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The Other Greek Philosophers

Philosophy’s Roots and Branches

Will Bouwman on how Thales, Anaximander, Pythagoras, Parmenides & Zeno established empiricism, maths & logic as dominant features of Western thinking.

According to Aristotle, the first Greek philosopher was Thales of Miletus. His historical details are vague, contradictory even; there are conflicting stories about whether Thales married, one being that he did and had a son, another that he didn’t, at first telling his mother that he was too young to marry, and later, that he was too old. He also set the standard for intellectual distraction, falling into a well, or maybe a ditch, because he was so busy studying the stars. What isn’t in doubt is his influence on Western thinking: within a few generations, the philosophers he inspired, in particular Anaximander, Pythagoras and Parmenides, had established empiricism, mathematics and logic, the three disciplines that dominate thinking today.



Thales (c.624-c.546BC) was the son of nobles. It was common for rich Greeks to send their young men on educational ‘Grand Tours’ of Mesopotamia (essentially modern day Iraq) and Egypt, much as Eighteenth and Nineteenth Century aristocrats would visit Rome and Athens to broaden their minds (at least, that was the idea).

Even in Thales’ time, Mesopotamia and Egypt were ancient civilizations. Their antiquity was due in part to the ease with which agriculture, and hence large populations, were established and sustained by the regular flooding of the Tigris/Euphrates and the Nile.

The waters’ retreat leaves a film of fertile soil; as the resultant vegetation dies and decays underwater, it produces methane, which can be seen bubbling to the surface, and is a flammable gas. Hence the so-called ‘Greek’ elements – water, earth, air and fire – are all present where humans first settled, and seem to be linked; the belief was that one thing changed into another. Accustomed to things that change and develop being alive, people attributed change in nature to life; it is only a short step to give form to this life in the shape of gods. The creation myths of Mesopotamia and Egypt reflect this. For instance, the Enuma Elisha, the Babylonian ‘Bible’, tells how in the beginning there was no Heaven and Earth: there were instead Apsu, god of fresh water, and Tiamat, goddess of salt water. Their waters joined and from this union came Lahmu and Lahamu, the gods of soil. In Mesopotamia, where fresh water meets the sea, the Tigris and Euphrates rivers deposit enough silt to advance the coast by up to fifty metres each year; as an illustration, the city of Ur was a coastal port four thousand years ago: the site is now two hundred kilometres inland. The Enuma Elisha continues with the marriage of Lahmu and Lahamu producing Anshar, the sky. In Egypt, where civilization arose away from the coast, there was only one water god, Nun, who gave birth to Atum, initially as a mound of earth; Atum in turn created Nut, the sky.

The written Greek creation myth, the Theogeny (c.700 BC), is slightly different. According to its author, Hesiod, it was written on the slopes of the sacred Mount Helicon, where water is more likely to be seen springing from the hillside than dumping the silt it has picked up on its journey. So in this mythology the primordial god – the first to emerge from Chaos – was Gaia, Mother Earth. However, the belief that one thing turned into another, a sort of transmutation of elements, is the same.

What distinguished Thales was that he tried to explain how these changes happened without reference to gods. In Thales’ time Miletus was a busy Aegean maritime port at the mouth of the river Meander, from which we get the verb. The ruins of Miletus, in Turkey, are now ten kilometres inland, thanks to the soil deposited by that slow-winding river. Seeing this process at home as well on his travels, it’s little wonder that Thales concluded that the primordial substance was water; but Miletus being a mercantile city where the power of the religious establishment was not as pervasive as in other Greek cities, Thales was free to account for movement and change in some other way, without the gods pulling the strings. His solution was simply to dispense with the gods and apply ‘life’ directly to the water, and so to the world the water gave birth to. So for Thales the world grew and developed not because gods were moving things around, but because the world itself was alive. Thus Thales formulated the first naturalistic explanation of the cosmos.

To support the questionable hypothesis of matter being alive, Thales gave two examples of apparently lifeless things that do have the power to cause movement: magnets, which get their name from the lodestones found in the Greek region of Magnesia; and amber, which when rubbed with fur like children rub balloons on their jumpers will be charged with enough electricity to make your hair stand on end. The Greek word for amber was electron. Even as late as 1818, when Mary Shelley wrote Frankenstein, people still equated electromagnetism with life.

The fact that the power to move things could be found in otherwise unexceptional pebbles was enough for Thales to extend that capacity to the entire contents of the universe. Given the power of life, Thales believed the primordial water metamorphosed into earth, to air, to fire, creating the universe we are familiar with – much as the Egyptians and Mesopotamians had envisaged, but, as he was now committed to explaining events without the intervention of the gods, he tried to show how what happened could be attributed to natural causes.

