The Eleatic School

The Eleatic school is so named because it originated during the 6th century BC in the eastern Greek colony city of Elea, in the region of Lucania (present day, southern Italy).  There is some debate as to who to ascribe as the founder of this school of philosophy, the candidates being Xenophanes and Parmenides.  However, it seems that Xenophanes first put forward the basic concepts, and Parmenides later developed these concepts and organized them into a philosophical doctrine.

The doctrines of the Eleatic School appear to have been in direct opposition to the doctrines of Heraclitus, although it is debatable whether any of it was inspired as such.  The Eleatic School was based on two fundamental principles.

  1. All individual, separate things to be in fact the one inseparable whole, the “One Being”.
  2. The process of change from one thing to another, and therein the multiplicity of different, separate things, to be in fact an illusion.

Thus, the ultimate message of the Eleatic School could be summarized by the statement that, ”all things in the universe are in reality One Unchanging Inseparable Unity”.

Below we will examine three of the principal characters of the Eleatic School, Xenophanes, Parmenides, and Zeno.

1: Xenophanes

Xenophanes is believed to have been born in Colophon in Asia Minor and lived circa 570 BC to 480 BC.  It is thought that he may well have been a disciple of Anaximander before leaving Ionian.  At one stage in his life, he is believed to have wandered Greece and Sicily as a minstrel, before eventually settling in Elea in 536 BC.  It was there that he is reputed to have founded the Eleatic School.

Xenophanes was primarily a satirist.  And as such, he focused his attention on the anthropomorphic religions of the day.  [Note: Anthropomorphism is the tendency of human beings to ascribe human form or characteristics to that, which is not human.]  Xenophanes ridiculed these religions for their belief in the many human-like gods of mythology.  He is meant to have said, “If Oxen could paint and sculpt, their deceptions of their gods would have resembled Oxen”.  He is said to have reduced many of the gods of mythology (such as the god of thunder etc) to mere weather phenomena.  Xenophanes urged his fellow citizens to reject anthropomorphic polytheism (belief in many gods) and instead embrace the concept of all of nature being the “One Being”, the one single indivisible entity that permeated all things in the universe.

This apparent Monotheistic religious creed (belief in one god), in what is essentially a Pantheistic doctrine (belief that God is in everything and everything is God), can be explained by the fact that Xenophanes essentially equated all of Nature as the “One”.

2: Parmenides

Parmenides was born in Elea, Lucania and lived circa 510 BC to circa 445 BC.  He was a slightly younger contemporary of Heraclitus and a disciple of Xenophanes.  He is said to have been responsible for expanding the ideology of Xenophanes and structuring the concepts into organized system of thought.  For this reason, he too is sometimes seen as the founder of the Eleatic School.  Nevertheless, irrespective of who was the original founder of the school, Parmenides was certainly the most influential architect of the doctrine.  He essentially agrees with the Xenophanes concept of the fundamental “Oneness of all things”.  However, Parmenides took this idea forward and effectively developed the doctrine of the Eleatic School into a system of the conceptual.  As a result, he is often seen as the founder of Western Metaphysics.  It is said that Eleatic philosophy was a precursor to, and heavily influenced, the metaphysical system of Plato.

[Note: For the uninitiated student, some of the ideas and concepts of metaphysics can be quite confusing, verging on the irrational.  Suffice to say that for the metaphysical philosopher, these ideas are born of reason alone.]

The belief that everything that existed had always existed was not an uncommon idea for the time.  It was only in later years that religious scholars placed the creation of the universe at around 5,000 BC, having used ancient sacred scriptures to determine the date.  It was, therefore, not unusual for Parmenides to believe, as many others did at the time that, all which existed could not cease to exist, and that no thing could come from nothing.  Thus, Parmenides reasoned that, “whatever is in existence had always existed and would never cease to exist”, and in a similar vein, “whatever is nonexistent does not exist and therefore can never exist”.  Consequently, if this be so, there could be no sure thing as “not being” or as he put it “non-being”, as non-being means nonexistent and thereby, logically, does not and cannot exist.  Therefore, he concluded; between being and non-being, there is only “Being”

This reasoning meant there could be no such thing as “the void” or empty space, because empty space implied space occupied by nothing (no material thing), and since nothing did not exist, empty space therefore could not exist either.  If empty space did not exist, there was nothing to separate one thing from another.  Consequently, there could be no separation of one thing from another, and hence the multitude of different separate things had to be an illusion and the reality was that everything is “One”.

