The period of Greek philosophy that followed the Presocratics begins around 400 bc; the most important figures are Socrates (470–399 bc), Plato (427–347 bc), and Aristotle (384–322 bc). It is possible to discern a shift in interest in Greek philosophy away from explanations of the natural world to moral concerns, in the sense of discovering the best way for men to live. The difficulties of determining what were the objective or real features of the world, as opposed to those only apparent features which depended on a point of view (and hence were subjective), began to undermine the early explanations of natural science. If we are uncertain about what features of the world are real and what are only apparent, then it is unsurprising that such doubt will extend to the objectivity of moral standards. The threat was of moral anarchy.

To understand later Greek philosophy it is necessary to remember some unsolved problems derived from the Presocratics. In one sense Heraclitus stands at one extreme, Parmenides at the other. For Heraclitus everything is in flux; there is no being, only becoming or processes – although this becoming is subject to a cosmic logos or law of change. Heraclitus holds a compositional theory of identity whereby something remains the same thing only if the stuff out of which it is made remains exactly the same stuff. The world as it appears to the senses is argued by the Parmenideans to be an illusion: it is a world that appears to involve change and plurality, but these are impossible.