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On the Definitions, Postulates, and Common Notions of Euclid’s Elements

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Euclid’s Elements (“Stoikheîon”) is the foundational text of classical, axiomatic, and deductive geometry (“earth-measurement”). The Elements is composed of thirteen books, each filled with propositions that beautifully unfold a theory of number, shape, proportion, and measurability. The Elements was the essential geomtery textbook for nearly 2,000 years thanks to the preservation efforts of the Byzantines, Arabs, and English. Sadly, the Elements fell out of favor for students in the 20th century and very few, if any, students attempt to summit the extraordinary heights of Euclid in our modern era. The Elements has been cited by every major mathematical and scientific figure including Copernicus, Galileo, Kepler, Newton, Hobbes, Descartes, Spinoza, Whitehead, Russell, Einstein, and so on.

We know almost nothing about Euclid. The only two things we infer about his life, as referenced by ancient sources (primarily Diogenes Laërtius), is that he lived after Plato (died 347 BC) and before Archimedes (287 BC). He worked or perhaps founded a school in Alexandria, Egypt. Thomas L. Heath surmises that Euclid was originally schooled in Athens under the geometric pupils of Plato (in many ways we can see echoes of Plato found in Euclid’s Elements -recall the mathematical instruction of the boy in Plato’s Meno). Take note of a common mistake: Euclid, the author of the Elements, is distinct from Euclid of Megara who appears in Plato’s Theaetetus.

Euclid appears briefly in Archimedes’s On the Sphere and the Cylinder and also in Apollonius’s Conics. There were other “Elements” books circulating in antiquity by Hippocrates, Leo, and Theudius, but Euclid superseded them all and none of the other books have fully survived into the modern day.

Euclid begins his Elements not with a series of “problems” or “equations” like many math modern textbooks but rather with a list of foundational metaphysical claims: Definitions, Postulates, and Common Notions. The Definitions appear first and a general descent occurs. The Postulates follow the Definitions, and lastly we are offered a list of Common Notions. Things that are common occur last in order of importance.

Definitions
The Definitions are 23 statements (they were later numbered by 16th century editors after the advent of the printing press). The Definitions proceed from small elements to constructions of shapes. They are brief declarations that we can imagine as a response to Socratic questions, “what is…?” The Definitions do not permit a modern conception of the infinite. The first Definition is of a point -an irreducible and indivisible element (“A point is that which has no part”). A point gives us a sense place, perspective, and grounding. A point grants permission to draw a line (“breadthless length”) between two points. Where do we draw these elements? On a surface (“that which has length and breadth only”). A surface is presumed to be flat, unlike modern formulations of elliptical and non-linear geometry (i.e. Lobachevsky). This is evidenced by the final Definition of parallel lines (“straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction”). The assumption is that a) the straight could be produced indefinitely in a hypothetical situation and b) the straight lines are produced on an indefinitely flat plane/surface. This is distinct from modern conceptions of rounded or spherical surfaces upon which to conduct geometric demonstrations. We imagine an ancient geometer demonstrating Euclid’s Definitions in the dirt or on a chalk board.

As the Definitions descend we begin with foundational elements like points and lines (Definitions 1-7), then with Definitions pertaining to proportions between foundational elements like angles (Definitions 8-13), and then Definitions concerning shapes or figures (A figure is defined in Definition 14, Definitions 13-18 concern circles, and Definitions 19-23 concern rectilinear figures). It is worth noting that a plane surface does not appear first in the list of Definitions. Instead human activity (i.e. creating a point and a line) takes precedence over the plane surface. Perhaps Euclid’s Elements was not intended to be translated from the conceptual to the physical world (“earth-measurement”). Perhaps it is meant to be an exploration of the Platonic eidos.

Postulates
While the Definitions are firm and unquestionable, the Postulates are a series of “requests” or “demands” placed upon the reader. They are a demonstration of the authority or authorship of Euclid. The Postulates do not necessarily deductively follow from the Definitions, rather they are five rules offered by Euclid.