Parmenides further stated that nothing could be anything other than what it really was.  He argued that something either existed or it did not exist, there could be no middle state as the idea of “becoming” implies.  The nature of “becoming” entails something coming into being.  Something coming into “being” would imply that previous to its arrival, it was “non-being”.  Since “non-being” does not exist, “becoming” is impossible.  Because of this reasoning, Parmenides negated all forms of “becoming”, and this led him to assert, in what seems to be direct and conscious opposition to Heraclitus, that there could be no such thing as “Change”.  Thus, Parmenides concluded by the power of his reason, that reality must be a “Single, Indivisible, Unchanging Oneness of Being”.

However, he did accept that he saw and experienced change and the multiplicity of all around him.  This, therefore, led to a conflict between what his senses were telling him and what his reason was concluding.  In this conflict between the senses and reason, Parmenides sided with reason.  As mentioned before, this absolute faith in human reasoning is referred to, as Rationalism, and therefore Parmenides was one of its first exponents.

Parmenides, therefore, had to believe that the senses were unreliable in interpreting what was truly real.  This led him, inevitably, to the conclusion that the experience of the senses of the multitude and change in nature were in fact an illusion with no real existence, “they only seemed to exist”.  By using this line of reasoning, Parmenides was also one of the first exponents of Idealism (everything being a product of the mind).

Parmenides does explain how this illusion comes about.  This explanation has been described as an elaborate and obscure discussion on motion and change being the interplay of the principles of being and non-being.  Some scholars have argued that in his explanation for the apparent illusion, Parmenides almost contradicts his own logic, as some of his reasoning uses concepts contrary to his own fundamental doctrines.  Nevertheless, it must be remembered that any such explanation comes second hand, and due to the nature of the subject matter, it is bound to be littered with obscurities.

Parmenides taught that there were two paths of knowledge, one leading to truth that could only be arrived at by philosophical reasoning, the other path led merely to ill-informed opinion.

Finally, Parmenides preached the concept of the existence of Absolute Being.  He described how Absolute Being was inconceivable to man, due to the limitations of the human mind.  True Being, which he stated to be the understanding of the existence of Absolute Being, was however, conceivable by means of human reason.  In fact, so convinced was he of his own logic that Parmenides reasoned the non-existence of Absolute Being to be inconceivable.

[Parmenides arguments rely heavily on the concept of the continuous nature of things, the continuous nature of time; the continuous nature of space.  This continuous nature of things means that it is difficult to separate one thing from the next.  It assumes that things can constantly be divided ad-infinitum.  Implicit in this assumption is the idea that there is no smallest unit.  Thus, this is basically an argument that assumes a continuous nature of the universe, as opposed to a possible discrete nature of the universe.]

3: Zeno of Elea

Zeno was born in Elea and lived circa 488 BC to 428 BC.  Zeno is referred to as Zeno of Elea to distinguish him from Zeno of Citium, who comes later in classical history.  Zeno is believed to have been a favorite disciple of Parmenides, whom he accompanied to Athens sometime around 450 BC.  Here he remained to become a teacher in philosophy, teaching primarily the metaphysics of the Eleatic School.  It is believed that during this time he either met, or taught, Socrates.

Zeno is remembered, not for having essentially added anything in particular to the doctrine of the Eleatic School, but for the way he defended the doctrine, and Parmenides in particular.

Parmenides ideology stated that the universe was an undifferentiated oneness and that all change was impossible.  This, therefore, implied that the multitude of all things was an illusion, and all motion or movement was also an illusion.  These ideas however seem to have been ridiculed at the time by the Pythagorean, who saw them as nonsensical.  In response to this, Zeno constructed arguments that were probably not intended as a proof of doctrine, but instead, purely to demonstrate that the belief in the so-called common sense idea of the “diversity and changing nature of all things” could also lead to logical absurdities.

As is normal with history, there is some debate among scholars as to whether Zeno’s arguments where meant as a defense of Parmenides, or simply to show that any idea or concept could fall prey to logical absurdities.  Regardless of the reason, what is of most interest is the nature of the arguments themselves.  Zeno constructed his arguments in the form of Paradoxes.  The idea was to take what appears to be a rational concept and show through logical reasoning, that the concept leads to unacceptable or absurd conclusions.  Zeno focused primarily on destroying the logical acceptance of the concepts, such as “change” and “motion” and “the plurality of things” (the idea of the one thing being made up of many smaller parts).

