Often, when thinking about Socrates (or about Plato’s depiction of Socrates), we need to remember that he is reacting to the Presocratics, but the re… - Catherine Rowett

Parmenides did for science what Plato would later do for morality and aesthetics as well: he alerts us to the fact that opinions are just opinions, and they may differ widely. There may yet be a single truth, which need not be as anyone thought. To search for knowledge is to search for access to the truth, not to collect other people’s opinions, and philosophy conducts its unrelenting search for truth in the steps of Parmenides, by respecting sound and rigorous logical argument rather than the variegated tapestry of unexamined opinions.

Plato not only permitted live philosophical enquiry to take place in the course of every reader’s every reading of the dialogue, by putting tempting and plausible views on trial, in a situation as near as possible to the open-minded exploratory give and take of dialectical debate with a real interlocutor. He also created a most fitting memorial to the real Socrates – the man himself, who lived and died for the idea that philosophy is best done in open-ended dialogue, and with your whole way of life at stake should you be refuted.

Whether or not Zeno was merely trying to defend Parmenides from the ridicule of others, there is no doubt that he has pushed the analysis of reality onto a new plane. He makes us think not just about objects in space, but about space as a structure within which they exist; about motion not just as the behaviour of physical bodies, but as a theoretical concept involving conceptual divisions in space and time; about number not just as a way of counting finite bodies but as a rational system potentially (or actually) continuing ad infinitum, with the problematic consequences that that might entail; about the notions of ‘before’ and ‘after’ in time, and how long the duration of the present is.