Parmenides and Zeno

Parmenides and Zeno :[Elea, 515 - ? BC]

Heraclitus maintained that everything changes, and since philosophers love to argue, it is perhaps unsurprising that someone stated the exact opposite, namely that nothing ever changes. This view was put forward by Parmenides, son of Pyres who came from Elea, a Greek foundation in southern Italy.

The chronicle describes Parmenides as a nobleman who once established a new law for Elea, which became so popular that all new officials of the city had to swear they will abide by the Parmenidean law before they were inaugurated. Parmenides is also known for the philosophical school he established in his city, the Eleatic school. It is further said that Parmenides and his main disciple, Zeno, once came to Athens for the festival of the Great Panathenaea where they had an encounter with the young Socrates. Although the narrative is uncertain, there is no doubt that Socrates, Plato, and Aristotle were strongly inspired by the Eleatic school.

Parmenides stated that the senses deceive us and, hence, our perception of the world does not reflect the world as it really is. Instead, the real world is something above our apprehension and can only be apprehended through logic. His chief doctrine is that the only true being is "the One" which is indivisible and infinite in time and space. But "the One" is not conceived by Parmenides as we conceive God, neither is it reminiscent of the Hindu "Brahman". Instead he thinks of it as a material being with infinite extension, which he concludes from logical reasoning.

He argues that the perception of movement and change is an illusion and says that everything that is, has always been and will ever be, since it can always be thought and spoken of. The essence of this argument is: If you speak or think of something, the word or thought relates to something that actually exists, that is both thought and language require objects outside themselves, otherwise they would be inconceivable. Parmenides assumes a constant meaning of words and concludes from there that everything always exists and that there is no change, for everything can be thought of at all times.

In fact, he did not express his ideas so straightforwardly. His writings are in awkward hexameters, its contents intermixed with unfathomable symbolism, as in the following example: "The mares that carry me as far as my heart may aspire were my escorts; they had guided me and set me on the celebrated road [...] Only one road, one story is left: that it is. And on this there are signs in plenty, that, being it is unborn and indestructible, whole of one kind and unwavering, and complete. Nor was it, nor will it be, since now it is, all together, one, continuous. [...] That it came from what is not I shall not allow you to say or think - for it is not sayable or thinkable that it is not." (Simplicius, Commentary on the Physics, 144.25)

Melissus, an eminent citizen of Samos and admirer of Parmenides produced a book approximately 50 years later, rendering Parmenides' doctrines in clearer prose. In the following excerpt he explains the canon of infinity and perpetuity of the One: "Since what comes into existence has a beginning, what does not come into existence has no beginning. But what exists has not come into being. [which was deducted before in the text] Therefore it has not got a beginning.

Again, what is destroyed has an end, and if something is indestructible it has no end. Therefore what exists, being indestructible, has no end. But what has neither beginning nor end is in fact infinite. Therefore what exists is infinite. If something is infinite, it is unique. For if there were two things they could not be infinite but would have limits against one another. But what exists is infinite. Therefore there is not a plurality of existents. Therefore what exists is one." (Simplicius, Commentary on the Physics, 103.13)

The above states the gist of classical monism. It is obvious that Parmenides is wrong, although his deductions are logically correct. The problem lies in the axiom; he assumes that the intelligible word and the things themselves have a common form of existence. Parmenides attempted to build his metaphysics on basis of the logical conclusions derived from this axiom. Although the resulting theory is erroneous, his methodology was a genuine innovation.

Parmenides profoundly influenced later philosophers with this method and possibly supplied the spark for Plato's theory of ideas. Since Eleatic philosophy grossly contradicts common sense, it is unsurprising that his teachings brought forth critical challenge and ridicule among his contemporaries. It was Parmenides' brightest disciple, Zeno (some say he was his lover, too), who became the chief defender of his master's position. Again, the methodology is conclusive argument.

Zeno followed his master's advise to disarm his adversaries by leading their argument ad absurdum and thus became famous for his paradoxes. That the senses give us no clue to reality but only to appearance was proved by Zeno in the following manner (Zeno speaks to Protagoras, the sophist): "'Tell me, Protagoras,' he said, 'does one millet-seed - or the ten-thousandth part of a millet-seed make a sound when it falls or not?' Protagoras said that it did not. 'But,' he said, 'does a bushel of millet-seed make a sound when it falls or not?'

When he replied that a bushel does make a sound, Zeno said: 'Well, then, isn't there a ratio between the bushel of a millet-seed and the single seed - or the ten-thousandth part of a single seed?' He agreed. 'Well, then,' said Zeno, 'will there not be similar ratios between the sounds? For as the sounders so are the sounds. And if that is the case, then if the bushel of millet-seed makes a sound, the single seed and the ten-thousandth part of a single seed will also make a sound.' That was Zeno's argument." (Simplicius, Commentary on Physics, 1108.14-28)

To evince that motion and change is an illusion, Zeno presented the following paradoxes:

1. The Racecourse. Imagine a racecourse of a given length, say 100m. The runner starts at the beginning of the racecourse and reaches the goal in a given time. In this example of motion, the runner traverses a series of units of distance, foot perhaps. Zeno holds, that each unit of distances can be divided into smaller distances, 1/2 foot, 1/4 foot, 1/8 foot and so on, until at last we have an infinite number of distances. How can the runner traverse an infinite number of distances in a finite amount of time?

2. Achilles and the Tortoise. The swift Achilles and the tortoise hold a race contest. Because Achilles is a sportsman, he gives the tortoise a head start. While the tortoise is already moving towards the goal, Achilles starts and pursues the tortoise. In a few seconds he reaches exactly the point, where the tortoise has been when Achilles started. However, during this time the tortoise has moved forward and it takes Achilles a certain amount of time to make up for this distance. Again, the tortoise has moved on in that time and Achilles needs another, smaller amount of time to make up for it. The distance between Achilles and the tortoise will always be divisible and, as in the case of the racecourse, no point can be reached before the previous point has been reached, thus Achilles can never overtake the tortoise.

3. The Arrow. Does the arrow move when the archer shoots it at the target? If there is a reality of space, the arrow must at all times occupy a particular position in space on its way to the target. But for an arrow to occupy a position in space that is equal to its length is precisely what is meant when one says that the arrow is at rest. Since the arrow must always occupy such a position on its trajectory which is equal to its length, the arrow must be always at rest. Therefore motion is an illusion.

There are more of Zeno's paradoxes; almost all involve dichotomy and the mathematical problem of infinity. Although these paradoxes are confusing, it is quite evident to us that the conclusions derived from them are nonsensical. Yet, this was not obvious to Zeno's contemporaries. In the early beginnings of philosophy, these logical pitfalls presented a major obstacle to progressive thought, and Parmenides maintained a significant influence on Greek thought for some time.

The paradoxes illustrate the sort of problems we encounter in language and logic. Zeno's arguments are fallacious and may be refuted, once the correct premises are applied, yet the correct premises are less than obvious. Therefore, Parmenides and Zeno can be credited with having demonstrated, contrary to their intention, that logic alone is no sure-fire way to attain meaningful knowledge. They have instead shown that the opposite is occasionally true and that we must beware of logical pitfalls. Philosophical reasoning is only as sound as the premises it rests on.