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A Resource Guide for Philosophy Students

Created by Jennifer Leslie Torgerson, MA

Visiting Associate Professor of Philosophy, CCBC

This page last modified:  September 6, 2012

© copyright, 1997 - 2012 ~ Jennifer Leslie Torgerson


School of Athens


The Pre-Socratics

The Pre-Socratics: and the Problem of the One and the Many




F. M. Cornford.  Plato and Parmenides.  (Indianapolis, IN:  Bobbs-Merrill Company, no date).


__________, Before and After Socrates.  (Cambridge, UK:  Cambridge University Press, 1999 [1932]).


__________, From Religion to Philosophy:  A Study in the Origins of Western Speculation.  (Mineola, NY:  Dover Books, 2004 [1912]).


Frederick Copleston, S.J., A History of Philosophy:  Book One.  (New York, NY:  Doubleday, 1985 [1944]). 

Walter Kaufmann, Philosophical Classics Volume I:  Thales to Ockham, 2nd Edition.  (Englewood Cliffs, NJ:  Prentice Hall, 1968 [1961]). The majority of the primary source quotes were taken from this text.

A. A. Long, Editor; The Cambridge Companion to Early Greek Philosophy.  (Cambridge, UK:  Cambridge University Press, 1999).

Merrill Ring, Beginning with the Pre-Socratics.  (Mountain View, CA:  Mayfield Publishing, 1987).




The Pre-Socratics


c. date BCE


basic stuff(s)










































All is One






All is One






earth, air, fire water +

2 forces (love and strife) 

















Elea or Miletus?




(N/A means not answerable in this form. For example, Pythagoras was a dualist?)

There are three groups of Pre-Socratics:

(1) The Ionians, (2) The Italians, and (3) The Pluralists.

Other divisions, or groups can be made such as:

The Milesians are those Ionian Pre-Socratics from Miletus.

(1) The Ionians: Thales, Anaximander, Anaximenes, Xenophanes, and Heraclitus.

(2) The Italians: Pythagoras, Parmenides, and Zeno.

(3) The Pluralists: Empedocles, Anaxgoras, Democritus, and Leucippus.

Ancient Greek concept of the cycling of the elements:

Elements were thought to change from one to another, earth to water to air, but it is unclear how fire comes from air (since fire is mystical and air invisible) and it is unclear how fire comes from the earth (also mysterious).

Some key terms to know:

(1) substance: (or essence), what a thing is opposed to the way it appears to be. (Lockian definition or Modern definition)

(2) monist: one who believes that there is one kind of basic stuff or substance to the universe, from which everything is composed.

(3) pluralist: one who believes that there is more than one basic stuff, or many substances in the universe, from which everything is composed.

(4) apeiron: indefinite, or boundless (infinite).

(5) ousia: ‘primary substance’ or being in the Classical sense; the character, or a thing’s nature; it is what it is, in and of itself: meaning it is what it is and its’ nature is independent of any other nature (can be explained only in terms of itself).

(6) arche:  stuff (material cause or basic stuff).

Some Fragments (if possible):


Anaximander: ONLY FRAGMENT: “Existing things perish into those things out of which they have come to be; for they pay reparation to each other for their injustice according to the ordinance of time.”

Anaximenes: ONLY ONE FRAGMENT remains- one line of a text which is now lost.  The fragment is:  "As our soul, which is air, holds us together, so do breathe and air encompass the whole world."

Heraclitus: MANY MORE FRAGMENTS REMAIN- 120+: Here are a few: #55: “The things of which there is seeing and hearing and perception, these I prefer.” #50: “Listening not to me but to the Logos it is wise to agree that all things are one.” #7: “If all things turned to smoke, the nose would be the discriminating organ.” #10: “I sought myself.” #118: “A dry soul is wisest and best.” #93: “The lord whose oracle is in Delphi neither speaks out nor conceals, but gives a sign.” #41: “Wisdom is One, knowing the thought by which it steers all things through all things.” and the most quoted: #12: Upon those who step into the same river, different and again different waters flow.” #91: “It is not possible to step into the same river twice.” #60: “The path up and the path down are one in the same.” #119: “Character is a man’s fate.” #49: “One man to me is ten thousand if he is best.” #110: “It is not good for men to obtain all they wish.” #112: “Sane thinking is the greatest virtue, and wisdom is speaking the truth and acting according to nature, paying heed.” #42: “Homer deserves to be thrown out of the contests and whipped, and Archilochus too.” #62: “Immortals are mortals, mortals immortal, each other’s death, dying each other’s life.”

