Speusippus was Plato's successor at the head of the Academy. He was an important philosopher of the 4th c. with contributions in metaphysics, theory of knowledge, and ethics. All of his works are lost.
Speusippus was an Athenian, and Plato's nephew (son of his sister Potone). He was a member of the centre of the platonic circle. He must had also been among the founders of the, and the one to become its second scholarch upon Plato's deathin 347 B.C. However, we do not have any reliable information regarding the circumstances of this succession. Speusippus remained at the post until his death in 339 B.C.; he was followed by .
(Lives of Eminent Philosophers IV, 1-5) reports a few telling (but unreliable) episodes about Speusippus' character; but he says almost nothing about his philosophy. Nonetheless, Diogenes registers a list of 30 titles of Speusippus' works, none of which is extant. This catalogue shows that Speusippus was a prolific writer of dialogues (e.g., Aristippus, Cephalus), moral treatises (e.g., On Friendship, The Citizen), treatises on nature and metaphysics (On Philosophy, On the Soul), and manualson dialectics and rhetoric (Divisions and Hypotheses relating to the Resemblances,Criticism of the Arts,Treatise on System).
As it is the case with all of Plato's main students, Speusippus grounds his philosophy on a version of the late platonic ontology; particularly, on the so-called "". According to them, Plato produced both the sensible and the intelligible reality ( , mathematical beings, and the sensibles) from two superior principles: the One and the Indefinite Dyad. In a like manner, Speusippus postulates two principles: the One and "plurality" - the latter being construed as the principle of multiplicity and indeterminacy. But, even though Plato thought that first came the (rational) generation of the Forms through the "partaking" of the Indefinite Dyad in the One, Speusippus, au contraire, seems to have rejected the existence of the Forms by assuming that the first ontological level, right after the Principles, consists of the Numbers. That said, even Plato, at least according to a certain interpretation, identified the Forms with formal Numbers (i.e., single and autonomous Numbers that cannot be employed in operations in the way that mathematical numbers are). Hence, the numbers ushered by Speusippus were not the platonic Form-Numbers, but mathematical numbers. This preference of the mathematical numbers over the Forms meshes well with the common idea that Speusippus and Xenocrates attempted to combine Platonism and .
Aristotle, who didn’t think much of Speusippus, accuses him oflaying out an “episodic” configuration of the world. The probable reason for this critique lies with the hierarchy of being that Speusippus designed: numbers come first; magnitudes follow; then souls; and perceptible beings rest at the bottom. Numbers are generated from the 1 (which Speusippus, against the Greek tradition, thought to be the first number); geometrical magnitudes from the "point"; souls and sensible beings from other principles. Thus, what Aristotle characterizes as "episodic" is the independent, self-contained generation of each level of being. The properties of beauty and goodness would only appear, according to Speusippus, in the second ontological level (the geometrical magnitudes), whereas evil only in the third and fourth. The principles, however, were not susceptible of any ethical properties. What is more, Speusippus, possiblyinkeeping with Plato's pronouncement that the Good "transcends being" (509b2-10), considered that his One is not a being, but superior to beings. Lastly, a special role in Speusippus' ontology appears to be played by the perfect number10 (the Pythagorean "tetractys"). But the information we draw do not suffice for a clear understanding.
In the Posterior Analytics (97a6-8),repudiates those who reject the methods ofdefinition and division. According to them, the proper definition of a being (and the proper division alike) presuppose full knowledge of every other being. Both ancient and contemporary commentators believe that Aristotle'scritiquetargets Speusippus - to whom he credits a "holistic" approach to knowledge. In the face of that, it is rather improbable that Speusippus undermined every possibility of knowledge. More likely, his claim was that knowledge of the sensibles, through the discernment of only a small number of differences and similarities between them, could not measure up to the knowledge of numbers and magnitudes which are the only original beings.
In the same vein, Speupissus repudiates knowledge of the sensible beings in an interesting passage coming from Sextus Empiricus: "...but Speusippus said that, since of things some are perceptible and others intelligible, the criterion of the intelligible ones is the scientific account, and that of the perceptible ones is the scientific perception". Hence, mere perception cannot grasp the essence of things; what makes a perception "scientific" is its participation in reason, that is, its submission and orientation according to reason.
There is evidence that a controversy regarding the nature of the good was at work in the premises of the ancient Academy: on the one side stood hedonism (represented by Eudoxus), and on the opposite anti-hedonism, developed both by Plato and Speusippus. It is plausible that the platonic Philebusis echoing this dispute: there is a reference to "people with a tremendous reputation in natural science" to whom "a certain harshness in their nature" is ascribed, and who deny the existence of pleasure in its own right by identifying it with the escape from pain (44b-c). Scholars believe that the allusion of the harsh people is made to Speusippus. This interpretation is on all fours with Clement of Alexandria's testimony that Speusippus identified the good with "untroubledness" (aochlesia) - a position that in a way anticipates the "undisturbedness" (ataraxia) of the Hellenistic philosophical systems.
Even with Aristotle's (who, by the way, remains our basic source, since none of Speusippus' works is extant) hostility against Speusippus, it seems that the latter was not gratuitously appointed the second headmaster of the Academy. Speusippus made his contribution to every area of interest that was explored by Plato's students. Especially, his input in the theory of knowledge and ethics may have laid the ground for the development of Hellenistic philosophy. By all means, Aristotle has in mind Speusippus when he contradicts those who have superseded philosophy with mathematics (Metaphysics I 992a32-33). Nevertheless, the mathematical reappropriation of the theory of Forms had already started with Plato. In that sense, Speusippus carries on with his teacher's work - granted the freedom of thought that characterized the Ancient Academy.
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