1. It is customary to distinguish among the followers of Plato three, or in more detailed division five, successive phases or schools of thought: the Old Academy, the Middle, and the New. The Old Academy includes the first of the five schools; the Middle, the second and third; the New Academy, the fourth and fifth.
2. By the representatives of the Old Academy the central doctrine of Plato's system, his theory of Ideas, was interpreted, under the influence of Pythagorean notions, in combination with a theory of numbers. With this was associated a theology partly mystical, and partly popular, in which, at a later period, demonology occupied an important place. To the Old Academy belong: --
(a.) Speusippus, a son of Plato's sister, and his successor in his teaching functions (head of the Academy, 347-339). Speusippus is said to have maintained the doctrine that to define anything we must know everything, for in definition we must state the differences between things, and to do this we must discover all the resemblances and differences of things. (Speusippus himself is said to have attempted this in a work containing ten books). He asserted further that the Good and the Perfect in se cannot be the first basis of things or the One; that which is best and most beautiful does not exist at the beginning, it is the ultimate term of evolution from the beginning. His fundamental ethical principle is happiness, obtained by acting as nature directs.
(b.) Xenocrates of Chalcedon, successor of Speusippus as leader of the Academy (339-314), "endeavoured to reduce philosophical concepts to mathematical formulae. In the effort to express, in all clearness, by numerical notation the manner in which God, by many intermediate stages and processes, enters into and manifests Himself in the world of phenomena, he was led into all kinds of sensuous, fantastic, and superstitious notions."
(c.) Heraclides of Pontus -- "a distinguished astronomer, who discovered the diurnal revolution of the earth on its axis from west to east, and the immobility of the heaven of the fixed stars" -- Philip the Opuntian -- the reputed author of the Epinomis -- Polemo, Crantor, and Crates, who devoted themselves mainly to ethical studies, and abandoned more and more completely the speculative or dialectical elements of the Platonic philosophy.
3. The Middle Academy is characterized by an ever-increasing tendency to scepticism. To it belong: --
(a.) Arcesilaus (315-241), a pupil of Crantor and Polemo, the founder of the so-called Second Academy. He combated the dogmatism of the Stoics, and professed the opinion that certain knowledge is not possible, and that the wise man should never give assent to any assertion. This attitude of mind he calls Forbearance (apochê), i.e., forbearance from the exercise of judgment. Equally valid reasons can always be adduced in favour of either of two contradictory propositions. We cannot, therefore, know anything, not even the fact that we know nothing. Accordingly, Arcesilaus himself did not advance any proposition whatever, but permitted his disciples to dispute amongst themselves or with him. Certain knowledge is impossible, but probable opinion is attainable, and this is sufficient in order to act rationally. Arcesilaus was followed by Lacydes, Telecles, and Evander.
(b.) Carneades of Cyrene (214-129), the founder of the Third Academy, who, in the year B.C. 155, was sent as ambassador to Rome, in company with Diogenes the Stoic and Critolaus the Peripatetic. He advanced still further in the path marked out by Arcesilaus. If, he says, we wish to decide whether a given perception be true or false, we must have some certain standard to judge by; this can be no other than the true perception; with this we must compare the perception of whose truth or falsity we wish to judge. But the true perception is precisely what we are seeking to find; sensuous perception cannot, therefore, be a criterion of truth. Neither can the concept of the intellect; for our concepts are derived from the perceptions of sense. There is, therefore, no criterion of truth. What we take to he truth is only the appearance of truth, is only a phainomenon alêthes pithanê phantasia, probabile visum (Cic.). We can attain no more than probability. We experience certain perceptions repeated frequently, occurring in the same way, and in accord with one another. In consequence, a certain feeling of complacency or approval arises within us, and on this ground we hold them to be true, and we assert them (emphasis); the perceptions of a different kind we hold to be false, and we deny them (apemphasis). In this probability there are, however, different degrees. We must distinguish three degrees of probability: the perception is either probable in itself only; or, when taken in relation to other perceptions, it is found uncontradicted and probable; or lastly, it is not only probable and uncontradicted, but is confirmed in all respects (Sext. Emp. Adv. Math. vii. 166). We have further to mention that Carneades was celebrated as an orator. Clitomachus was a pupil of Carneades.
4. The New Academy returned again to dogmatism. It includes
(a.) Philo of Larissa, the founder of the Fourth Academy, a pupil of Clitomachus, who lived in the time of the first Mithridatic war. He seems to have reverted to the older Platonic teaching, and to have given his attention chiefly to ethics, inclining in his views to the system of the Stoics.
(b.) Antiochus of Ascalon, a pupil of Philo, and founder of the Fifth Academy, who, in the effort to combine the theories of Plato with certain Aristotelian principles, and still more largely with principles adopted from the Stoics, prepared the way for the Neo-Platonists. He endeavoured to show that the scepticism of the later Academy was not justified by the Platonic doctrine, and that the chief points of the doctrine of the Stoics are to be found in Plato. He differed from the Stoics by denying the equality of vices, as well as by asserting that virtue, though it leads to a happy life, does not of itself produce the happiest life. Otherwise he is almost entirely in accord with them. (Cic. Acad. Part II. 43.)
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