One of the best known examples he gave of this was earthquakes. In Greek mythology, earthquakes were caused by Poseidon, a god and so an actual physical giant, who would wreak havoc by stamping the sea floor petulantly. Thales believed that the Earth floated on the primordial ocean, and so in contrast he reasoned that earthquakes could be caused by waves shaking the world, as a ship might be tossed in a storm.

Never mind that the best of Thales’ ideas were speculative, and that many were wrong; they could be challenged and tested in a way that the whim of divine beings could not. However, the philosophers he inspired could no more agree about what the world is ultimately made from than could the priests and poets before them. For instance, Anaximenes, a student of Thales’, favoured air. In keeping with the master’s example, he offered the evidence of his own breath. Depending on the circumstances breath can provoke sparks into flames or on a cool morning will condense into vapour, which Anaximenes interpreted as air turning into water. He reasoned that if water was condensed even further, it would turn into soil and rock. But he went further than his predecessors by suggesting how this transformation might happen. He used the example of felt, which is made by squeezing together soggy fibres and drying them out. Thus the Earth formed as fibrous congealed water was forced together. The heavens were formed in the same way, making a felt cap that shrouded the world.

In fact, all the elements had their advocates as the ultimate substance of reality, the archetype. To complete the set, Xenophanes and Heraclitus opted for earth and fire respectively. A Xenophanes fragment reads “all things come from earth, and all things end by becoming earth”; and a lot of what Heraclitus said about what the world is made of is summed up in one of his remaining fragments: “This cosmos, the same of all, no god nor man created, but it always was and will be: everliving fire, kindling in measures and being quenched in measures.”

Miletus, birthplace of Western philosophy


As was becoming clearer to the Greek philosophers, not only were gods a matter of taste and circumstances, their metaphysical, protoscientific hypotheses were subject to how the evidence – the appearance and behaviour of the world – was interpreted.

This point was taken up by Anaximander (c.610-c.546 BC), another student of Thales’. Rather than quibble about which element was primordial, he suggested instead that the different elements were all states of some underlying stuff that he called the apeiron, which means ‘the boundless’ or ‘the undefined’. This otherwise-undefined stuff was a smooth mixture of opposites, hot and cold, wet and dry. This is clearly a volatile mixture, and at some point it started to curdle, separating into the familiar Greek elements, earth, water, air and fire.

There is only one piece of the written work of Anaximander that survives. It is the oldest quote attributed to a philosopher in the Western tradition:

“Whence things have their origin,
Thence also their destruction happens,
As is the order of things;
For they execute the sentence upon one another
–The condemnation for the crime –
In conformity with the ordinance of Time.”

It is difficult to tell from a few lines of poetry how Anaximander’s system worked in any detail, but the core seems to be that, depending on its blend of competing properties – hot and cold, wet and dry – the apeiron could become anything. The different ways these contrarieties – hot, cold, wet and dry – were mixed defined an element: fire is hot and dry; air is hot and wet (think steam); water is cold and wet; leaving earth cold and dry. This idea was taken up by Aristotle, who says in On Generation and Corruption: “Our own doctrine is that although there is a matter of the perceptible bodies (a matter out of which the so-called ‘elements’ come-to-be), it has no separate existence, but is always bound up with a contrariety.”

According to this view, the stuff that the universe is actually made of is unknown to us, as we cannot perceive it directly. To Anaximander and Aristotle, what we can perceive, and what defines elements, at least as they relate to us, is their measurable qualities. This is still the case. Physics can describe the measureable qualities of fundamental particles with breathtaking accuracy. However, it cannot tell you what they are made of.


In his middle-age, Pythagoras (c.570-c.495 BC) emigrated from his native Samos – an island a few miles up the coast from Miletus – to Croton in southern Italy. There he started a sect that looks like a template for cults ever since: members were not allowed any possessions, they were forbidden to eat beans, and they used music to cure illness. But what made Pythagoreanism uniquely penitential was its insistence on the study of numbers; indeed, elite members of the sect were known as mathematikoi, ‘the mathematicians’. Unfortunately, despite the great discoveries attributed to Pythagoras and his teaching, no one thought to write any of it down until a hundred years after the event.