Pythagoras: ALL OF HIS IDEAS COME FROM UNDERSTANDING HIS BROTHERHOOD- and it is hard to separate his ideas from those of others. The most important Pythagorean contribution to Philosophy is the discovery of Form.

Parmenides and Zeno: BOTH WROTE AN ENTIRE BOOK- we have Parmenides’ poem, but must rely upon quote for our knowledge of Zeno. Parmenides wrote a poem entitled “The Way of Seeming and the Way of Truth”. Zeno, Parmenides’ student, logically argued against pluralism to defend their shared view of monism. Parmenides: “Come, I will tell you; hear my word and carry it away. These are the only ways of inquiry that can be thought of [literally: that exist for thinking] one way, that it is and cannot not be, is the path of persuasion, for it attends upon truth, the other, that is-not and needs must not-be, that, I will tell you, is a path all together unthinkable. For you could not know that which is-not (that is impossible), nor utter it.” (Section, or fragment #2)  Zeno’s arguments come to us via Aristotle (in his Metaphysics) and Plato (in his dialogue entitled Parmenides). Simplicius quoted a great deal from Zeno’s book as well. Zeno employs the reductio ad absurdum (to reduce to absurdity) form of argumentation to attack pluralism.

Xenophanes: 35+ FRAGMENTS REMAIN- here are a few: #11: “Homer and Hesiod have attributed to the gods everything that, among men, is shameful and reproachable: stealing, adultery, mutual deceit.” #32 (about a rainbow) “She whom men call Iris, she too is a cloud, purple, red, and yellow to sight.” #14: “Mortals think that the gods are born and have clothes and speech and bodies like their own.” #34: “No man knows or ever will know the truth about the gods and about everything of which I speak. For even if someone were, by chance, to speak the whole truth, he would not know it- in all things there is opinion.” #18: “Not from the beginning have the gods revealed all things to mortals, but by long seeking men find what is better.” #16: “The Ethiopians consider the gods flat-nosed and black; the Thracians blue-eyed and red-haired.” #27: “Everything comes from earth and returns to earth in the end.”

Empedocles: 136+ FRAGMENTS REMAIN- here are a few: #8: “I shall tell you another thing: there is no creation of substance in any one of mortal existences, nor any end in execrable death, but only mixing and exchange of what has been mixed; and the name “substance” (physis, “nature”) is applied to them by mankind.” #27: “(The sphere under the dominion of love); Therein are articulated neither the swift limbs of the sun, nor the shaggy might of earth, nor the sea: so firmly is it (the whole) fixed in a close-set secrecy, a rounded sphere enjoying a circular solitude.” #25: “For what is right can well be uttered even twice.” #136: “Will ye not cease from this harsh sounding slaughter? Do you not see that you are devouring one another in the thoughtlessness of your minds?”

Anaxagoras: WROTE ONE BOOK- still on sale in Athens in the 1st century CE for one drachma- but only 21+ fragments of it survive today- here are a few: #7: “So that number of the things separated off cannot be known either in thought or in fact.” #8: The things in one Cosmos are not separated off from another with an axe, neither Hot from Cold, nor the Cold from the Hot.” #9: “Thus these things circulate and are separated off by force and speed. Their speed is not the speed of any of the Things now existing among mankind, but altogether many times as fast.” #10: “How can hair come from not-hair, and flesh from not-flesh?” #11: “In everything there is a portion of everything except in Mind; and some things contain Mind also.” #17: “The Greeks have an incorrect belief on Coming into Being and Passing Away. No Thing comes into being or passes away, but is mixed together or separated from existing Things. Thus they would be correct if they called coming in to being “mixing” and passing away “separation-off”.” #18: “It is the sun that endows the moon with its brilliance.” #21: “Through the weakness of the sense perceptions, we cannot judge the truth.”

