We don’t know much about Zeno of Elea. He was active during the fifth century B.C. and was a student or younger associate of Parmenides
. Like Parmenides, Zeno was from Elea, a small city in contemporary Campania, southern Italy. In the dialogue Parmenides, Plato recounts that Zeno and Parmenides jointly visited Socrates in Athens around 450 B.C. It seems plausible, indeed, that Zeno had quarters in Athens for some years, although he most certainly spent most of his life in Magna Grecia (southern Italy).
Zeno is re-known for having formulated some of the most ingenious philosophical paradoxes to date, alongside with Eubulides
. Zeno’s paradoxes can be divided into four groups: the four paradoxes against motion; the two paradoxes against plurality; the paradox of the millet seed; and a paradox of place. The goal of Zeno’s arguments is to prove Parmenides’s monistic philosophy. This philosophy stood probably also as a reaction to Pythagorean science, which tried to explain worldly phenomena in terms of a multiplicity of opposing principles. For Parmenides there is just one principle, Being, which never moves, never changes, is everywhere, all the times, and so on. Zeno’s paradoxes of movement aim precisely at showing that movement is apparent; those who claim that movement is real, run into inconsistent claims.
Zeno’s philosophy is one of the clearest examples of the power of rational argumentation in Ancient Greek philosophers
: by reasoning alone (hence without relying on any specific observation) one can prove that the world has a certain structure. This is a radical methodology, which by and large diverges from the methods of inquiry employed in contemporary science.
The Paradoxes of Motion:
The paradoxes of motion are Zeno’s most famous ones. Their original formulation is lost; luckily, they are available through the recounting of other philosophers, including Aristotle
, who discusses them in some depth in the Physics. The lack of textual evidence, however, adds one layer of interpretative difficulty. Not only it is difficult to comprehend the details of the paradoxes: depending on the details of the formulation, different interpretations will be suggested. In other words, the interpretation of the paradoxes risks of being skewed depending on how they are formulated.
Pythagorean science explained worldly phenomena in terms of the interaction of atoms; Zeno’s aim is to show the absurdity of such a conception. He does so by considering whether space or time in which atoms exists is either continuous (thus infinitely divisible) or discrete. The paradoxes of motion thus recombine all different options for space and time to be either continuous or discrete. (i) When both space and time are discrete, we have the so-called paradox of the stadium. (ii) When space is discrete and time continuous, we have the so-called paradox of Achilles and the Tortoise. (iii) When space is continuous and time discrete we have the so-called bisection paradox. (iv) When both space and time are continuous we have the so-called paradox of the arrow.
Under this reconstruction, the four paradoxes comprise one long argument against the plausibility of any atomistic philosophy. If true, they threaten to undermine not only Pythagorean philosophy: atomism played a central role also in early modern science and philosophy, and still enjoys the favors of some scientists and metaphysicians. This is the reason why the paradoxes still receive close attention to date.
The Paradoxes of Plurality:
The paradoxes of plurality, also discussed by Aristotle, aim at showing that there cannot be a plurality of entities. In the first one, Zeno assumes that the number of things be finite; if so – he observes – then there are infinite things because between the finite things there have to be infinitely many dividing them.
The other paradox deals with the concept of infinitely small and infinitely large. If there are infinitely small things (say, the points of a line), then adding one of them to the other we still have the same amount, which means we added nothing (adding two – or finitely many – points does not make a line.) If, on the other hand, things occupy space, then they will have infinite parts and, hence, they will be unlimited – which is absurd.
The Millet Paradox:
The millet paradox deals with the difficulties of explaining changes caused by the joint action of multiple things. If a good bunch of millet seeds makes a sound when – say – dropped into an empty bucket, then also each seed, or part of seed never mind how small, also has to make a sound – which is absurd.
The Paradox of Place:
The paradox of place has it that if everything that exists has a place, then place itself – which is an existent thing – must have a place; but the place of place must have a place on its owns; and so on ad infinitum. Thus, nothing can have a place, which is absurd.
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