Good.

The advance from the plurality of Forms to their source is in consequence regarded as the ultimate stage in human study, megiston math?ma;²¹ it is a step which will be taken by only a few, but for the welfare of mankind it is important that a few should take it. Within the dialogue it is described but cannot be accomplished. There are hints of a methodical derivation of the other Forms from the Good; but for the present the image, whereby the Good is shown to have the same relation to other objects of intellection as the sun has to other visible things, takes its place. In reading the Republic and later dialogues, one must therefore reckon with the possibility that in the school Plato amplified or corrected the exposition which he chose to commit to writing.

The Athenians thought it suitable that young men should exercise themselves in argument on abstract themes before turning to serious business, and were prepared to tolerate “philosophy” on these terms. But Plato, as has been said, speaks out against this practice and holds that it has brought philosophy into discredit. Indeed, according to him, the order of procedure should be reversed. Argument, or its theory, is the hardest branch of philosophy and should come later. Men and women to whom legislation and administration are ultimately to be entrusted should undergo discipline in the sciences (including reflection on their interrelation) before they embark, say, at the age of thirty, on dialectical treatment of matters which have to be grasped by the intellect without the help of images. Such a discipline will single out those who have capacity for dialectic. To them will fall the task of making good laws, if these are not found in existence, and of interpreting and applying them if they are. For this purpose knowledge must be reinforced by experience.²² Lawless government is the common fault of despotism and democracy.

Plato holds that ignorance of mathematical truths which are in no way recondite, for example, the wrong belief that all magnitudes are copoensurable, is a disgrace to human nature.²³ It is not, however, this that is emphasized in his educational plan in the Republic. He explains that it is characteristic of mathematical studies that they gently disengage the intellect from sensible appearances and turn it toward reality; no other discipline does this. They induce a state of mind (which Plato terms dianoia, discursive thought) clearer than “opinion” and naive trust in the senses but dimmer than knowledge and reason. In geometry, for instance, the learner is enabled or compelled, with the aid of figures, to fix his attention on intelligible objects. Also, mathematicians “lay down as hypotheses the odd and even, various figures, and the three kinds of angles and the like”²⁴ but leave them unexamined and go on to prove that the problem that gave rise to their investigation has been solved. In this respect mathematical procedure tends to divert the mind from reality and can provide only conditional truth. But such studies, pursued steadily and without continual talk of their practical use, are a good preparation for methodical treatment of such relations among Forms as cannot be visibly depicted.

Arithmetic and plane geometry will be the basis of an education which is to end in knowledge; the geometry of three-dimensional figures must also be studied. When, in the dialogue, Glaucon observes that this hardly yet exists as a science, Socrates says that there are two reasons for this: first, no state at present honors the study and encourages men to devote themselves to it; and second, a director is needed in order to coordinate the research.²⁵ Such a man will be hard to find; and at present even if he existed the researchers are too self-confident to defer to him. Even without these conditions, and even when the researchers do not succeed in explaining what they are striving to achieve, the intrinsic charm of the study of three-dimensional figures is carrying it forward. This is one of the passages in which speakers in Plato’s dialogues refer prophetically, but in veiled terms, to circumstances at the time of writing. It is somewhat enigmatic for us. The intention is perhaps to compliment Theaetetus, who had discovered constructions for inscribing in a sphere the regular octahedron and icosahedron. Either he or Plato himself is cast for the role of a director, and there is a plea for public support of the Academy so that research can continue.

