Zeno’s paradox isn’t just about motion — it’s about the assumption of continuity and identity through time.
Identity as the Deeper Problem
Zeno’s paradox isn’t just about motion — it’s about the assumption of continuity and identity through time.
The idea that “Achilles” is the same Achilles at each point in time, crossing an infinite sequence of positions, assumes that:
- He has a stable identity across time, and
- Time itself is composed of discrete, measurable slices that can be traversed in order.
But if we question those assumptions, the paradox becomes more than a mathematical puzzle — it reveals a problem of identity in motion.
Time as Undivided Flow
Philosophers like Bergson and Heidegger argue that time is not really composed of discrete, divisible units. Time, in its lived reality, is duration — a flow, not a sequence. When we chop it into parts (moments, milliseconds, etc.), we impose an artificial framework onto something that only exists as a whole.
In this view:
- Motion is not a sum of still positions.
- Selfhood is not a fixed identity moving through frozen snapshots of time.
- Reality is process, not structure.
So Zeno’s paradox exposes the absurdity of thinking about movement and identity in terms of static points and divisible instants. Achilles is never really “at” a series of points. He is in motion, which is fundamentally not a sequence of stops, but a flow that can’t be broken without distorting its nature.
- The true problem is not the tortoise’s head start, but our need to imagine continuity as a chain of identical selves moving through identical points in time.
- If identity is not fixed and time is not truly divisible, then motion is not a series of positions, but something qualitatively different — more like music than a line of dominos.
Is time dividable ? no. But we can make it cyclic on basis of the rule of identity. Achilles would never overtake the tortoise because their identity syncs periodically only on fixed situation (like start or end) but never in-motion. In the duration of movement, identity of difference distances, one of Achilles, one of the Tortoise are not identical, not something we can ‘measure’ or ‘compare’, non rational.