The man to do so was called Philolaus. He was born in Croton a few decades after the death of Pythagoras, and wrote what is thought to be the first Pythagorean book. In it Philolaus argues that the universe is constructed from two sorts of things. The first are the measureable things identified by Anaximander – matter and properties. Like Anaximander, Philolaus called them ‘boundless’ or ‘undefined things’. The other things needed to make a universe are more distinctively Pythagorean: these are the ways that the undefined things are mixed and shaped to define what we experience. These ways of defining the world are, in the words of Philolaus, ‘things that limit’: quantities and sizes, ratios and proportions, shapes and patterns. They are mathematical objects, and to Pythagoreans, they’re the things that, when applied to matter and its perceptible qualities, create order and beauty in the world. For instance, where the rules of good proportion are successfully applied, you will find armonia, harmony. It was said that Pythagoras had discovered the relationship between physical proportion and musical pitch when passing a forge. The notes that rang out as the blacksmiths hammered struck Pythagoras as harmonious, and (in one version of the story) he subsequently discovered that one of the anvils being struck was twice the size of the other. Regardless of whether the story is true, it illustrates Pythagoras’s understanding of the way mathematical proportions affect our perception and appreciation of the world.

To Pythagoreans, the pleasing sounds of a harmonious scale were however of secondary importance – a by-product of the fact that the ‘limiting things’, the mathematical rules, were applied appropriately. The main purpose of the Pythagoreans’ intellectual endeavour was to discover and contemplate these mathematical rules that they believed governed the world, so that they could lead well-ordered, harmonious lives. Such was the Pythagorean faith in numbers that they were prepared to believe in theoretically-derived things they had no physical evidence for. That has never been unusual, but as far as the Pythagoreans were concerned, not only could the visible universe be described by numbers, it was possible to infer facts about reality according to mathematical premises. For instance, Aristotle notes in the Metaphysics that to Pythagoreans, “the number 10 is thought to be perfect and to comprise the whole nature of numbers. They say that the bodies which move through the heavens are 10, but as the visible bodies are only 9, to meet this they invent a tenth, the ‘counter-Earth’.”

With hindsight, the Pythagoreans’ hypotheses don’t look very sophisticated, but the idea that there are mathematical patterns in nature that can tell us things we don’t already know is now well established. A good example is the discovery of the planet Neptune. Astronomers had noticed that Uranus wasn’t behaving quite as Newton’s law of universal gravitation predicted it should. Such was the stature of Newton that it was assumed there must be an unseen source of gravitational disturbance. The maths was done, a telescope was pointed at the place the source of gravity was calculated to be, and there was Neptune. Today, analogous discrepancies in the rotation of galaxies predicted by General Relativity imply either that there is another source of gravity that we can’t see – ‘dark matter’ – or that this time, the underlying mathematical model needs an upgrade. Both options are being explored.

Presocratic graphic © Rian Hughes 2014


The fact is that even with the particle accelerators and space telescopes we now have at our disposal, we can never be sure that some even more sophisticated hardware won’t tell a different story by revealing new evidence to us. So we can never be certain that the mathematical models we use to describe the behaviour we are familiar with will adequately explain everything we see in the future. We don’t ‘know’ reality with any certainty. This was recognised millenia ago by the Eleatic School, which found its voice in Parmenides (early 5th C. BC).

What was unusual about the Eleatic school is that it ignored the evidence. Instead, they sought to understand the universe by starting with what one can know through reason, and create a coherent story out of that. The lesson wasn’t lost on Euclid, and it was Descartes’ reapplication of this principle that’s usually credited with kick-starting modern philosophy.

All that remains of Parmenides’ work are bits and pieces of a poem he wrote that others have quoted. Called On Nature, it tells how a goddess promised to teach him about reality. The goddess says: “It is necessary for you to learn all things, both the abiding essence of persuasive truth, and men’s opinions, in which rests no true belief.” The opinions of Anaximander or Pythagoras can possibly give us ‘true belief’ about the world, but we can never be sure about their conclusions. Is there anything that we can know with certainty? Parmenides’ innovation was to strip away ‘men’s opinions’ about the world and test what remains. His ‘persuasive truth’ was that regardless of what we might see or calculate, something exists: as he said: “Being is.” Whatever we might think about reality, it is self-refuting to argue that nothing exists. The challenge then is to examine the concept of ‘being’, and see what we can discover from it.

As with the conclusions of Pythagoras, Parmenides’ conclusions aren’t so very compelling with hindsight:

“[Being] is universal, unique, immovable and complete;
Neither was it ever nor will it be, since it now is, all together,
One, continuous. For what birth would you seek of it?
From what and how did it grow?
I will not allow you to say or think that it came from nothing;
For it cannot be said, nor even perceived by the intellect
That not-being exists. And what would have stirred it into action
Later rather than earlier to arise from nothing?
So it must be absolutely or not at all.”