There is a similar personal reference in the treatment of the sciences of astronomy and musical theory.²⁶ Socrates dissociates himself from the Pythagoreans while approving of their statement that the two sciences are closely akin. Their theory of harmony is restricted to a numerical account of audible concords; and the aim of their astronomy is to discover the proportion between month, year, and the period of revolution of the planets. Instead of this, heard harmonies should be studied as a special case of the harmonies between numbers; and the proportion between month, year, and so forth (which is doubtless not unvarying) as an application of some wider theory dealing with the spatial relations of any given number of bodies of any shape, moving at any regular speeds at any distances. The visible universe will be to the “true astronomer” what a beautifully contrived diagram might be to the geometer, that is, an aid to the science, not the object of contemplation. Here Plato is indicating that he has not simply established on Athenian soil a replica of the Pythagorean schools. Attachment to the sense world must be loosened and the sciences taught with emphasis on their affinity to one another; for it is the power of synopsis, the perception of common features, that is to be strengthened. Those few who excel in this are to be set apart and trained to pursue another method which treats hypotheses as provisional until they have been linked to the unconditionally real and so established.²⁷

There is no question here, as some have thought, of a fusion of the existing special sciences. The ideal held out is probably this: The One is an aspect of the Good (this was common ground to Euclid of Megara and Plato); from the concept of unity, the number series can be made to emerge by deduction; and from the Good, by a process which makes more use of Socratic questioning, the system of moral and aesthetic concepts can likewise be evolved.²⁸

Boys will have some introduction to all the sciences that have been mentioned. Compulsion is to be avoided in the training of the mind, especially since what is learnt under duress leaves no lasting impression. At the age of twenty when state-enforced physical exercise is to cease, those judged capable of further progress must begin to bring together the knowledge that they have hitherto acquired randomly and to consider in what way the sciences are akin to one another and to reality. Until they are thirty this will be their occupation. After this there can follow five years of that dialectical exercise that Athenian custom regards as a fitting occupation for mere adolescents.²⁹

The program here outlined is our safest guide to the actual institutions of the Academy. But it is an ideal that is sketched, and one need not insist that it was carried out in detail. For instance, Plato did not admit women, and it is highly improbable that he gave no philosophical instruction to those under thirty; it would doubtless occur to him that since he could not prevent them from obtaining such instruction, it would be better to make sure that they were well taught.

“Academy” was an area to the northeast of the city which had been laid out as a park, including a public gymnasium. According to Lysias, the Spartans encamped there during the troubled year 403 B.C. Plato may have copoenced teaching in the gymnasium itself; but he soon purchased an adjoining garden and erected buildings there, and from this moment he may be said to have instituted a school. Hitherto he could not exclude chance listeners. The buildings may have included lodgings for students or visitors, and Plato himself presumably lived in the neighborhood. Common meals had been a feature of Pythagorean life, and this precedent was followed. Legal recognition was secured by making the Academy a religious fraternity devoted to the Muses.

Plato nominated his nephew Speusippus to be his successor, but later the head seems to have been elected. Presumably the power of admission rested with the head, and those accepted contributed to the maintenance of the school according to their means. The story that the words “Let no man unversed in geometry enter” were inscribed over the door cannot be traced back further than John Philoponus (sixth century). In the first century B.C., “academic” teaching was being given in the gymnasium of Ptolemy near the agora of Athens.³⁰

In the teaching, Plato will doubtless have been assisted from an early stage by Theaetetus, who, as the dialogue named after him shows, was a boy of exceptional promise in 399 B.C. He was an Athenian. The dialogue records his death from wounds received in battle at Corinth, complicated by illness, and was obviously written soon afterward (ca. 368–367 B.C.). Hence his collaboration with Plato may have lasted about fifteen years.

Somewhat later, Eudoxus of Cnidus resided occasionally at the Academy. He is known to have died at the age of fifty-three, and the dates for his life now usually accepted are ca. 400-ca. 347 B.C. in mathematics he was a pupil of Archytas, but it is not clear when this instruction was received. During a first visit to Athens at the age of twenty-three, he heard lectures from Plato. Later he established a school at Cyzicus in northwest Asia Minor, one of those Greek cities which had been abandoned to Persian control under the Peace of Antalcidas in 387 B.C.; Eudoxus probably felt insecure there and was glad to maintain a connection with the Platonists.

