In the 399, at the death of Socrates his disciples dispersed and some of them founded philosophical schools. None of them represent the genuine thought of Socrates, but they develop with autonomy some of the themes whose treatment the master began to deal with which would add numerous elements taken from the sophists and even from the philosophers presocratic.
The scientific and psychological aspects of Socratic doctrine are developed in The Academy. Plato elaborates his own doctrine of Ideas from the Socratic search for definition and concept. And taking inspiration also from Pythagoras will deepen the subject of the soul.
It continues the doctrines of Parmenides and Zeno of Elea, with some modifications that were suggested to Euclides after contact with Socrates.
Euclid identifies Self with Good and God (Socrates may have defended some sort of monotheism) and considers that all virtues are reduced to one, but designated by different names (doctrine that is also reomonted to Socrates).
Estilpon, one of the followers of Socrates, attacked the Platonic doctrine of Ideas, stating that there is only the present singular and denying the existence of universal genera and species. His ethics will influence the appearance of stoicism, since apparently Zeno of Citius was his disciple.
Antistenes (disciple of Gorgias and then Socrates) taught in Athens in a gym called Kynosarges (dog tomb) from which derives the name of “cynics” (dogs) they would receive later.
He rejected the Platonic theory of Ideas and defended a policy of self-sufficiency and independence. He also propagated the ideal of natural life and cosmopolitism, rejecting the existence of the state and the family and affirmed that for the wise there is no fatherland, no laws, no family, no class differences.
Diogenes of Synope was the clearest exponent of the attitude of cynics: he attacked social conventionalisms, sought the natural in the life of animals, barbarian peoples and was absolutely independent.
The cynical school, with various comings and goings that led it at some point to be confused with stoicism, lasted until the fall of the Roman Empire.
Aristipo, disciple of Protagoras and then of Socrates is the clearest representative of the morality of hedonism. There is no source of knowledge but sensation and it only has a subjective value (relativism of Protagoras). The feeling is, therefore, the only guide of man. The purpose of all morals is to seek pleasant sensations, current and mainly bodily. The reason, however (and here the seal of Socrates is observed) should direct man in the choice of such pleasures. Because of its rejection of all kinds of social conventionalism, Cyrene's school is quite close to the cynical school.