The five Postulates begin with three active requests: first that it is possible to “draw” a straight line between any two points; second that it possible to “produce” a finite straight line; and third that it is possible to “describe” a circle with any center and distance. The descent of the Postulates begins with three active possibilities: ‘drawing’ lines between points in practice and ‘producing’ lines as well as ‘describing’ circles in concept.

The fourth Postulate concerns the equality of all right angles (in other words, there are no modern notions of gradation), and the fifth and final Postulate concerns lines that pass through parallel lines at an angle which will meet if produced indefinitely, and that the intersecting lines will meet at interior angles that are less than two right angles.

Common Notions
The Common Notions are the most democratic of Euclid’s metaphysical claims. They are ideas everyone understands -common to everyone. They are visual, whereas the Definitions and Postulates are more conceptual and analytical. There are five Common Notions: the first four Common Notions concern equality, and the fifth defines the “whole” as greater than the parts (i.e. a triangle is not superseded by its lines or points -it is a whole triangle).

Unlike Aristotle who often begins his books with commonly held opinions and then proceeds into nuanced discussions of greater depth which ultimately yield a higher perspective, Euclid begins his Elements in Platonic fashion -answering Socratic questions as if posed to a geometer -“What is a point?” “What is a line?” “What is a plane surface?” “What is a figure?” Thus, Euclid’s book is as much an examination of the human mind as it is a lesson in mathematics.

For this reading I used the wonderful translation of Euclid’s Elements by Thomas L. Heath for Green Lion Press. Mr. Heath was a Cambridge scholar who translated Euclid directly from the original Greek in the early 20th century.

The Sicilian Expedition: Alcibiades and Nicias in Thucydides’s Peloponnesian War (Books VI-VII)

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Thucydides claims the Peloponnesian War is the greatest event or movement in human history, and the most important part of this great war takes place in Books VI-VII: The ill-fated Sicilian Expedition.

The Sicilian Expedition represents the turning point in the war. Thucydides begins to explain the expedition by offering a history of the origins of Sicily and its people. He continues by discussing the current zeitgeist in Athens. A rising and powerful love of Athens or a fervent patriotism arises among the Athenians. The old, middle-aged, and young citizens all see an easy occupation of Sicily that will yield great riches and power (i.e. the old and young, rich and poor are all united in support of the expedition as is necessary for an empire), while the skeptics are forced into silence for fear of being unpatriotic.

Thucydides offers two contrasting views on the Sicilian proposition: Nicias, the sober-minded Athenian general (or strategos) who is fervently opposed to interventionism. Nicias was the voice for moderation in Athens. Nicias had negotiated the aptly-named Peace of Nicias previously in 421 BC which paused the ongoing conflict between Athens and Sparta until the Athenian Sicilian Expedition 421 BC.

In contrast to Nicias’s moderation, Thucydides also shows us Alcibiades, the demagogic follower of Socrates and bombastic son of the old Athenian aristocracy, who successfully takes up the mantel of Pericles. Alcibiades rouses the passions of the Athenian public by claiming an either/or situation with regard to Sicily. The choice is between conquering or being conquered, though the idea that Athens is facing imminent conquest is absurd. Alcibiades is a proponent of aggressive expansionism and, in the end, he wins the day and leads the expedition to Sicily. Consider the way Thucydides describes the general mood of the Athenians regarding the invasion of Sicily:

“Everyone fell in love with the enterprise. The older men thought that they would either subdue the places against which they were to sail, or at all events, with so large a force, meet with no disaster; those in the prime of life felt a longing for foreign sights and spectacles, and had no doubt that they should come safe home again; while the idea of the common people and the soldiery was to earn wages at the moment, and make conquests that would supply a never-ending fund to pay for the future. With this enthusiasm of the majority, the few that did not like it feared to appear unpatriotic by holding up their hands against it, and so kept quiet” (6.24).

According to Thucydides, there is a kind of erotic love for conquest that grips the people of Athens, and the ‘tyranny of the majority’ as Madison would have called it, takes hold. However, this eroticism takes different forms depending upon age and station: the older men thought their army was so powerful it could not possibly be defeated, those in the prime of their lives were longing for adventure (new things, ‘foreign sights and spectacles’), and the common people and soldiery were hungry for riches and security. In war, each group sees their own deprivation as an opportunity: strength, adventure, and riches, respectively.

