The Laws, which, according to the most probable opinion, was
written by Plato, though it was not made public until after his death,
bears evidence of the influence which, in the later years of his life,
the philosophy of the Pythagoreans exercised on his mind, inclining him
to attach more and more importance to the mystic element in
philosophy and to the number theory. It was this phase of
Platonic thought that was taken up and developed by the Platonic
Academies, while in the bands of Aristotle the teachings of the earlier
dialogues were carried to a higher development. During the lifetime of
Plato there was little, if any, dissension among the members of the
school which assembled in the grove of Academus; after Plato's death,
however, Aristotle set up a school of his own, in opposition to the
members of the Academy, who claimed to possess in their scholarch the
authorized head of the Platonic school.
The first scholarch was Speusippus, the nephew of Plato, who, according
to Diogenes Laertius,  received his appointment from Plato himself.
He in turn was succeeded by Xenocrates,  and in this manner the
succession of scholarchs continued down to the sixth century of the
Christian era. 
 IV, 1.
 Ibid., IV, 14.
 Cf. Ueberweg, op. cit., I, 485 ff.
It is customary to distinguish in the history of the Platonic school
three periods, known as the Old, the Middle, and the
New Academy. To the Old Academy belonged Speusippus,
Xenoerates, Heraclides of Pontus, Philip of Opus,
Crates, and Crantor; Arcesilaus and
Carneades are the principal representatives of the Middle
Academy, while Philo of Larissa and Antiochus of
Ascalon are the best-known members of the New Academy.
Sources. Our sources of information concerning the history of
the doctrines of the three Academies are for the most part secondary;
they are scanty and cannot be relied upon in matters of detail. As far,
however, as a general characterization of each school is concerned, our
materials are sufficiently ample and trustworthy.
Old Academy. The Old Academy flourished from the death of Plato
(347 B.C.) until the appearance of Arcesilaus as scholarch (about 250
B.C.). It is distinguished by its interpretation of the Platonic theory
of Ideas in accordance with the number theory of the Pythagoreans.
Speusippus seems to have substituted numbers for Ideas,
assigning to them all the attributes, including separate existence,
which Plato in his earlier dialogues had attributed to the Ideas.
Although, according to Theophrastus, Speusippus devoted but little
attention to the study of the natural sciences, on one important point
of physical doctrine he differed from Plato, maintaining, if we are to
believe our Neo-Pythagorean authorities, that the elements are five,
not four, and deriving these five, after the manner of Philolaus, from
the five regular figures.  If, as is probable, Aristotle, in
Analytica Posteriora, II, 13, 97 a, 6, is speaking of
Speusippus, the latter maintained that in order to know anything we
must know everything.
 Arist., Met., VII, 2, 1028 b, 19.
 Cf. Zeller, Plato, p. 578, n.
Xenocrates continued to combine, as Speusippus had done, the number
theory of the Pythagoreans with Plato's doctrine of Ideas. He went
farther, however, than Speusippus in his application of number to
theological notions, developing a
system of demonology which suggests in its elaborateness the doctrines
of the Neo-Platonists.
Heraclides of Pontus is remarkable for having taught the diurnal
revolution of the earth on its axis, and the immobility of the
fixed stars. These views were first proposed by Hicetas of Sicily and
by Ecphantus, who was also a Sicilian. Our authorities are
Theophrastus  and Plutarch.
 apud Cicero, Acad., II, 39.
 Placita, III, 13.
Philip of Opus is generally believed to be the author of
Epinomis and the editor of the Laws, of which the
Epinomis is a continuation.
Crates and Crantor devoted themselves mainly to the study
of ethical problems.
Middle Academy. The Middle Academy was "characterized by an
ever-increasing tendency to scepticism." Chronologically, it belongs to
the third period of Greek philosophy, and in its spirit and contents it
is more in keeping with the post-Aristotelian age than with the time of
Plato and Aristotle.
Arcesilaus, who was born about 315 B.C., is regarded as the
founder of the Middle Academy. He combated the dogmatism of the Stoics,
maintaining that as, according to the Stoics, the criterion of truth is
perception, and as a false perception may be as irresistible as a true
one, all scientific knowledge is impossible. It is, therefore, he
concluded, the duty of a wise man to refrain from giving his assent to
any proposition, -- an attitude of mind which the Academicians called
forbearance (apoche). Still, Arcesilaus would grant that
a degree of probability sufficient for intelligent action is
 Cf. Cicero, De Orat., III, 13.
Carneades lived from about 210 to 129 B.C. Consequently, he was
not the immediate successor of Arcesilaus, whose principles he
developed into a more pronounced system of Scepticism. He held that
there is no criterion of truth; that what we take to
be true is only the appearance of truth, -- phainomenon
alÍthes which Cicero renders probabile visum. 
 Cf. StŲckl, Lehrbuch, I, 173; English trans.,
Vol. 1, p. 95; Zeller, Stoics, etc., p. 538.
New Academy. After the death of Carneades, the Academy abandoned
Scepticism and returned to the dogmatism of its founder.
Philo of Larissa and Antiochus of Ascalon introduced into
the Academy elements of Stoicism and Neo-Platonism which belong to the
third period of Greek philosophy.
Historical Position. The Academics, although they were the
official representatives of Platonic philosophy, failed to grasp the
true meaning of the theory of Ideas. By introducing Pythagorean and
other elements they turned the tradition of the Platonic school out of
the line of its natural development, and ended in adopting a scepticism
or a dogmatic eclecticism, either of which is far from what should have
been the logical outcome of Plato's teaching. They are to Plato what
the imperfectly Socratic schools are to Socrates. The continuity,
therefore, of Platonic thought is not to be looked for in these schools
but rather in the school founded by Aristotle.