Zeno of Elea
c. 490-c. 430 B.C.
Greek Philosopher
The accomplishments of the Eleatic philosopher Zeno illustrate the law of unintended effect. Setting out to justify the propositions put forth by his teacher Parmenides, namely that change is impossible, Zeno achieved something quite different. Intentionally or not, his famous paradoxes showed both the power and the limitations of logic, and philosophers' interest in the challenges posed by these problems led to the formalization of logic, or dialectic, as a discipline.
Like Parmenides (b. c. 515 B.C.), Zeno came from Elea, a Greek colony in southern Italy. At about the age of 40, in 449 B.C., he accompanied his teacher to Athens, where he met and impressed Socrates (c. 470-390 B.C.) In fact, much of what is known about Zeno's career comes from the writings of Socrates's own pupil, Plato (427-347 B.C.).
Parmenides taught that nonbeing is an impossibility; only being—timeless, changeless, and all of one substance—exists. Of course this account of reality, tempting as it might seem in some regards, is hard to maintain in the face of sensory data that forcefully suggests not only the variety of substance within the world, but also the changing nature of that substance.
Parmenides had attempted to deal with this by maintaining that the only real knowledge resides in the intellect itself, not in the world of experience; but in Zeno's generation it became apparent that the Eleatic school would have to furnish some sort of proof. This Zeno attempted to do with his paradoxes, which, rather than prove the Eleatic position directly, sought to make ridiculous its opponents' propositions regarding the reality of change and motion.
Zeno reportedly wrote the paradoxes—of which Plato claimed there were 40 or more—in a work called the Epicheiremata. Both it and the majority of the paradoxes have long since disappeared, though it is likely that the other problems in principle resembled the four that survive.
In one paradox, Zeno referred to an arrow being shot from a bow. At every moment of its flight, it could be said that the arrow was at rest within a space equal to its length. Though it would be some 2,500 years before slow-motion photography, in effect he was asking his listeners to imagine a snapshot of the arrow in flight. If it was at rest in that snapshot, then when did it actually move?
Another paradox involved Achilles, hero of the Iliad and "swiftest of mortals," in a footrace against a tortoise. Because he was so much faster than the tortoise, Achilles allowed the creature to start near the finish line—a big mistake, because as Zeno set out to prove, Achilles could then never pass the tortoise. By the time he got to the point where the tortoise started, it would have moved on to another point, and when he got to that second point, it would have moved on to yet another point, and so on. There would be no point at which Achilles could pass the tortoise.
These and Zeno's other two paradoxes, which were similar in concept, failed to prove that motion was impossible, but they did impress philosophers with the importance of logic itself.Through use of logic, Zeno seemingly created a series of statements that could not possibly be true. Thus was born the scientific study of the dialectic, which has captured the imagination of philosophers and mathematicians ever since.
Advances in the study of calculus by Karl Weierstrasse (1815-1897), and in logic and language by Ludwig Wittgenstein (1889-1951) and his friend Bertrand Russell (1872-1970), helped thinkers unravel the mystery of Zeno's paradoxes and their hidden assumptions. In each problem, Zeno treated either space or time as though they were made up of an infinite number of points—for instance, infinite arrow "snapshots." This is true in the ideal world of geometric theory, where a line does indeed have an infinite number of points; but those points are without extension, whereas a "point" in the real world has some length.
Of course Zeno did not deliberately build in this paradox-within-a-paradox, any more than he intentionally created the revolution in thinking that his work spawned. Undoubtedly, however, he possessed a certain "pugnacity" (Plato's term) in defending his point of view. Later this fighting spirit would put him at odds with the Eleatic tyrant Nearchus, who had him put to death.
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