This is now known as the method of indirect proof, or reductio ad absurdum, and it appears to have been used first by Zeno.
There were, it seems, several discourses, in each of which he made a supposition, or hypothesis, and then proceeded to show the absurd consequences that would follow. Zeno's contribution to the literature of the school consisted of a treatise, now lost, in which, according to Plato, he argued indirectly against the reality of motion and the existence of the manifold. The chief doctrine of the school was the oneness and immutability of reality and the distrust of sense-knowledge which appears to testify to the existence of multiplicity and change. At his birthplace Xenophanes and Parmenides had established the metaphysical school of philosophy known as the Eleatic School. Greek philosopher, born at Elea, about 490 B.C. It should give pause to anyone who questions the importance of research in any field.48256 Catholic Encyclopedia, Volume 15 - Zeno of Elea William Turner (1871-1936) But the way mathematicians and philosophers have answered Zeno’s challenge, using observation to reverse-engineer a durable theory, is a testament to the role that research and experimentation play in advancing understanding. That answer might not fully satisfy ancient Greek philosophers, many of whom felt that their logic was more powerful than observed reality. Any distance, time, or force that exists in the world can be broken into an infinite number of pieces-just like the distance that Achilles has to cover-but centuries of physics and engineering work have proved that they can be treated as finite. Not just the fact that a fast runner can overtake a tortoise in a race, either.
#CENON DE ELEA SERIES#
The convergence of infinite series explains countless things we observe in the world. “It’s easy to say that a series of times adds to ,” says Huggett, “but until you can explain in general-in a consistent way-what it is to add any series of infinite numbers, then it’s just words. No matter how quickly Achilles closes each gap, the slow-but-steady tortoise will always open new, smaller ones and remain just ahead of the Greek hero. The upshot is that Achilles can never overtake the tortoise. To Achilles’ frustration, while he was scampering across the second gap, the tortoise was establishing a third. The new gap is smaller than the first, but it is still a finite distance that Achilles must cover to catch up with the animal. While Achilles is covering the gap between himself and the tortoise that existed at the start of the race, however, the tortoise creates a new gap. Before he can overtake the tortoise, he must first catch up with it. Achilles’ task initially seems easy, but he has a problem. For those who haven’t already learned it, here are the basics of Zeno’s logic puzzle, as we understand it after generations of retelling:Īchilles, the fleet-footed hero of the Trojan War, is engaged in a race with a lowly tortoise, which has been granted a head start. “Achilles and the Tortoise” is the easiest to understand, but it’s devilishly difficult to explain away. The Greek philosopher Zeno wrote a book of paradoxes nearly 2,500 years ago.
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