Eudoxus was at Athens when Aristotle first arrived as a student in 367 B.C., and it is plain from several Aristotelian passages³¹ that he deeply influenced his juniors and played an important part in the life of the school. In Plato’s Philebus there is probably some concealed allusion to him. Mathematics and astronomy were his main business, but he took part as a friendly outsider in philosophical debate arising from Plato’s writings. He was not one to pledge himself to accept philosophical dogmas, nor was this expected of him, and his work exhibits the close attention to phenomena which the Socrates of the Republic deprecates.

But Eudoxus recognized that philosophy has a legitimate role in criticizing the procedure of specialists. His explanation of the celestial movements in terms of homocentric spheres, rotating about a stationary spherical earth, was put forward in answer to a problem posed by Plato: “What are the uniform and ordered movements by the assumption of which the apparent movements of the planets can be accounted for?” Eudoxus did not abandon his own school and merge it with that of Plato; and Proclus’ statement that he “became a companion of Plato’s disciples” does not mean this, for we know that Aristotle later carried on the connection with Cyzicene mathematicians which Plato had established. Epistle XIII, ascribed to Plato, mentions Helicon as a pupil of Eudoxus and implies the presence of other Cyzicenes at Athens in the period 365–362 b.c.

If we consider Plato’s relation to Theaetetus and Eudoxus and also bring in the evidence of Aristotle, his personal role in the Academy begins to appear. He probably committed all the specialist instruction to them. He took note of their research and sometimes criticized their methods, speaking as a person with authority; he guided the juniors in that reflection about first principles and about the interrelation of sciences that in Republic VII is designated as suitable for them;³² and he confided to some an ethico-mathematical philosophy in which two ultimate principles, from which Form-Numbers were derived, were found by analysis.

The last item is outside the scope of this article, and concerning the other two a few examples must suffice. Theaetetus added to previously known constructions of regular solid figures those for the octahedron and icosahedron, and gave a proof³³ that there can be no more than five regular solids. He also tried to classify incopoensurable relations, connecting them with the three kinds of means. Plato’s inspiration may be seen in this effort to systematize. Plato is credited by Proclus with beginning the study of conic sections, which his followers developed, and with either discovering or clearly formulating the method of analysis, which proved fruitful in geometry in the hands of Leodamas of Thasos.³⁴ According to Plutarch, Plato criticized Eudoxus, Archytas, and Menaechmus for trying to effect the duplication of the cube by mechanical means and so losing the benefit of geometry.³⁵ Aristotle says that Plato (in oral instruction) “used to object vigorously to the point, as a mathematical dogma, and on the other hand often posited his indivisible lines.”³⁶

The view that the sciences contemplate objects situated halfway between Forms and sensibles and having some of the characteristics of both, which is not found in Plato’s dialogues, was probably at home in the same discussion. Observation of the heavens went on, perhaps under the direction of Eudoxus or his companions. Aristotle says that he had seen an occultation of Mars by the moon (then at half-moon); this must have been in April or May 357 B.C., a calculation first made by Kepler.³⁷

It was maintained by H. Usener in 1884 that the Academy was the first known institute for scientific research, a statement which initiated a debate not yet closed. It has been opposed from one point of view by those who compare the Academy to a modern school of political science (and perhaps jurisprudence) thoroughly practical in its orientation; and from another especially by Jaeger, who thinks that it was no part of Plato’s intention to teach science in encyclopedic fashion and promote its general advance.³⁸ The Academy was not a place in which all science was studied for its own sake but one in which selected sciences were taught and their foundations examined as a mental discipline, the aim being practical wisdom and legislative skill, which in Plato’s opinion are inseparable from contemplative philosophy.