At any rate, as happens with the superstitions of crowds, on the eve of the Sicilian Expedition all the stone statues of Hermes, the “Hermae,” are mutilated throughout the city of Athens. And rumors surface about drunken parties in private homes where the Mysteries of profaned (for reference see Socrates in Plato’s Symposium). Immediately, Alcibiades is blamed and it bears a foreboding sign for the expedition, while the enemies of Alcibiades hope to elevate the rule of the People, rather than leaders like Pericles and Alcibiades. These leaders win the moment and Alcibiades is brought to trial but he flees in exile to Sparta -his allegiances now in question, Alcibiades defects to the enemy. Meanwhile, the Sicilian Expedition ends in disaster as the Athenian invasion fails to claim ground, and all the retreating Athenians are slaughtered in Syracuse.

Later, Thucydides makes note of the foremost cause of ruin for the Athenian army:

“Indeed the first and foremost cause of the ruin of the Athenian army was the capture of Plemmyrium [a harbor port near Syracuse where the Athenians retreated], even the entrance of the harbor being now no longer safe for carrying in provisions, as the Syracusan vessels were stationed there to prevent it, and nothing could be brought in without fighting; besides the general impression of dismay and discouragement produced upon the army” (7.24).

In response, Athens votes to send a massive force of reinforcements led by the general Demosthenes, not be confused with the great Athenian orator and speechwriter, but the Athenian armies become separated, decimated, enslaved, starved, and both Demosthenes and Nicias are executed. A few Athenian prisoners escape to deliver the dismal news back home in Athens.

Timeline of Events in the Peloponnesian War:

  • 6th-5th Centuries BC: The Peloponnesian League is created and led by Sparta over the surrounding Peloponnesus: Corinth, Elis, Tegea, and others. Also the Delian League was created under the leadership of Athens.

  • 435 BC: The city of Epidamnus, a colony of Corcyra located right at the entrance to the Ionic Gulf, undergoes an internal revolt and requests help from Corcyra which is denied so they request help from soft rival to Corcyra, Corinth. It causes a proxy war between Corinth and Corcyra, with Corcyra winning back its colony. In response Corinth begins building up a vast navy.

  • 433 BC: Both Corinth and Corcyra call upon Athens, a fellow member of the Delian League, for aid. After both making their cases, Athens votes with an eye toward war with the Peloponnesus by siding with Corcyra. However, when both sides do battle, Corinth wins the day so they send reinforcements and the escalation calls upon the Peloponnesian League to break the standing peace treaty.

  • 432 BC: Athens fortifies its new ally Corcyra against Corinthian forces at Potidaea, as well. The Siege of Potidaea brings an end to Sparta’s inaction, with many denouncing Athens. Athens sent a fleet to Potidaea after Sparta and allies encouraged a revolt on the island in response to Athenian support for Corcyra against Corinth. Sparta declares Athens to be the aggressor and declares war on Athens.

    The powerful orator Pericles rises in Athens who is vehemently opposed to any conciliation with Sparta, in contrast to Archidamus King of Sparta, who urges caution, tact, and discipline. Sparta peddles a rumor that Athens is cursed by the goddess (thus subtly implicating Pericles as accursed). Athens, under Pericles, rejects offers to allow the Hellenes to remain free.

  • 431 BC: War begins. Thebes attacks and defeats Plataea, with Athenian help for Plataea arriving too late. Sparta invades Attica. Athens sends a fleet to attack the Pelopponesus and draw troops off their country farms. Pericles delivers his famous “Funeral Oration Speech” in Winter 431 BC.

  • 430 BC: Again Sparta invades Athens and shortly thereafter a great plague falls upon the land “a pestilence of such extent and mortality was nowhere remembered.” It began perhaps in Egypt or Ethiopia and infected Athens through the Piraeus. A rumor spreads that Sparta poisons the water of Athens. The plague brings lawlessness and mass death.

    Pericles “The First Citizen” of Athens delivers a more tempered speech in Summer defending himself and wishing the Athenians had heeded all of his advice and not capitulated in any way to Sparta.

