Zeno’s paradoxes

Zeno of Elea (c. 490 – c. 430 BC) is one of the most enigmatic pre-Socratic philosophers. Though none of his own works have survived, there are fragmentary mentions of his on the classics like Aristotle and Plato. He was a member of the Eleatic School and, according to Plato at least, aimed to reinfoced Parmenides’s arguments (Parmenides being the founder of the school). While we know very little of Zeno himself, other than some […]

Thomson’s lamp and a lump of chocolate, or Zeno part 4

After considerations on Zeno’s paradox (part 1 and part 2), and the humorous possibilities to Zeno’s paradox of motion (part 3), it is time to take beef with the paradox on the nature of what is called a super-task. As stated in the previous post on Zeno, Thomson thought super-tasks to be impossible. It is not, as he points out, that we do not repeat the same tasks indefinitely; but rather that the infinity sequence […]

The Ross-Littlewood paradox, or Zeno part 3

The Zeno paradox discussed in the previous posts (part 1 and part 2) has one of the most fascinating variations known to man. It is so sublime, that one is stunned by the grand ingenuity of it. No kidding, for a few milliseconds you will literally be stunned. The idea dates back to a publication from 1954 by J.F. Thomson with an interesting title: “Tasks and Super-tasks” (free to read on JSTOR, given you register). A ‘supertask’ (coined by […]

Zeno’s paradox of motion – part 2

In this post we return to Zeno’s paradox of motion in order to point out another aspect of it. Where in the previous post, we concluded that his paradox points towards motion being inconceivable due to infinite divisibility of space (Aristotle calls it “bisection”), in this one we’ll refer to time. Zeno’s paradox is best explained through his example of a flying arrow. As Aristotle describes the paradox: “if everything when it occupies an equal […]

Zeno’s paradox of motion – part 1 (Achilles and the tortoise)

The most famous of Zeno’s paradoxes, and also the one with amusing historical examples: Zeno’s paradox of motion. In one version of the paradox Zeno proposes that there is no such thing as motion. There are many variations, and Aristotle recounts four of them, though essentially one can call them variations of two paradoxes of motion. One concerning time and the other space. For today, let us focus on space and recount the Achilles and […]