Parmenides
Hans Georg Gadamer, on of Germany’s most important 20th century hermeneutical philosophers and classical scholars, emphasizes in particular the importance of Parmenedes and the Eleatics for Plato’s later theory of the forms. Like Plato, already Parmenides, as well as Zeno and other Eleatics, dismisses sense experience as a source of truth. For these thinkers, it is the analysis of concepts that leads to a truth that one must affirm regardless of how out of sync it is with our common understanding of the world.
In Parmenides case, the great rational revelation concerned the constancy and unchangeability of Being. “What is is,” he wrote, “and what is not is not.” If something were to come into being, then it would now be nothing. But nothing cannot exist. Similarly, if something now existed it could not later no longer exist. If so, where there is now something there would later be nothing. But nothing cannot exist.
For Parmenides, the eyes and ears lead us astray. As he notes: “Seeing, they saw in vain; Listening, they failed to hear.” In his view, following the logic of the argument, we should recognize that Being is unitary and unchanging. Our ordinary, temporal understanding, it follows, must be illusory. Being must, by definition, be eternal without beginning and without end.
Further Eleatics
Other Eleatics, like Zeno, followed in Parmenides’ footsteps. Zeno developed a series of logical paradoxes to underline the Parmenidean view that change as perceived by sense experience is illusory. Zeno’s arrow paradox plays on a concept of time. If an arrow is shot toward a target, at any given instance in time it would find itself at rest at some place on the trajectory. Since at every instant the arrow is at rest, it could never move from the arrow to the target. Logic, Zeno argues, disproves that movement is possible. We should thus not trust our senses. His race course paradox reaches a similar conclusion. Imagine Homer running toward a target. To get there, he would first have to get half way there, and to get half way, he would first have to get to the half-way point of that half-way, ad infinitum. Between each space, however, there would be an infinite number of points to cross from one to another, since each half can again, mathematically be divided in half, ad infinitum. It is impossible to cross an infinitude, so the motion can never occur. The race could never start.
Though these paradoxes clearly have something wrong with them, they are mind bending. What are the problems with taking logic and applying it to realities of space and time in this way? Aristotle criticizes Zeno, as well as Plato.
Plato, for his part, follows the lead of the Eleatics. He thinks we should follow reason even if it conflicts with sense experience. He like the Eleatics is thus known as a rationalist.
Proceed to the Problem of the One and the Many