    Athens conquers Potidaea. Sparta attacks Plataea.

  • 428 BC: Sparta invades Athens again, Lesbos revolts from Athens. Mytilene turns to Sparta for help but Athens votes to spare Mytilene against the advice of Cleon a zealot and war hawk.

  • 425 BC: The Athenians outmaneuver the Spartans at Pylos under the generalship of Demosthenes (not be confused with the great Athenian orator).

  • 422 BC: War hawks Cleon (Athens) and Brasidas (Sparta) battle to the death at the Athenian colony of Amphipolis.

  • 421 BC: After the deaths of Cleon and Brasidas, the moderate Athenian leader Nicias is able to negotiate a peace – the Peace of Nicias which lasted six years.

  • 415 BC: The ill-fated Sicilian Expedition is undertaken initially by Alcibiades who takes up the expansionist agenda from Pericles and Cleon, but the expedition ends in 413 BC in spectacular failure. Both leaders Nicias and Demosthenes are executed in the surrender at Syracuse.

  • 413 BC: In order to escape punishment in Athens, Alcibiades defects to Sparta and advises them on how to attack Athens. From here, Athens was beset by revolts, both internal and external by allies, as well as a troubling alliance between Persia and Sparta.

  • 407 BC: Alcibiades returns to Athens only to be exiled once again over questions of his loyalty.

  • 404 BC: Athens finally surrenders to Spartan general Lysander who defeated the Athenian navy and claimed the Dardanelles, a chief source of Athenian grain. Amidst death and starvation Athens surrenders. Sparta welcomes Athens into its network of allies but destroys Athens’s wall, navy, and riches.

For this reading I used the impeccable Landmark edition of Thucydides’s History of the Peloponnesian War by businessman-turned classical scholar Robert B. Strassler.

Anglo-Saxon England, Part II

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With the arrival of the Anglo-Saxons a panoply of changes took effect across Britain. Old English replaced Latin as the lingua franca, the island of Britannia was renamed Aengla Land after the Angles, and perhaps most significantly, there was a political shift. The Saxons brought with them the idea of kingship by consent. That is, the Saxons selected ‘kings’ from amongst themselves, and the kings ruled with limited authority. It was not yet a monarchy familiar to modern minds but it was rulership by the consent of the governed and it was entirely foreign to a culture that carried the fresh memory of the decadent Roman Empire. The legacy of self-government from the Anglo-Saxons is still with us today.

This Anglo-Saxon epoch was captured wonderfully in the epic folk-poem, Beowulf. The hero, Beowulf, is an elected leader who becomes king, ruling for ‘fifty winters.’ Upon his death, a great pyre is built and valuables are buried in an Anglo-Saxon rites ceremony. Anthropologists of Anglo-Saxon culture were delighted when in 1939 the ceremonial practices described in Beowulf were triumphantly confirmed at Sutton Hoo, Suffolk where vast riches, likely once the possessions of a great king, were unearthed along with an entirely buried Dark Age Anglo-Saxon ship. Perhaps this king was Redwald of East Anglia. His iron helmet indicates royalty and the vast riches unearthed matched time period -including Merovingian coins dating to AD 625 (the most successful Anglo-Saxon kings built alliances with the powerful Frankish kingdom in contemporary France).

A partially reconstructed helmet found at Sutton Hoo. It was buried in AD 625 and is believed to have belonged to King Redwald of East Anglia.

Over time, Anglo-Saxon England was divided into seven chief kingdoms, sometimes referred to as the “heptarchy.” The regional names have continued to this day, like Northumbria (“north of the Humber River”), Essex (“East Saxony”), Wessex (“West Saxony”), and Sussex (“South Saxony”). Each king jockeyed for power to rule over the others as bretwalda (“Britan-Ruler”). Names like Redwald of East Anglia (mentioned above) and Offa of Mercia loom large over this period (he called himself Rex Anglorum, “King of the English”). Some consider Redwald to be the occupant of the massive ship excavated at Sutton Hoo. During his lifetime, Offa led some remarkable advances in Roman-styled coinage throughout his kingdom, and across the Channel his rule coincided with Pepin the Short’s Carolingian Revolution of the Frankish kingdom (Pepin usurped the throne in AD 751, 49 years later his son Charlemagne was crowned Holy Roman Emperor on Christmas morning AD 800).

