“[I]f we revert to history, we shall find that the women who have distinguished themselves have neither been the most beautiful nor the most gentle of their sex.”
Mary Wollstonecraft, A Vindication of the Rights of Woman
Progress on the “Philosophy Narratives” has been remarkable, covering the span of two ages. Our opening act was the “Pre-Socratic Four” of Thales, Pythagoras, Xenophanes and Heraclitus which culminated in the grand finale featuring the dynamic duo of “The Eleatics,” Parmenides and Zeno. Six remarkable men engaged in the search for knowledge and understanding, whose observations would influence generations that followed.
The more I read about the lives of ancient philosophers, the more I value humanity’s need to understand its place within the framework of existence. Philosophical inquiry demands our full participation. We are engaging in the monumental task of fashioning the society in which we want to live. Moreover, we are determining what our obligations are to each other, our descendants, and the environment.
Which brings me to the subject of enquiry for the coming week – women. The story of philosophy has many brilliant, dynamic, even formidable women with remarkable narratives that have added depth and nuance to the history of intellectual growth and expansion. It is time to add a few names to the roster of ancient thinkers.
“If women are expected to do the same work as men, we must teach them the same things.”
Plato, The Republic
“The goal of life is living in agreement with Nature.”
Zeno of Elea is renowned for his paradoxes. Indeed, they continue to challenge, confound, inspire and amuse even until this day. We can thank Plato for what little we know of Zeno’s life. Plato wrote in his Parmenides dialogue of a meeting in Athens between Parmenides, Zeno and a young Socrates. I can only imagine the intellectual energy generated by their conversation.
Zeno defended Parmenides’ views against the followers of Pythagoras by introducing a series of paradoxes to argue that change and plurality (a belief in the existence of many things rather than only one) are illusory. It seems that there may have been up to 40 paradoxes; unfortunately, only two have survived over the centuries.
The paradox that I recall suggests that Achilles of The Iliad fame, at his best speed, could never catch a tortoise that had been given a head start. Suppose you want to walk to the other side of a room, the end point. Before you reach the end point, you must first reach the halfway point, but before that, you must reach the halfway point of that, and the halfway point of that, and so on. If space consists of an infinite series of points, to complete the walk across the room, you must pass every one of those points. Bottom line – you can never move through all of those infinite points within a finite timeline. A tortoise, with the benefit of a head start, will outperform even the great Achilles.
“if being is many, it must be both like and unlike, and this is impossible, for neither can the like be unlike, nor the unlike like”
“It is all one to me where I begin;
for I shall come back again there.”
Parmenides, On The Order
Parmenides of Elea, a poet-philosopher, willingly challenged Heraclitus on his premise of continual change. Parmenides’ poem “On Nature,” which has come to us in the form of fragments, presents one of the first examples of a reasoned argument that change is impossible and that reality is singular, undivided and homogenous. Parmenides, in “The Way of Truth,” the first section of his poem “On Nature,” wrote of his rendezvous with a goddess who taught him how to make a distinction between an inquiry into what is, and an inquiry into what is not.
Parmenides believed that to think of something is to give it a manifestation of existence. For example, a phoenix does not exist in the material world, but it has a place in our thoughts and imagination. Hence, to think of the phoenix implies its existence even though it never existed except in Greek mythology and the legends of ancient Egypt. Similarly, if we can visualize something that will exist in the future, then it must already exist in our minds. If we remember something or someone who is no longer with us, then they continue to be present at the moment we thought of them.
I confess that I was amazed to meet a philosopher who had divine revelation. Nevertheless, Parmenides started a dialogue on the connections between thoughts, words and things. It is a debate that has ignited the thoughts of every key thinker down through the centuries.
Perhaps, some credit should go to the goddess.
“We can speak and think only of what exists. And what exists is uncreated and imperishable for it is whole and unchanging and complete. It was not or nor shall be different since it is now, all at once, one and continuous…”
“No man ever steps in the same river twice, for it’s not the same river and he’s not the same man.”
I love to quote Heraclitus, because he seems so gentle and serene. Think again!
