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| ANCIENT GREEK PHILOSOPHY From Thales to Boethius | Philosophers | Texts | Timeline |
| Bibliography | Links | Glossary |
Included here are: (1) philosophical terms (Greek and Latin), (2) sources (authors) of the Presocratic fragments, (3) place-names ....
Abdera: A town in the north-east of Greece (now: Avdira). It was founded c. 650 BCE by colonists from Clazomenae, and in 544 BCE absorbed many of the inhabitants of Teos. Its inhabitants eventually acquired a reputation for such stupidity that ‘Abderite’ became a term of abuse among the ancient Greeks. Democritus, and possibly Leucippus were both from Abdera.
Academy: Plato’s Academy was, by tradition, the first European institute of higher learning — a university, if you will — founded by Plato in 387 BCE and closed by the Roman (and Christian) Emperor Justinian in 529 CE. The truth is likely more complicated than this. It was located in a park dedicated to Academus (thus the name), which included an olive grove and various shrines. Some ancient authorities (Cicero) claimed that the school pre-dated Plato, and that Socrates was once its head. Other evidence suggests that it was not in existence during the 1st century BCE nor the century after that. A nice write-up can be found here.
The Achilles: This is one of Zeno’s Paradoxes of motion. Achilles and the tortoise have a race, with the tortoise given a head start. Achilles begins running at time t1, but he will never catch up with the tortoise; for by the time (t2) that Achilles reaches the place where the tortoise was at time t1, the tortoise will have moved a bit farther, and so on into infinity. As long as we can keep dividing the distance travelled and the time travelled in, then Achilles will never catch the tortoise. Cf. Aristotle, Physics (239b15-18): “The second is the so-called ‘Achilles’, and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.” As it is set up, this paradox is not obviously against the reality of motion, for it appears that Achilles and the tortoise are both moving — the problem being simply that the faster never catches the slower. But consider that the headstart given to the tortoise can be made infinitely short; here, there is no motion at all (or precious little).
Aeolian: See Greeks.
agathon: The good.
aisthesis: Sense perception.
aitia: (pl. aitiai) Cause; explanation.
akrasia: Incontinence.
aletheia: Truth.
amathia: Ignorance.
ananke: Necessity.
anamnesis: Recollection.
apeiron: The unlimited.
apodeixis: Demonstration.
aporia: (pl. aporiai) Insoluble puzzle.
arche: Origin; first principle.
arete: (pl. aretai) Virtue.
arithmos: Number.
The Arrow: This is one of Zeno’s Paradoxes of motion. A flying arrow will always be in some place (some quantum of space) at any instant of time; and thus it will be at rest. But this means that it will be at rest at all instants of time (and thus cannot move), for in any instant, it will be either in one quantum of space or in another, but never will it be passing between quanta (since the instants are infinitely short). [Aristotle, Physics (239b5-7)]
This paradox is avoidable by assuming that space is continuous; it would seem to remain, however, even where time is atomic. That is, the assumption of atomic space will lead to this paradox, regardless of the nature of time, unless we define, with Aristotle, “being at rest” as “occupying the same space for a definite period of time (Physics, 238b28); Aristotle seems to read this as time being atomic (a series of “nows”).
autokinesis: Self-movement.
Cosmogony: An account of the origin of the universe (from the Greek kosmogonia, from kosmos [order or world] + -gonia [-begetting]). A traditional, pre-philosophical cosmogony is found in Hesiod (normally dated to the century before Thales) [text].
Delphic Oracle:
Diels-Kranz: Of the writings of the Presocratics [see], only quotations embedded in the works of later authors have survived. These quotations, along with reports about the Presocratics and imitations of their works, were first compiled into a standard edition (Die Fragmente der Vorsokratiker) in the nineteenth century by Hermann Diels (1848-1922) with revisions by Walther Kranz and subsequent editors, in a complete edition of all the works of Presocratic authors which has become standard in the field of ancient philosophy. The works of Presocratics, therefore, are normally referred to by DK numbers. In Diels-Kranz, each author is assigned a number and, within that author’s number, entries are divided into three groups labeled alphabetically:
a. testimonia: ancient accounts of the author’s life and doctrines.
b. ipsissima verba (literally, exact words of the author), sometimes also called “fragments.”
c. imitations: works which take the author as a model
Within each of these three groups, individual fragments or testimonia are assigned sequential numbers. So, for example, since Protagoras is the eightieth author in Diels-Kranz, the third testimony concerning him, a generally unreliable short biography by Hesychius, is referred to as DK80a3. Cf. Diels/Kranz[1903] and Freeman [1948]. Freeman offers a complete English translation of the 'b' passages — the so-called “fragments” — from Diels/Kranz]
DK: See Diels-Kranz
Dorian: See Greeks.