With the rise of the Frankish kingdom and the decline of Offa’s family, the kingdom of Wessex arose as the dominant power in Anglo-Saxon England. In AD 827 Egbert, a former exile at Charlemagne’s court during the Offa years, returned to England and claimed the throne of Wessex. He dominated many of the surrounding kingdoms, calling himself the new Rex Anglorum. He was followed by his son Aethelwulf in AD 839, a devoutly pious man and father of five sons, including Alfred the Great (Aethelwulf took young Alfred on a trip to Rome to see the Pope -a trip that would have remarkably lasting consequences). Each of Aethelwulf’s sons then ruled in turn: Aethelbald (Aethelwulf’s second son) took the throne of Wessex in AD 858. He was in some sort of conflict with his father while Aethelwulf traveled with Alfred abroad and after his father’s death, Aethelbald later married his stepmother, causing condemnation from the church. At the time, the church in Rome had a somewhat uneasy relationship with the British Isle.

All across the isle was a religious schism. The ashes of Rome had left a Christian heritage, while the Anglo-Saxons had remained largely pagan, with many leaders claiming to descend from Woden, himself. In the 5th century, a Roman Briton St. Patrick was living somewhere on the British Isles. He was captured and enslaved by a band of marauding Irish pirates. He was forced into servitude, tending animals in Ireland but he escaped after six years only to return to the Emerald Isle and spread the faith across Ireland and Scotland, with the help of his follower, St. Columba who founded the important Abbey at Iona (a small island off the coast of western Scotland). Thus, the form of Christianity that took hold among the Celts was monastic, ascetic, and characterized by vast abbeys and monasteries, as well as sacred and ornately decorated books, like the famous Book of Kells (9th century). In parts of England, Ireland, Scotland, and Wales Christianity grew entirely apart from mainland papal authority. One unique example of the unusual character of early British Christianity is the cult of St. Alban, in honor of the martyrdom of Alban at the Romano-British city of Verumalium, today known as St. Albans.

However, this unique Christian heritage was not always entirely popular with mainstream Roman Christianity. For example, a well-educated, ascetic monk living somewhere on the British Isles named Pelagius (354-418) taught a controversial doctrine that was highly antithetical to the apostolic and Augustinian tradition, namely that humans were not fallen as a result of “original sin” and instead could achieve goodness and grace through their own free will (i.e. without divine intervention). This “Pelagian Heresy” -as it came to be known- needed to be stamped out by the church (Pope Innocent I condemned Pelagius at Augustine’s behest).

In an effort to spread the ‘true faith’ Pope Gregory “The Great” sent a cohort of bishops led by a man named Augustine (not to be confused with St. Augustine of Hippo.) Today he is known as “Augustine of Canterbury” because his cohort reluctantly landed at Kent after expressing their wish not to continue with the mission -the British isle seemed far too dangerous a place, so the group initially landed at Gaul requesting permission to abandon the mission from the Pope, but their request was denied. With no other options, they set sail across the Channel to Kent.

The Southeastern region of Kent had recently been conquered by the dominant Anglo-Saxon kingdom of Wessex and King Aethelbald’s brother was put in charge. When Augustine and his group landed, they were met by the pagan King Aethelbert (brother of Aethelbald) who had married the Christian princess Bertha of the Franks. A pagan king and a Christian queen. Bertha brought to Kent her Frankish, Christian bishop, Luidhard, and King Aethelbert gave Bertha a little church originally from the Romano-British era called St. Martin’s to worship (she named it after Martin of Tours, the patron saint of the Merovingian family). This church is now the oldest still active church in England today. It was located just outside the capital city of Kent at Canterbury. On the ruins of this ancient church, Augustine founded the British Christian tradition (he later died before completing the construction of his prized cathedral at Canterbury which was first founded in AD 597 and then entirely rebuilt between 1070-1077 by the Normans). Initially skeptical of the newcomers, Aethelbert had Augustine confined to the island of Thanet. He consulted his advisors about the ‘magical powers’ of this new preacher, but the allure of a strengthened relationship with the Franks was too promising a prospect, thus Aethelbert allowed Augustine entry and free-reign to preach the gospel in Kent. Augustine first arrived in Canterbury clad in robes, singing the litany in Latin, while also carrying a large icon of Jesus -a scene which must have seemed magical to the Anglo-Saxons. Augustine’s preaching caught hold among the populace and he baptized thousands, including King Aethelbert, himself, who eventually converted to Christianity -much to Queen Bertha’s delight. After his conversion, Aethelbert issued a new series of laws much like the Byzantine Justinian Code.