Evidently the crux of this matter is whether empirical sciences, which had no place in the curriculum projected for the guardians in the Republic, were, in fact, pursued under Plato’s auspices. Jaeger seems to be right in his skepticism about the apparent evidence of such activity. It may be added that proofs that Plato was personally interested in (for instance) medicine and physiology, which Timaeus affords, are not quite what is wanted. One might argue that he was indeed an empirical scientist manqué, pointing to his interest in the manufacturing arts in the Statesman, his marvelous sketch of the geology of Attica in the Critias, and his attention to legislative detail in the Laws. It was an imperfectly suppressed love of the concrete and visible, rather than any retreat from his avowed opinions, that led him to pose the problem concerning celestial phenomena which Eudoxus later solved. But it is a long step from these admissions to the pronouncement that the Academy became an institute of scientific research.

Plato’s activity at Athens was interrupted by two more visits to Sicily. When Dionysius the Elder died in the spring of 367 B.C., two problems in particular demanded solution: what the future form of government Syracuse itself should be; and when and how several Greek cities, whose populations had been transferred elsewhere under Dionysius’ policy, should be refounded. Plato’s admirer Dion planned to make his nephew, Dionysius the Younger, a constitutional monarch, and appealed for Plato’s aid in educating him for his responsibility. His proposal was that Plato should come to Syracuse and take charge of a group of earnest students, which Dionysius might unobtrusively join.

Plato yielded to pressure and arrived in the spring of 366 b.c. But, according to Epistle VII, he found a situation of intrigue. Some Syracusans believed that Dion’s aim was to occupy his nephew with interminable study while he himself wielded effective power. From another side there was pressure for the restoration of full democracy. A war with Carthage (or against the Lucanians) was in progress. Three months after Plato’s arrival the young ruler charged Dion with attempting to negotiate with the Carthaginians and expelled him. Plato left the following year (365 b.c.), after obtaining what he took to be a promise that Dion would be recalled.

In 362 b.c. he once more left the Academy (appointing, it is said, Heraclides Ponticus as his deputy) and returned to Syracuse. There were reports that Dionysius was now genuinely interested in philosophy; but in consenting to go Plato was more influenced, according to Epistle VII, by a promise that a favorable settlement of Dion’s affairs could be reached on condition that he return. Dion had spent his years of exile in Athens and had become a friend of Plato’s nephew Speusippus.

Plato’s mission ended in failure. Dion’s agents were forbidden to send him the revenue from his estates; and Plato made his escape with some difficulty, returning home in 361 b.c. Dion thereupon took steps to effect his return to Syracuse by force, urging Plato to aid him and to punish Dionysius as a violator of hospitality. But Plato answered (still according to the Epistle) that he was too old, that after all Dionysius had spared his life, and that he wished to be available if necessary as a mediator. Other members of the Academy, however, joined the expedition. Dion succeeded in his enterprise but failed to reconcile the warring parties; and after a brief period of power he was murdered by the Athenian Callippus (354 b.c.). Epistles VII and VIII, addressed to Dion’s partisans, belong to this time or were fabricated as belonging to it. They contain constructive advice which, in language and spirit, closely resembles Laws III. Plato died in 348/347 b.c., at the age of eighty.

Was Plato at all influenced in his later years by progress in the special sciences? It may be replied that later modifications in his general theory of knowledge seem to have been the product of his own reflection rather than of any remarkable discoveries and were not such as to affect his educational ideals. He did, however, absorb new scientific ideas and make use of them for his purposes as a moralist. This is seen in one way in the Timaeus, where the world is shown to be a product of beneficent rational design, and in another in the Laws, where theological consequences are drawn from the perfect regularity of the planetary movements.

