Zeno of Elea · Philosophy
At any single instant, a flying arrow occupies a space exactly equal to itself - and so, at that instant, it is at rest. But time is made of instants, and if the arrow is at rest at every instant, it is at rest throughout its flight. So the flying arrow does not move. Zeno’s arrow probes the deepest puzzle: what is motion <em>at an instant</em>?
Zeno’s Arrow is the most metaphysically penetrating of all his paradoxes, for it attacks motion not through the puzzles of infinite division (as the Achilles and Dichotomy do) but through the nature of the instant - the single, durationless moment of time. The argument is short and devastating. Consider a flying arrow at any one instant of its flight. At that instant - a single, indivisible now, with no duration - where is the arrow? It is somewhere; it occupies a definite place, a space exactly equal to its own length, neither more nor less. But to occupy a space exactly equal to oneself, taking up just that much room and no other, is precisely what a resting arrow does - an arrow lying still on the ground also occupies a space equal to itself. At that single instant, then, the flying arrow is doing exactly what a motionless arrow does: occupying its own space. So at that instant, the flying arrow is at rest - it is not moving, for nothing moves within a single durationless instant; motion would require getting from one place to another, and there is no ‘getting’ in an instant with no duration.
Now comes the fatal generalisation. What is true of one instant is true of every instant: at each and every instant of its flight, the arrow occupies a space equal to itself, and so at each instant it is at rest. But the entire flight of the arrow is composed of these instants - the whole stretch of time the arrow is in the air is made up of all its instants. And if the arrow is at rest at every single instant that makes up its flight, then it is at rest throughout the whole flight. It is never, at any instant, moving. Therefore the flying arrow does not move. Motion is impossible. The conclusion is, once again, absurd - we see the arrow fly - but the reasoning has a terrible plausibility. The arrow really does, at each instant, occupy just its own space; nothing really does ‘move’ within a single durationless now; and the flight really is composed of such instants. How can a sum of motionless instants add up to motion?
The modern resolution of the Arrow paradox is one of the most elegant moves in the philosophy of physics, and it consists in rejecting the paradox’s central assumption while accepting its starting point. Zeno is right, the modern answer says, that at any single instant the arrow is not ‘moving’ in the sense of having some special extra property of motion residing in that instant - there is, indeed, no such instantaneous property of ‘moving-ness’ over and above where the arrow is. But Zeno is wrong to conclude from this that the arrow is therefore ‘at rest’ and never moves. The mistake is in his concept of motion. Motion, on the modern view - called the ‘at-at’ theory - is not some mysterious additional property that an object has at each instant. Motion just is being at different places at different times: an arrow is in motion if and only if it is at one place at one instant and at different places at other instants. There is nothing more to motion than this pattern of positions-across-times.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned Zeno’s Arrow paradox: at any single instant, the arrow occupies exactly one space equal to its own size, doing in that frozen instant just what a stationary arrow does - so at each instant it is at rest; and since the whole flight is a sum of such instants, the arrow is at rest throughout, i.e. never moves…
Leads to Heraclitus.
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