In the coming years, the authority of the church in England was established in a series of letters between Pope Gregory and St. Augustine of Canterbury. The Pope was to be the supreme authority, but England would be self-governing for all internal matters by two archbishops -one in the north in York and the other in the south in Canterbury. This dual leadership was novel but would cause future political strife -Augustine declared himself the superior authority as the first archbishop of Canterbury. Augustine died in AD 605, and Aethelbert died nearly a decade later. Both were buried at the splendid abbey at Canterbury which was later named in the honor of “St. Augustine” (not to be confused with Canterbury Cathedral where Chaucer’s famous pilgrims ventured). In the end, church and state both found their final resting place alongside one another in the cemetery at St. Augustine’s: Augustine and his followers were buried on one side of the church, and Aethelbert, Bertha, and their successors on the other.

In the north, in AD 664, the King of Northrumbria issued a proclamation regarding the church. He made the heavy decision to side with Catholic Rome, rather than the Celtic monks. However, tensions would remain in place between north and south, Celtic and Catholic for years to come.

After the death of Aethelbert, the throne of the House of Wessex passed to Aethelred, the fourth son of Aethelwulf. His reign oversaw the violent arrival of the Vikings and their takeover of the surrounding Anglo-Saxon kingdoms of Kent, Northumbria, and Mercia. However, Wessex had the advantage over the Vikings with minimal rivers with which the Danes could use to sail inland and pillage the many English commercial ports (including an occupation of London). Through the year AD 871, Aethelred, ever the pious Christian, waged a divinely ordained war alongside his younger brother against the invaders, including an impressive victory at Ashdown, but Aethelred caught a sickness late in the year AD 871 and he died after ruling for six years. Following Aethelred’s reign came the most consequential Anglo-Saxon king who would ever take the throne: Alfred “The Great,” the fifth son of Aethelwulf. Alfred assumed the kingship of Wessex while still in his early twenties.

For this reading I used Winston Churchill’s essential History of English Speaking Peoples, David Starkey’s Crown and Country, Peter Ackroyd’s Foundation: The History of England From Its Earliest Beginnings To The Tudors, and the writings of Gildas, the Venerable Bede, and Asser’s Life of Alfred the Great.

Perception in Aristotle’s On The Soul

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Aristotle’s On The Soul (or “De Anima” as the Latins transcribed it) addresses the question of what it means to be alive. It explores the self-organization of all natural and living things, from the perspective and perception of an observer. The text is a qualified addendum to the Physics, and its corollary is a short treatise called On Memory and Recollection, part of the eight short works known as Parva Naturalia, brief writings pertaining to nature.

At first glance to the unsophisticated mind, we may look around the world and recognize a part of ourselves in nature. Living things are born, grow, reproduce, and die. How is it that our perception and our senses allow us to understand these things, by nature, things like the difference between a human being and a dog? Even if we see a human being with no arms, legs, or hair, we still have the capacity to understand that the creature we are beholding is still a human being, and not a separate species. This is the central question of eidos, which Socrates is always questioning in the Platonic dialogues. Observing nature, and the nature of living things, reminds us that we have souls. Or, perhaps, that we are souls. But the ontological questions are best addressed in Aristotle’s Metaphysics.