In the Timaeus, Plato has not abandoned his theory of Forms, for Timaeus declares that the perpetually changing, visible cosmos can at best be an object of “right opinion.” The view earlier attributed to Socrates in Phaedo—that the only satisfactory explanation of physical facts is a teleological one—is assumed from the start and carried out in detail. Timaeus opposes mechanistic views with a superior atomism, in which Theaetetus’ construction of the mathematical solids plays a part. Sicilian influence is especially strong. From Empedocles“system the doctor Philistion of Locri, with whom Plato was personally acquainted,³⁹ developed a theory whereby the heart is the center of life and consciousness, and the veins and arteries carry pneuma along with blood. Timaeus adopts this physiology and the explanation of disease which went with it, except that in making the brain the organ of consciousness he follows Alcmaeon. (It appears then to have been the Academy, with its Sicilian connections, which brought the knowledge of Empedoclean medicine to the mainland.) All this leads up to the conclusion that man can learn to regulate his life by study of the cosmos, which is a divine artifact but also an intelligent being.

The Athenian Stranger in the Laws says that he was no longer a young man when he became persuaded that each of the planets moves in a single path, and that we malign them when we call them “wanderers.” He evidently speaks for Plato, and the remark is a formal withdrawal of what was said in RepublicVII of the erratic celestial movements; but in favor of what new system? Surely that of Eudoxus. This may not have lasted long, and was open to an objection that was soon seen, but it was the first scientific astronomy. From it Plato could, and did, argue that all movement stems from a soul (matter is inactive); perfectly regular movement stems from a wise and beneficent soul; and the rotation of the stars, sun, and planets is perfectly regular.

In these later developments Plato may appear not as a lover of science but as a biased user of it. But “an intense belief that a knowledge of mathematical relations would prove the key to unlock the mysteries of the relatedness within Nature was ever at the back of Plato’s cosmological speculations” (Whitehead, Adventures of Ideas, p. 194).⁴⁰

NOTES

1. Proclus in his copoentary on Euclid’s Elements gives a summary account of the development of geometry from the time of Thales. He claims that Plato brought about a great advance, and names some of those who worked with his encouragement in the Academy. Closely similar language is used in a fragmentary papyrus found at Herculaneum, “Academicorum philosophorum index Herculanensis,” where Plato’s role is said to be that of a supervisor who propounded problems for investigation by mathematicians. Simplicius in his copoentary on Aristotle’s De Caelo informs us that Eudoxus’s astronomical system was a solution of a carefully formulated problem set by Plato. The common source of the first two reports is probably the history of mathematics by Eudemus of Rhodes, and Simplicius says that his statement is derived from Book 2 of Eudemus’ History of Astronomy. Greek texts are in K. Gaiser, “Testimonia Platonica” (Appendix to Platons Ungeschriebene Lehre), nos. 15–21, 460–479. An English translation of the latter part of the Proclus passage is in Heath, A Manual of Greek Mathematics, 184–185.

2.Apology 34a; RepublicII , 368a.

3.Memorabilia III, 6.

4. For a family tree, see John burnet, Greek Philosophy From Thales to Plato (London, 1924), appendix; or C. Ritter, Platon, I, 13.

5.Epistles VII, 324–326.

6.Apology 34a.

7.Ibid., 38b.

8.Phaedo 59b, c.

9. Diogenes Laertius III , 6, and II , 106, quoting Hermodorus, a pupil of Plato.

10.Phaedo 78a, 107b.

11. W. and M. Kneale, The Development of Logic (Oxford, 1962), ch. 3; B. Mates, Stoic Logic (Berkeley-Los Angeles, 1961), intro.

12. Aelian, V, 16; VII 14; and Diogenes Laërtius, III, 8, where there is confusion between Plato and Socrates.

13. Robin, Platon, pp. 101–103.

14. Cornford, Republic of Plato, Intro., p. xvii.

15.EpistlesVII , 326–327.

16.De RepublicaI , 10.

17.Phaedo 61d.

18.De finibusV , 29.87.

19.Metaphysics, 987a32.

20.Phaedo 75E, 76e.

21.RepublicVI , 503–505.

22.RepublicVI , 484c, d.

23.LawsVII , 819–820.

24.RepublicVI , 510c.

25.Ibid., VII , 528b.

26.Ibid., 528e ff.

27.Ibid., 533.

