Parmenides · Philosophy
Parmenides’ ‘Way of Opinion’ - his account of the deceptive world of the senses - and the brilliant defence mounted by his pupil Zeno of Elea, whose paradoxes of motion and plurality turned the tables on common sense, showing that the world of the senses leads to contradictions of its own.
After the rigorous Way of Truth, Parmenides’ goddess turns to the second part of the poem: the Way of Opinion, or Seeming (doxa). Here she gives a detailed account of the sensible world - the world of change, plurality, and motion that the senses report - but she frames it from the start as deceptive: ‘Here I cease my trustworthy discourse and thought about truth; henceforward learn the opinions of mortals, giving ear to the deceptive ordering of my words.’ This is the world as it appears, not as it truly is - the realm of mortal belief, in which ‘there is no true belief,’ constructed by mortals out of the names they have given to things.
The Way of Opinion builds the apparent world out of two opposed principles or ‘forms’ - Light (or Fire) and Night - and from their mixture derives an account of the heavens, the stars, the moon, the origin of living things, and even human thought and reproduction. It was, by ancient report, a sophisticated cosmology, containing genuine astronomical insights (Parmenides may have been the first Greek to identify the morning and evening star as a single body, Venus, and to hold that the moon shines by reflected light). But all of it is presented under the sign of seeming: this is the best possible account of a world that, from the standpoint of Truth, is not ultimately real. Parmenides thus gives us two levels of discourse - the unshaken truth of changeless Being, and the ‘deceptive’ but best-possible account of the appearances - and insists we keep them sharply distinct, never mistaking the seeming for the real.
Parmenides’ doctrine - that motion and plurality are illusions - seemed so absurd to common sense that it invited ridicule. His devoted pupil Zeno of Elea came to his defence with one of the most ingenious strategies in the history of argument. Zeno did not try to prove directly that Being is one and motionless. Instead, he turned the attack around: he set out to show that the opponents’ position - the common-sense belief in motion and plurality - leads to contradictions and absurdities. If believing in motion and plurality lands you in contradiction, then (Zeno argued) that belief must be false, and Parmenides’ denial of motion and plurality is vindicated by default.
This is the method of reductio ad absurdum - refuting a thesis by showing it leads to contradiction - and Zeno developed it into a fearsome instrument. According to Plato, Zeno’s book contained some forty such arguments, each designed to show that if you assume plurality (that there are many things) or motion (that things move), you can derive contradictory conclusions. The most famous are his paradoxes of motion: Achilles and the tortoise (the swift Achilles can never overtake the slow tortoise given a head start, because he must first reach where it was, by which time it has moved on, and so on forever); the dichotomy (you can never even begin to move, because to cross any distance you must first cross half of it, and half of that, and so on, requiring infinitely many steps); and the arrow (a flying arrow, at every instant, occupies a space equal to itself and so is at rest, so the arrow in flight is always motionless). Each paradox aims to show that motion, which the senses report and common sense assumes, dissolves into contradiction under rigorous analysis - so that Parmenides was right, and the senses deceive.
Zeno’s paradoxes are among the most famous and influential arguments ever devised, and their importance far exceeds their immediate purpose of defending Parmenides. Aristotle called Zeno the inventor of dialectic - the art of refuting an opponent by drawing contradictions out of his own assumptions - and the reductio ad absurdum he perfected is one of the most powerful tools in all of logic and mathematics, used to this day in countless proofs. But the deepest significance of the paradoxes lies in the genuine and profound problems they exposed about infinity, continuity, space, time, and motion - problems that common sense never suspects and that took the greatest mathematicians over two millennia to resolve.
By showing that the innocent-seeming ideas of motion and continuous magnitude conceal deep puzzles about the infinitely divisible and the infinitely small, Zeno set a problem at the very foundations of mathematics and physics. The effort to answer him - to make rigorous sense of infinite division, convergent series, the continuum, and the nature of the infinite - runs through Aristotle’s distinction of potential and actual infinity, through the medieval analyses of the continuum, through the invention of the calculus by Newton and Leibniz (which tames the infinitely small), and through the nineteenth-century rigorous theory of limits and the twentieth-century theory of infinite sets. Bertrand Russell, no mean judge, called Zeno’s paradoxes ‘immeasurably subtle and profound,’ and credited them with forcing the clarification of the infinite that modern mathematics achieved. Few arguments produced in defence of a false conclusion (that motion is impossible) have been so fruitful for truth. Zeno’s paradoxes are the perfect emblem of the whole Eleatic achievement: a magnificently wrong conclusion, reached by a rigorous argument so sharp that answering it advanced human understanding for two thousand years. In defending the changeless One of Parmenides, Zeno opened the deepest questions about the infinite, and so helped found the mathematics of the continuous world he was trying to deny.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that Parmenides assigned the world of change and plurality to the deceptive ‘Way of Opinion,’ and that his pupil Zeno of Elea defended him with paradoxes (Achilles and the tortoise, the arrow) showing that motion and plurality - what the senses report - lead to contradictions. Explain the Way of Opinion an…
Leads to Zeno of Elea.
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