The word Aristotle uses for soul is “psuche” or “psyche.” Much can be said about this word, but in essence it refers to a creature observing nature with intellect, and observing its changes and sameness while also being-at-work and staying-itself and, at the same time, still being open to potentia, or to becoming (see the anecdote in the preceding paragraph regarding observing nature). Nature, to Aristotle, is living, organic, and it is also ordered. It has a certain logos to it. In essence, Aristotle seeks to examine the potency that perceives the world (i.e. the perceiver perceiving his own perception and its consequences).

In contrast to Descartes, Aristotle suggests (in Book I) that it would be unwise to merely trust things that are immediately “clear and distinct” to our senses, because the senses are deceptive. Instead, we should proceed from what is familiar. The moderns, following from Descartes, are doubters that knowledge can ever be attained because proceeding from common opinions is suspect to the modern mind. Most notably in his Meditations on First Philosophy, Descartes sits alone in a room and he fabricates an imagined world for himself, that is perfectly knowable, and that somehow corresponds to the world we live in, as well. This is attained through instruments and mathematical precision, not through the facticity of human awareness. Thus, geometry comes to prominence in Descartes’s writings. Nevertheless, the central epistemological problem persists in Descartes –what is the thinking and perceiving thing that is Descartes? He seems to suggest his own perceiving mind and God are the only two things he can be sure of. The human element of perception is minimized with the moderns via a forceful negation or naysaying of all things susceptible to doubt. They seek to find the superior, more democratically approved theory, in order to posit a world picture (excluding souls), not to explore the world as a soul perceiving other souls and natural phenomena.

In contrast, Aristotle suggests that self-discovery comes not from solitary self-examination of the senses, but rather from experience and observations of living things. At least Aristotle acknowledges the possibility of human experience. While Platonic dialogues frequently (and exoterically) ask the question ti esti or “what is it” in attaching universal names to particular things, but Aristotle is interested in how the world sorts itself out. Living things are being, and insofar as they are living, they are beings at work. And Aristotle is also concerned with what keeps these beings in order amidst nature at all. Thus, he looks for beings who are actively-at-work-staying-themselves.

Plato, in his Timaeus, offers a pleasurable myth that seriously addresses deep questions in a playful manner, rather than a rational examination of the cosmos. Elsewhere in the Phaedrus, Socrates tells Phaedrus that he much prefers myth-making and story-telling to sober and rational criticisms, because self-knowledge is better attained through myth-making.

In Aristotle’s On The Soul, he proceeds from commonly held assumptions, upward toward a glimpse at truth, or at least a deeper understanding of the nature of things. He begins with the commonly held belief that knowledge is “something beautiful and honored” (Book I, 402a), and begins with an inquiry into the soul, since the soul “is in some way the governing source of all things.” He runs through various impasses when defining the thinghood of the soul -Democritus, Pythagoras, and even Plato in his Timaeus. All these thinkers define soul by three things: motion, sense perception, and bodiliness (405b 12).

In Book II, we get Aristotle’s definition of the soul (summarized here by Joe Sachs): “The body (soma) is material for the soul (psyche or psuche) which is its invisible look (eidos) because the body has being as a potency for the being-at-work-staying-itself. The body’s thinghood that keeps it being a body at all by means of speech, is its soul. The soul constantly maintains the body as a kind of living thing that remains in its self-same category, and the soul is nutritive, as it transforms material from the natural world into perceptible and necessary ingredients to sustain the soul.” Book II, explores the varying powers of the soul, such as the nutritive, reproductive, perceptive potential and so on. The final section of On The Soul is Book III which explores several of the most important ways the soul thinks. Only now, do we see Aristotle using “clarity” and “distinctness” to explore what comes to light with greater certainty.

The past two thousand years have brought considerable criticisms of Aristotle’s notion of “soul,” though most have originated in the last two hundred years in the modern era. Typical criticisms have attempted to push Aristotle’s definition into one of two camps: pure materialism, or else Aristotle is some manner of neo-Christian “ghost in the machine” dualist (i.e. a soul-body distinction is made, which, of course, is never explicated in Aristotle’s On The Soul. He does provide one artless metaphor wherein the soul is like the captain of a ship, but this should not be taken too heavily).

For these readings I used the magnificent Joe Sachs translation of Aristotles On The Soul.