Xenophon of Elea: The Inventor of Dialectics
Introduction:
Xenophon is considered a prominent figure in the Eleatic school, which originated in the city of Elea in southern Italy during the 5th century BC. According to Walter Stace, Xenophon marked the beginning of true philosophy. Before Xenophon, the first philosophical movement in Greece was the Ionian school, which emerged in the Greek colonies on the western coast of Asia Minor. The Ionians were known more as naturalists than philosophers, and their focus was on explaining the universe through natural and scientific means. Some of the most notable Ionian philosophers include:
- Thales, who was the first Ionian to separate thought from mythology and made mathematics a foundation of philosophical inquiry. He also proposed water as the primary element from which the universe is composed.
- Pythagoras, who belonged to a religious organization devoted to order and harmony. He was interested in mathematics and music, and he coined the term "philosophy," defining it as a system of knowledge based on numerical relationships.
However, Walter Stace argues that the Eleatic school was the first to introduce the concept of truth, albeit in a weak and imprecise form. He states, "Philosophy, as many suppose, is not a mere collection of disconnected reflections to be studied in historical order; but, on the contrary, the history of philosophy represents a definite line of development in which truth gradually reveals itself with the course of time."
This paper delves into the following questions:
- Who was Xenophon of Elea?
- What were the characteristics of his philosophical approach?
- What was the significance of his impact on the history of Greek philosophy?
To address these questions, we will begin by examining Xenophon's time and place, particularly his teacher Parmenides, who played a crucial role in his intellectual development.
Chapter 1:
Section 1: The Life and Philosophy of Xenophon of Elea
Xenophon was born in Elea, on the western coast of southern Italy, in 490 BC. He studied under the philosopher Parmenides, "and in no respect did he disagree with his teacher, even in the part concerning natural philosophy, never departing in the least from what Parmenides had said."
Walter Stace highlights that Parmenides introduced a fundamental distinction in philosophy: the distinction between sense perception and reason. Parmenides argued that the world of appearances, the world of change and non-being, is the world that we perceive through our senses. However, true and real existence cannot be known through the senses but only through reason or intellect. Therefore, according to Parmenides, the senses are sources of illusion and error, and truth resides solely in the intellect. This notion is considered the cornerstone of idealism.
Abdul Rahman Badawi describes Parmenides as the first true philosopher of the Eleatic school and the first metaphysician in Greece. This is particularly evident in Parmenides' focus on the concept of being, which he viewed as an abstract concept rather than nature itself.
From Parmenides onward, Greek philosophy would take two paths: the path of Parmenides, which advocated for a fixed and unchanging being, and the path of Heraclitus, which advocated for a changing and evolving being. Subsequent philosophers would attempt to reconcile these two opposing views.
By establishing this distinction between rational and sensory knowledge, Parmenides placed the problem of knowledge on a solid foundation for the first time.
Xenophon defended Parmenides' doctrine of one, unchanging being and argued that opposing doctrines inevitably lead to contradictions. This implies that they are false, and since they are false, the doctrines that contradict them must be true. In this way, Xenophon employed reductio ad absurdum to prove his point. While this method involves verbal argumentation, it is distinct from Sophistry. The goals of the two approaches differ significantly. Xenophon's dialectic aims to establish a positive truth while adhering strictly to logical principles. In contrast, Sophistry seeks negative outcomes, namely the destruction of philosophy as it was understood at the time.
It is noteworthy that Xenophon's logical precision and rigor of argumentation were evident and followed established logical principles. This was not the case with the Sophists.
Section II: Zeno of Elea's Methodology
The hypothetical method is called dialectic because it is associated with Zeno of Elea, whom Aristotle called "the inventor of dialectic," meaning refutation. Here, "dialectic" refers to reductio ad absurdum.
Waterston considers Zeno's contribution to the Eleatic school to be extremely negative in a sense, in that he added nothing positive to the teachings of Parmenides while supporting his teacher's doctrine of Being. However, his additions came in the form of arguments he offered to support his teacher's conclusions. In his attempt to reaffirm Parmenides' doctrine from a new perspective, Zeno presented specific ideas about the ultimate nature of space and time, ideas that have since become of great importance in philosophy.
Plurality and motion are the two distinguishing characteristics of the false phenomenal world, and therefore Zeno directed his arguments against them. He indirectly tried to support Parmenides' conclusions by showing that plurality and motion are impossible and contradictory.