Democritus (and Leucippus): ALL LEUCIPPUS’ WRITINGS ARE LOST (or some of Democritus’ writings may be actually Leucippus’ own words) BUT THERE ARE 294+ FRAGMENTS FROM DEMOCRITUS SURVIVING, SOME FROM HIS TEXT CALLED “ON THE FORMS” He also wrote about Ethics and a text he may have called Gnomae- which we have complete- here are a few fragments: #7: “We know nothing about anything really, but opinion is for all individuals an inflowing.” #8: “It will be obvious that it is impossible to understand how in reality each thing is.” #9: “Sweet exists by convention, bitter by convention, color by convention; atoms and void (alone) exist in reality... We know nothing accurately in reality, but (only) as it changes according to the bodily condition, and the constitution of those things that flow upon it.” #10: “It has often been demonstrated that we do not grasp how each thing is or is not.” #39: “One must either be good, or imitate a good man.” #40: “Men find happiness neither by means of the body nor through possessions, but through uprightness and wisdom.” #41: “Refrain from crimes not from fear but through duty.” #42: “It is a great thing, when one is in adversity, to think of duty.” #44: “One should tell the truth, not speak at length.” #47: “Well-ordered behavior consists in obedience to the law, the ruler, and the man wiser (than oneself).” #49: “It is hard to be governed by one’s inferior.” #74: “Accept no pleasure unless it is beneficial.” #75: “Virtuous love consists in decorous desire for the beautiful.” #105: “Physical beauty is (merely) animal unless intelligence be present.” #110: “A woman must not practice argument: this is dreadful.” #111: “To be ruled by a woman is the ultimate outrage for a man.” #115: “It is better to be praised by another than by oneself. #208: “The self-control of the father is the greatest example for the children.” #210: “A rich table is provided by luck, but a sufficient one by wisdom.” #200: “People are fools who live without enjoyment of life.” #226: “Freedom of speech is the sign of freedom; but the danger lies in discerning the right occasion #236: “It is hard to fight desire; but to control it is the sign of a reasonable man.”



Empedocles’ Cosmic cycle from love- to the richest possible world- to strife- to the richest possible world- .... (ad infinitum)

Elements (earth, air, fire, water) under the force of strife/hate are separated.

Elements (earth, air, fire, water) under the force of love are mixed (one).

Empedocles' Cosmic cycle

Zeno: Arguments against plurality and motion

(1) The stadium- There are three sets of cars on three tracks- set A is stationary, set B and set C are moving in opposite directions. The sets of cars must be equal in number and equal in size, say 10 units long. At the beginning, prior to any movement, the trains are arranged as follows:

figure one













and in one minute the train cars look like the following:

figure two







Zeno asked, essentially, “what distance Train B has moved in that minute?” Car B1 has moved precisely opposite car A1, and each car is 10 units long, B has covered 10 units in that minute. But notice that B1 has also completely passed car C1 and come precisely opposite car C2. As each of those is just 10 units long, B has covered 20 units in the same minute. SO B has moved 10 units and 20 units during the same minute. In general, a moving thing will cover both n and 2n units of distance at one and the same time. Yet this is contradictory. Hence the concept of motion is reduced to absurdity (reductio ad absurdum).

(2) The arrow: Consider an arrow in flight. As is true of all objects, at every moment it must be in the place where it is and in no other. Yet a moving arrow, as with all objects in motion, in order to be moving, must be going from place to place. So at every moment it must be in a place and going from place to place at the same time. This is a contradictory state of affairs, and is absurd.

(3) Achilles example: You cannot transverse an infinity of points. Motion is impossible



Pythagorean Diagrams

Pythagoras Charts Clockwise from left to right-

Chart 1: Natural Number Series (1 is a point [no dimension], 2 points are a line [1 dimension], 3 points are a triangle [2 dimensions], 4 points are a pyramid [3 dimensions]);

Chart 2: Even Number Series 2-4-6-8-10 (rectangle);

Chart 3: Odd Number Series 1-3-5-7 (square);

Chart 4: Natural Number Series 1, 2, 3, 4 (triangle). The dots also represent an octave (ratio 2:1), a fifth (3:2), and a seventh (4:3); and if you add those together you get part of the odd number series: 3, 5, and 7.



Pyramidal Numbers


Pyramidal numbers have the same length on each side.