We will briefly review four of the better-known Paradoxes.  [These paradoxes are here paraphrased to facilitate easier comprehension].  The first two paradoxes deal with the concept of Plurality:

  • The first paradox is about density.  If we have a line segment, then according to the theory of plurality, the line segment is a made up of many points, a very large number of points.  However, between any two points, there cannot be “nothing”; therefore, there must be a third point.  Now we have three points where previously there were only two.  However, between the old first and the new third point, there again cannot be “nothing” so, therefore, there must be a fourth point, and similarly between the new third and the old second there also cannot be “nothing”, and therefore, there must be a fifth point.  Now we have five points where initially there were only two.  We can see that, logically, we can keep applying this argument until we end up with an infinite number of points with no end to the addition of more points.  Therefore, we are left with the conclusion that a finite line segment is made up of an infinite number of points.  This of course is absurd.
  • The second paradox is about size.  If we have a line segment, it is seen as a continuous thing.  A line segment has length and, therefore, can be divided in two.  The resulting two lines segments also have length and consequently they also can be divided in two.  Now we have four lines segments, each being one quarter the size of the original line segment.  If we keep splitting each segment in two, then the segments get smaller and smaller.  We can continue dividing the segments ad-infinitum until eventually (theoretically at least) we have an infinite number of infinitesimally tiny segments.  These infinitesimal segments can be seen as ”points” on the line.  Now, according to Zeno, this logically can only lead to one of two situations both of which are absurd.  The first situation is that, a point on the line while of infinitesimal size, still has some size.  Therefore, if we add these infinitesimally small points together, we will have to keep adding points ad-infinitum, because there are an infinite number of points.  This means that the line segment will constantly grow to become of infinite size.  As a result, this approach effectively says that anything of size must be of infinite size, which is of course absurd.  Conversely, the second situation is that, the points are small enough that they have no size.  In this case, we have an infinite number of things of no size, which when added together equal something of no size.  This conclusion says anything of size can actually have no size at all and, therefore, cannot exist.  This is equally absurd.

The next two paradoxes deal with motion or the concept of change.  These paradoxes are fairly well known and are a little easier to comprehend.

  • Achilles is the fastest of all the gods.  Achilles has a race with a tortoise, the slowest of all creatures, so Achilles gives the creature a head start.  The race starts, and Achilles quickly reaches the point from which the tortoise started.  The creature, of course, has moved on at this stage to a second point.  Achilles quickly reaches this second point, but the tortoise has moved yet again to a third point.  On reaching this third point, the tortoise has still managed to move slightly further forward to a fourth point.  This process goes on ad-infinitum, with the tortoise always having moved ever so slightly further ahead by the time Achilles reaches his last point.  Thus, we are forced to the absurd conclusion that Achilles can never catch up with the tortoise, let alone overtake him.
  • When an arrow is in flight, it occupies a given space in any given instant.  Thus, at any given instant, the arrow only occupies the amount of space necessary for its length, no more, no less.  Therefore, at any given instant, the arrow is in the same situation as it would be if it were at rest (picture a photograph of an arrow in flight).  Therefore, at any given moment in time, the arrow is not moving; consequently, the arrow must always be at rest.  Hence, the arrow never moves, thus proving the concept of motion to be absurd.

The primary focus of these Paradoxes was to show that the division of continuous space into individual points, and continuous time into individual instants led to logical absurdities.  Zeno’s idea was to arrest the senses and demonstrate that what appear to be common sense ideas are not always so.  In doing so, Zeno hoped to reveal that assumed common sense should not act as an obstacle to the contemplation of what might seem, on the surface, to be an implausible concept.

Zeno Paradoxes were very effective arguments, formulated as they were in such a way as to demonstrate the absurdity of what seemed like a reasonable initial premise.  The fundamental argument is basically along the lines of: “Let’s say you are right, then logically your argument leads to the following conclusions which make no sense at all, therefore your initial premise must in fact be wrong”.  This method of argument is now known as “Dialectic Argument” and Aristotle has credited Zeno with being the father of the “Dialectic Technique”.  The Eleatic Schools’ obsession with logical consistency effectively built the foundations for ”Argument from Reason” and ”The Science of Logic”.

[Down through the ages, the Paradoxes of Zeno became intellectual puzzles that many great men of wisdom attempted to solve.  However, the reader should not bother trying to unravel these paradoxes, because ultimately it is not possible to do so.  Like all paradoxes, they rely on confusion of concept that is hidden in the use of language.  The paradox will have us believe we are comparing apples with apples, when, in fact, we are actually comparing apples with oranges.  In order to make a fair comparison, we need to bring both things to the same basis.  In these Paradoxes, Zeno make much use of the concept of infinity, with both the infinite number and the infinitesimal size.  However, an infinite number is meaningless in terms of comparison, it is purely a name give to something that has the property of no end or no limitation.  Therefore, it is meaningless to make a direct comparison between one infinite number and another, and assume that they are the same.  They are the same in property only.]

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