28. Cornford, who gives this exposition, relies upon Parmenides 142D ff. See his trans. of the Republic, p. 245, and his “Mathematics and Dialectic in the Republic VI-VII.”

29.RepublicVII , 535–540.

30. See Cicero, De finibus V, 1, for an eloquent description of a walk to the gymnasium’s original site, now deserted.

31. Especially Nicomachean Ethics X, ch. 1.

32.RepublicVII , 535–540.

33. Euclid XIII, 18A

34. See Cornford, “Mathematics and Dialectic in the RepublicVI–VII ,” pp. 68–73.

35.Quaestiones convivales 718f.

36.Metaphysics A, 992a20; see Ross ad. loc

37. See Stocks’s note in oxford trans. of Aristotle, vol. II ; and Guthrie’s ed. of Aristotle’s on the Heavens (Loeb), p. 205.

38. Aristotle, p. 18 and elsewhere.

39.Epistles II, 314d.

40. That the system presented through Timaeus is formulated in antithesis to mechanist atomism—whether or not Plato knew of Democritus as its chief author—is clearly shown by Frank, Platon u. die sogenannten Pythagoreer, pp. 97–108. On the meaning of Timaeus 40b, c, concerning the earth’s rotation, see Cornford, Plato’s Cosmology, pp. 120–134. On Philistion, see Jaeger, Diokles von Karystos, pp. 7, 211. For the argument that laws 822a–e can refer only to the system of Eudoxus, and for Plato’s astronomy in general, see Burkert, Weisheit und Wissenschaft, pp. 302–311.

BIBLIOGRAPHY

I. Original Works. For present purposes the most important dialogues are Meno, Phaedo, Republic, Parmenides, Theaetetus, Timaeus, and Laws. The Epistles and Epinomis, even if they are not authentic, are informative. There are translations with introductions and notes in many modern languages.

Some useful English versions are Phaedo, R. Hackforth, trans. (Cambridge, 1955); Republic, F. M. Cornford, trans. (Oxford, 1941); Theaetetus, Parmenides, and Timaeus, F. M. Cornford, trans., in vols. entitled, respectively, Plato’s Theory of Knowledge (London, 1935), Plato and Parmenides (London-New York, 1939), and Plato’s Cosmology (London, 1937); Timaeus and Critias, A.E. Taylor, trans. (London, 1929); Philebus and Epinomis, A.E. Taylor, trans., R. Klibansky et al., eds. (Edinburgh-London, 1956), with intro. to the latter by A. C. Lloyd; Epinomis, J. Harward, trans. (Oxford, 1928); Epistles, J. Harward, trans. (Cambridge, 1932); Epistles, Glenn R. Morrow, trans. (Urbana, III., 1935; repr. New York 1961); Laws, A. E. Taylor, trans. (London, 1934; repr. 1960).

The appropriate vols. in the French trans., Oeuvres complètes, 13 vols. in 25 pts. (Paris, 1920–1956), published under the patronage of the Association Guillaume Budé, should also be consulted.

II. Secondary Literature. On Plato’s life, see H. Leisegang, Platon, in Pauly-Wissowa, Realenzyklop?die, 1st ser., XX. The following books and articles are important for his views concerning method and for an estimate of his understanding of science.

J. Adam, The Republic of Plato, II (Cambridge, 1902); W. Burkert, Weisheit und Wissenschaft (Nuremberg, 1962), containing a useful bibliography; F.M. Cornford, “Mathematics and Dialectic in the Republic VI–VII,” in Mind, 41 (1932), 37–52, 173–190, repr. in Studies in Plato’s Metaphysics, R. E. Allen, ed. (London, 1965), 61–95; and E. Frank, Platon und die sogenannten Pythagoreer (Halle, 1923).

