1. In the pre-Socratic period of Greek Philosophy, we can distinguish three well-marked currents of thought. The first is that of the Ionic School -- of the philosophers of external nature, who, true to the character of the Ionians, devoted themselves to the study of the world accessible to sense, and sought to discover an ultimate principle of all things in nature, and to explain their origin and their dissolution. The second is that of the Pythagoreans, whose investigations were more speculative in character, but who embodied their speculative notions in mathematical formulae, and, in general, made mathematics the basis of their speculative structure. The third is that of the Eleatics, who, passing beyond the sphere of mathematical conceptions into the realm of pure thought, aimed at building up a science of Metaphysics, strictly so called. The doctrines of the Pythagoreans and Eleatics spread chiefly among the Greeks of the Doric race, especially among the Greeks of Southern Italy. In this way the Ionians and the Dorians -- the most remarkable of the Hellenic races throughout the historic period -- were also the reresentatives of the earliest forms of Greek Philosophy. But the pre-Socratic philosophy was, in every school, merely a one-sided effort; the truth after which it aspired could not be reached by its methods; scepticism, as an ultimate result, was unavoidable. This stage of ultimate scepticism was reached in the teachings of the Sophists.{1}
2. We shall therefore treat first of the Ionic Philosophy, or Philosophy of Nature; then of the doctrines of the Pythagoreans; next of the Eleatic Philosophy; and finally, of the teaching of the Sophists.
{1} The fragments of the writings of the Pre-Socratic philosophers that still remain have been published by Guil. Aug. Mullach (Fragmenta philosophorum graecorum. Paris, 1860-1867.)