Examples of Pyramidal numbers:  3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210……

Corresponding side lengths:  2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20..

Sequence mathematically of Pyramidal numbers:  (3/2) = x1R1; (6/3) = x2; (10/4) = x2R2; (15/5) = x3; (21/6) = x3R3; (28/7) = x4; (36/8) = x4R4; (45/9) = x5; (55/10) = x5R5; (66/11) = x6; (78/12) = x6R6; (91/13) = x7; (105/14) = x7R7; (120/15) = x8; (136/16) = x8R8; (153/17) = x9; (171/18) = x9R9; (190/19) = x10; (210/20) = x10R10.....




Here is a Pythagorean Theorem Calculator:

The Pythagorean Theorem
Geometry's most elegant theorem- a(squared) + b(squared) = c(squared)




Timeline of important events in ancient Greek history

c. 1500 BCE

Mionian culture (Crete).

c. 1250 BCE

Trojan war may have occurred.

c. 1000 BCE

Homer may have lived.

1000-600 BCE

Dark Ages of Greece.

c. 600 BCE

Homer's epics written down.

585 BCE

Thales predicts eclipse, battle of the river Halys.

c. 550 BCE

Anaximander, Anaximenes, Pythagoras, Zenophanes wrote.

c. 510 BCE

Parmenides is born.

508 BCE

Athenian Constitution written by Cleisthenes.

c. 500 BCE

Pythagoras died, Heraclitus and Anaxagoras wrote.

499 BCE

Persian War begins.

c. 470 BCE

Birth of Socrates.

c. 460 BCE

Democritus wrote.

c. 450 BCE

Empedocles wrote.

449 BCE

End of the Persian War.

440 BCE

Melissus wrote.

432 BCE

 Anaxagoras, a philosopher from Clazomenae, is tried for impiety. Anaxagoras was a friend of Pericles, and was the first philosopher to be put on trial for impiety. The trumped up charge was based on the fact that Anaxagoras taught that the sun is a red hot stone and the moon is made of earth. (Apology, 26 d). Peloponnesian War begins.

427 or 428 BCE

Plato is born.

423 BCE

Aristophanes' The Clouds, a play which portrays Socrates as a buffoon, was first performed in this year.

405 BCE

The reign of the 30 Spartan tyrants in Athens begins and lasts 8 months.

404 BCE

Civil war ends of the reign of the 30 Spartan tyrants and the re- establishment of democracy in Athens. The Peloponnesian war is over.

399 BCE

The trial and death of Socrates.

388 or 387 BCE

 Plato visits Italy, where he was, or nearly was, (or it never even happened), sold into slavery by Dionysius, because his outspokenness excited Dionysius; but Plato was ransomed by a friend, and sent back to Athens.  Plato founds the Academy, and writes Republic.  Over the door of the Academy read:  "If you do not know geometry do not enter these doors."

384 BCE

Aristotle is born.

368 or 367 BCE

Aristotle enters Plato's Academy in one of these years at age 17.  Plato goes to Syracuse, Italy because Dionysius had died and Plato's friend Dion, (Dionysius' brother-in-law), invites Plato to teach Dionysius II geometry.   Plato was almost not able to leave again due to a dispute between the two brothers-in-law (Dion and Dionysius II); each wanted to be Master of Syracuse. Plato did return to Athens, where he continued his correspondence with Dionysius II.  

361/ 360 BCE

Plato made another voyage to Syracuse.

360 BCE

Plato returns to Athens.

357 BCE

Dion finally becomes Master (Tyrant) of Syracuse but was murdered in 353 to the grief of Plato who felt he had failed at his dream of a philosopher-king.

348 or 347 BCE

Plato wrote Laws just prior to death at 80. Plato dies in one of these years.

343 BCE

Aristotle was invited by Philip of Macedon to undertake the teaching of Alexander the Great, his son of 13. Philip I had conceived the idea of a Hellenic defeat of the Persians.

336 or 335 BCE

Alexander the Great ascended the throne, and Aristotle left Macedon, and returned to Athens and founded his own school, the Lyceum

322-321 BCE

Alexander the Great dies, and the Greek hate of Macedonian rule force Aristotle to leave Athens, for the second time, and he went to the estate of his dead mother in Euboea, where he died shortly after of an illness.