Heraclitus, who once said that “character is destiny,” believed that war and strife between opposites is the eternal condition of the universe. Considered the quintessential antagonist, he once declared that his fellow citizens of Ephesus were so witless they should hang themselves and leave the city to the rule of children. You can imagine the fracas that came out of that pronouncement. Even so, for those brave enough to invite him, he would be a riveting and entertaining dinner guest.
Heraclitus was quick to scorn Homer, suggesting that he should be turned out and whipped. Even Pythagoras and Xenophanes did not escape his ridicule. Instead, he argued that the three principal elements of nature were fire, earth and water, the primary being fire which he believed controlled and modified the others. The cosmic fire finds its complement in the human soul, which in weak men is contaminated by the ‘watery’ elements of sleep, stupidity and vice. The virtuous soul is able to escape death and unite with the cosmic fire. Much like the concepts of yin and yang within Chinese philosophy, Heraclitus suggested that strife and opposition are both necessary and good. Although the universe itself is eternal, permanence does not exist within it. Change is continual; everything is in a state of flux.
I have a feeling Heraclitus would thrive in our fast paced, ever-changing, mercurial world.
“Allow yourself to think only those thoughts that match your principles and can bear the bright light of day. Day by day, your choices, your thoughts, your actions fashion the person you become. Your integrity determines your destiny.”
“But if cattle and horses or lions had hands, or were able to draw with their hands and do their work that men can do, horses would draw the forms of the gods like horses, and cattle like cattle, and they would make their bodies such as they each had themselves.”
Xenophanes of Colophon
Xeonophanes, a free thinker and poet, was a contemporary and outspoken critic of Pythagoras. He mocked the idea of transmigration of souls and scoffed at the possibility that a human soul could inhabit another animal. Like Thales before him, Xenophanes argued for the principles of natural phenomena. Thales believed the first principle to be water, whereas Xenophanes argued for the possibility of mud. We may smile at this thought; however his proof was in the fossil remains of sea-creatures embedded in the earth. It seemed that the earth was at one time in a muddy state before drying up.
What was even more forward thinking, in my opinion, was his anticipation of Socrates’ caution regarding claims of certain knowledge. He stated that “no human being will ever know the Truth, for even if they happen to say it by chance, they would not even known they had done so.”
Xenophanes’ influence was keenly felt by those who followed him, especially given his criticism of the Homeric gods still revered throughout the Hellenistic world. He eschewed their shameful traits that imitated the flaws of humanity. He considered that they were simply a reflection of the prevailing society, undeserving of respect or worship. He declared, “If horses could draw, they would draw their gods like horses.”
One thing is certain; Xenophanes had a way with words and was not afraid to use them.
“It takes a wise man to recognize a wise man.”
Xenophanes of Colophon
Pythagorean Theorem — or Pythagoras’ theorem: in any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Pythagoras of Samos, the creator of one of the most famous equations of all time, has a rather obscure history. He wrote very little about himself, delegating the task of documenting his life and views to his followers. What we do know is that in his world of the mid-sixth century BCE, he was considered to be a thinker and a mystic.
In today’s world, Pythagoras’ school would be considered more like a religious cult than a philosophical establishment. His teachings included many eccentric doctrines including, the veneration for, and abstinence from, the eating of beans. He advocated reincarnation and the transmigration of souls. Most see him as the founder of the modern belief in numerology, later popularised by Nostradamus.
Pythagoras argued that the ultimate nature of reality is number, which he developed out of his theory of music. He claimed that music had a special power over the soul. The proof was found in the intervals between musical tones, which could be expressed as ratios between the first four integers, number 1 – 4. His discovery of irrational numbers did play havoc with his beliefs on the origin of the universe; however, they have proven to be a major and lasting development in mathematical thinking.
After his death, his followers split into two camps; one embraced his religious and mystical teachings, while the other pursued his scientific and mathematical philosophy. Ideas and beliefs, whether or not they prove to be valid, must be considered, lest we overlook the very insight that will bring us to the next stage of development.
“It is the mark of an educated mind to be able to entertain a thought without accepting it.”