Aristotle acknowledged that Zeno was the inventor of dialectic, which he defined as the method of reaching truth that Socrates followed in Plato's early dialogues. Socrates loved to engage people in conversation and ask them about their views to arrive at conclusions that they would not have thought of except for his penetrating questions. In this way, he was gradually able to undermine the foundation on which they had built their opinions and make them reconsider things more deeply to arrive at an answer to the questions before them. It seems that Socrates may have taken this method from Zeno's scrutinizing style.
Chapter Two:
Section One: Zeno of Elea's Arguments
Zeno raised a serious problem that played an important role in the history of philosophy after him. It is the problem of how, if we say division, we can explain continuity, because in reality, every division means separation, and this is a denial of continuity, and in denying continuity, we deny influence, and in denying influence, we deny change.
Adnan Malhem summarized Zeno's arguments in his article as follows:
"Zeno presented his famous arguments against plurality and motion to prove the correctness of Parmenides' doctrine that existence is based on two main principles: unity and stability. His arguments are divided into two sections: a section on plurality and a section on motion, and each of these sections has four arguments.
Zeno's arguments against plurality are: an argument about quantity, an argument about number, another about space, and an argument based on the idea of the total effect (the heap of wheat). The common theme of all these arguments is that if plurality is real, it must be as it is, neither increasing nor decreasing. But if it remains without increase or decrease, then it is limited and not plurality. And if plurality exists in reality, then it must be infinite, in the sense that it is a plurality of units, and the units are separated by intermediates, and the intermediates are separated by intermediates, and so on to infinity.
Zeno's arguments against motion are four, two of them deal with space, and they are based on the idea of dividing space into an infinite number of units. The difference between the two arguments is that the target in the first argument is fixed and limited, while in the second argument the target is moving and constantly changing. And two of them deal with time, and are based on the idea that the idea of dividing time into an infinite number of sections. In general, Zeno's arguments against plurality, as well as against motion, involve a number of fallacies."
Chapter II: A Critique of Zeno's Arguments
Zeno's paradoxes were fallacies, renowned for their absurdity, or as Plato put it, "serious jokes." However, they represented a novel philosophical concept, provoking philosophers of the time to respond, leading to an analysis of Plato's, and especially Aristotle's, understanding of extension, time, space, number, motion, and infinity.
While the ancients dismissed Zeno's idea of dividing distance into infinity and mocked him, modern mathematicians (with Leibniz taking the lead) saw this division as real and in need of calculation. Thus, calculus, or differential and integral calculus, was born.
In the 19th century, Newton and Leibniz established the operations of differential and integral calculus and infinitesimal limits, while some scholars merely asserted the impossibility of reaching limits for time, space, and motion. The most that can be done, they argued, is to get closer and closer, but certainly not with certainty. This is the current state of affairs in mathematics, physics, and philosophy. If you wish to confirm this, simply search for a perfect, complete, and finite real number that accurately expresses the value of one-third.
Despite all the objections and rebuttals we can raise against Zeno's arguments, we must acknowledge that his method of thinking had a significant impact on philosophy. Zeno's method was so novel that Aristotle considered him the inventor of dialectics. According to Abdel Rahman Badawi, the historical value of these arguments far outweighs their actual truth. These paradoxes raised the problem of change and phenomena and presented it in one of its forms. The natural philosopher had to take these arguments into account, which is why we see Plato and Aristotle compelled to respond to them before delving into motion.
Conclusion
We can conclude this brief research with what Walter Stace stated in his critical notes on the Eleatic school, as follows:
The Eleatic philosophy considers the world of the senses, despite its distinction by essential qualities of plurality and motion, not to be the true existence. They do not deny the existence of motion and plurality; no sane man denies that. Zeno, for example, does not deny the existence of the world, but what he denies is the reality of its existence. What he means is that the world present to our senses is not the real world but a mere illusory appearance, an external spectacle, a false mask that conceals the true existence of things.
However, history did justice to Zeno, not by revealing the good aspects of his life or proving the correctness of his conclusions, but by discovering a perpetually provocative and stimulating aspect of his paradoxes. As the philosopher and mathematician Alfred North Whitehead wrote in 1932:
"The mere fact that one continues to try to refute his paradoxes every century is a testament to Zeno's resounding success... No one has studied Zeno's philosophy without trying to refute it, and yet philosophers in every century still find his views worthy of refutation."