What makes Parmenides’ treatment so strange to us is that he appears to have had no concept of ‘being’ as anything other than material, in the way that the elements or the apeiron were supposed to be. To Parmenides, ‘being’ is some sort of ‘stuff’. This led him to some very bizarre conclusions.

A key point in his argument is that there can be no such thing as ‘not-being’; that the very idea of ‘not-being being’ is contradictory. Given the materialistic sense that Parmenides has of ‘being’, this means there is no such thing as empty space. As a result, change is impossible, because for any change to happen one bit of being would have to move into an unoccupied space, that is, somewhere there is ‘not-being’, but this is impossible, as there exists no ‘not-being’. Accordingly, ‘being’ is unified (‘one’), flawless, infinite, and eternal; hence reality is very different to most men’s opinions, and certainly to their experiences.

It’s not entirely clear what Parmenides thought the relationship between ‘being’ and the world we experience is supposed to be, but since ‘being’ definitely exists, he argued that it is more real than the world of appearances we think we inhabit.

Unsurprisingly, not everyone was convinced by his argument, at least not as he presented it.


Plato wrote a dialogue named after and in honour of Parmenides. It’s supposed to be an account of the meeting of the young Socrates with Parmenides and his disciple Zeno (this is Zeno of Elea, famous for his paradoxes, not the later Zeno of Citium, the founder of Stoicism). Parmenides is widely reckoned to be Plato’s most difficult work, and is one of few occasions when he allowed anybody to outshine Socrates, the dominant character in most of his books.

It is believed that Zeno (490-430 BC) formulated over forty of his famous paradoxes, not so much to show that Parmenides was right to claim that everything is one, as to show that everyone who believed that there are many different things was wrong. As Socrates says to Parmenides in the dialogue, “You affirm unity, he denies plurality. And so you deceive the world into believing that you are saying different things, when really you are saying much the same.”

Only a few of Zeno’s Paradoxes have come down to us, but they all aim to show essentially the same thing: that it is impossible to divide ‘being’ (or time and space as we are more inclined to think these days) up indefinitely. For example, the ‘Race-Course’ Paradox revolves around the idea that in order to finish the course, a runner must first reach half way; but to reach that point, they first must get halfway there; and halfway to that point also; and so on – one could keep halving distances to an infinite fineness, which would take forever; and so the runner would never reach the finishing line.

That a runner has to pass the halfway point before they reach the finishing line is obvious in a race of any appreciable distance; but what if the race-course were only a fraction of a millimetre long? Or suppose the runner were in a film, where the action takes place at 24 frames a second. If the film is slowed down, it becomes clear that the apparently smooth running motion is a series of images that jerk from one position to the next. Zeno’s argument would be that, in order to show completely smooth action, there would need to be a frame for every single change, no matter how tiny. This would require an infinite number of frames; however, if the film were infinitely long, it would take forever to show even the smallest change. So either Parmenides was right, and contrary to illusory appearances, the universe is one indivisible being in which nothing actually happens; or space and time cannot be chopped up indefinitely, and reality leaps from one very small step to the next.

The question of whether ‘being’ can appear from not-being is still unresolved. However, questions such as Parmenides and Zeno were asking don’t make any difference to what you see, or how you measure it: Anaximander and Pythagoras can get along perfectly well without them. In modern terms, the empirical data is what it is, and the maths either works on it or it doesn’t. To this extent, science doesn’t need philosophy. The point was famously made by Isaac Newton writing hypotheses non fingo – “I do not formulate hypotheses” [see PN 88]. More recently, the Copenhagen Interpretation of quantum mechanics has been caricatured as ‘shut up and calculate’. The point here is that it doesn’t matter what you think is responsible for quantum weirdness, the maths works, so get on with doing it.

As Thales’ followers discovered, different stories can account for the same facts. In the intervening centuries, there have been any number of theories about what it’s all about. Some are demonstrably untrue – the Earth isn’t the centre of the Solar System – but others are harder to dispel. One response is to accept that there are things that science alone simply cannot tell us, and if we wish to make sense of all the phenomena we experience, we have no option but to gather the most accurate data and try to create a narrative that fits with this data. Purely empirical science doesn’t need such stories – it doesn’t need philosophy. But we are storytellers, and what are facts without a context?

© Will Bouwman 2014

Will Bouwman is organiser of the Ealing School of Philosophy (along with Rian Hughes), and is a regular contributor to the Philosophy Now Forum (as uwot).

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