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.
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