See also K. Gaiser, Platons ungeschriebene Lehre, 2nd ed. (Stuttgart, 1968), which contains in an app. the Testimonia Platonica, ancient evidence relative to the organization of the Academy and to Plato’s esoteric teaching; and “Platons Menon und dic Akademie,” in Archiv für Geschichte der philosophie, 46 (1964), 241–292; T. L. Health, History of Greek Mathematics (Oxford, 1921), and Aristarchus of Samos (Oxford, 1913), esp. chs. XV and XVI ;G. E. R. Lloyd. “Plato as Natural Scientist,” inJournal of Hellenic Studies, n 88 919680, 78–92; C. Ritter, Platon, 2 vols. (Munich, 1910–1922), containing a chapter on plato’s doctrine of nature and his attitude toward the problems of science; L. Robin, platon (paris 1935); F. Solmsen, “Platonic Influences in the Formation of Aristotle and Plato in the Mid-Fourth Century Goteborg,1960);and A. E. Taylor, Plato, the Man and His Work, 4th ed. (London,1937).

There is a review of literature relating to plato, 1950–1957, by H. Cherniss in Lustrum, 4 (1959),5–308, and 5 (1960), 323–648; sec. II.B deals with the Academy, sec. V.E with mathematics and the sciences.

On the Academy, the comprehensive account in E. Zeller, Philosophie der Griechen, 6th ed. (Hildesheim, 1963), has not yet been superseded; and H. Usener, “Organisation der wissenchaftlichen Arbeit,” in Preussische Jahrbucher, 53 (1884), repr. in Vortrage und Aufsätze (1907), 67 ff., has been a starting point for later discussion. See also E. Berti, La filosofia del primo Aristotele (Padua, 1962), pp. 138–159; H. Cherniss, The Riddle of the Academy (Berkeley, 1945); H. Herter, platons Akademie, 2nd ed. (Bonn, 1952); W. Jaeger, Aristole, 2nd ed. (Oxford, 1948), Diokles von Karystos (Berlin, 1938), and Paideia (Oxford, 1944), II and III; G. Ryle, Plato’s Progress (Cambridge, 1966); P.M. Schuhl, “Une école de sciences politiques,” inRevue Philosophique de la France et de L’étranger, 84 (1959), 101–013; J. Stenzel, platon der Erzieher (Leipzig, 1928); and U. von Wilamowitz, platon (Berlin, 1919; 5th ed. 1959).

On Eudoxus, se K. von Fritz, “Die Lebenszeit des Eudoxos v. Knidos,” in philologus, 85 (1929–1930), 478–481; H. Karpp, Die philosophie des Eudoxos v. Knidos (Wurzburg, 1933); and E. Frank, “die Begründung der mathematischen Naturwissenschaft durch Eudoxus?” in L. Edelstein, ed., Wissen, Wollen, Glauben (Zurich, 1955),134–157.

On the mathematical intermediates in Plato’s philosophy, see W. D. Ross, Metaphysics of Aristotle (Oxford, 1924), I, 166 ff.; J. A. Brentlinger, “The Divided Line and Plato’s Theory of Intermediates,” in phronesis, 7, no. 2 (1963) 146–166; S. Mansion, “L’objet des mathematiques et de la dialectique selon platon,” in Reuue philosophique de Louvain, 67 (1969), 365–358.

On the number in RepublicVIII , 546, see The Republic of Plato, Adam. ed., II, 201–203, 264–312; A. Diès, “Le Nombre de platon,” in Mémoires de l’Académie des inscriptions, 14 (1940); Gasier, Platons ungeschribene Lehre, pp. 271–273,409–414. On the shape of the earth in the Phaedo, see Burkert, Weisheit und Wissenschaft, pp. 282–284, and earlier literature there mentioned. On Platon as geographer and as physicist, see P. Friedländer, Platon, 2nd ed. (Berlin,1954), I, chs. 14, 15. On the Epinomis and the history of science, see E, des Places, “Notice” to the Epinomis, in Platon, Oeuvres completes, Collection Bude, XII, 118–128.

D. J. Allan