Graeco-Roman Period: See Periodization.
Greeks: Aeolian Greeks lived to the north of the Ionians, and Dorian Greeks lived to the south. Nearly all of the Presocratic philosophers were Ionian Greeks. Crete was a Dorian settlement. On the mainland of present-day Greece, the southern half of the Peloponnesus (including Sparta) was Dorian, with Arcadian Greeks in the middle, and "Northwest Greeks" to the north and west. Ionians included those living in Attica (including Athens) and Euboea, with Thessaly being Aeolian. See a [map] of the larger Greek world, including the colonies on the Italian peninsula and in Asia Minor.
Hellenistic Period: Conventionally dated as 323-31 BCE, that is, the period between the death of Alexander (323 BCE) and the Battle of Actium (31 BCE), which ended Ptolemaic rule in Egypt, the last of the Greek dynasties to fall under Roman rule. Alexander’s death caused a power struggle between his various generals, ending in 281 BCE with the division of Alexander’s previous empire into four dynasties: Ptolemaic (Egypt, with the capital at Alexandria; defeated by Rome in 31 BCE), Seleucid (Syria and Mesopotamia, with the capital at Antioch; defeated by Rome in 63 BCE), Antigonid (Macedonia and central Greece; defeated by Rome in 168 BCE), and Attalid (the Turkish penninsula, with the capitol at Pergamon; peacefully transferred to Rome in 133 BCE).
Hesiod: .
Homer: .
Hyle: (who-lay) matter.
Ionia: Ionia was a narrow strip of land on the west coast of Asia Minor (what is now western Turkey), that part lying between the Black and the Mediterranean seas). It was colonized around 1000 BCE by Ionian Greeks, the earliest invaders of the Greek peninsula. All of the Presocratics were from Ionia, which included the cities of (from South to North) Miletus, Myus, Priene, Ephesus, Colophon, Lebedus, Teos, Erythrae, Clazomenae, Phocaea, and the island cities of Samos and Chios. Aeolian Greeks lived to the north, and Dorian Greeks to the south. [map]
Ionian colonies along the coast of Asia Minor contributing Presocratic philosophers included Miletus (Thales, Anaximander, Anaximenes, Leucippus), Ephesus (Heraclitus), Colophon (Xenophanes), Clazomenae (Anaxagoras), and Samos (Pythagoras, Melissus, Epicurus).
Ionian: See Greeks.
The Moving Blocks: This is one of Zeno’s Paradoxes of motion; also known as The Stadium or The Moving Rows. Here we have three blocks — A, B, and C — all the same size (equal lengths). Let A be stationary, and let B and C move in opposite directions past A. The paradox arises due to the relative motion of B to C, and of B and C to A. B and C will be moving twice as fast with respect to each other than they move with respect to A (which is stationary). This will mean that a unit of time or space will (in some instances) need to be divided in half to express the relative speeds; but space and time are atomic (by definition), and so the relative speed is impossible. [Aristotle, Physics (239b3-240a17)]
Nous: (noose) mind.
Olympiad:
Ousia: (oo-see-uh) substance.
Periodization: The timeline provided on this website is divided into the Pre-Socratic period (625-400 BCE), the 4th Century of Plato (427-347 BCE) and Aristotle (384-322 BCE), the Hellenistic period (323-31 BCE) [see], and the Graeco-Roman period (31 BCE-600 CE). The Hellenistic and Graeco-Roman periods are marked-off by the following events: (1) the dath of Alexander the Great in 323 BCE, which resulted in his empire being partitioned eventually into the kingdoms of Ptolemy, Cassander, Lysimachus, and Seleucus; (2) the defeat of the last of these successor states, the Ptolemaic Kingdom, in 31 BCE; and (3) 600 CE, a nice round number well after the demise of the Roman Empire.
Presocratics: This term was coined by Hermann Diels [1903], in his compilation of fragments [see] of Greek philosophers preceding Socrates, or else contemporaneous but uninfluenced by Socrates. None of the works of these philosophers have survived; all available texts are quotations included by later authors, principally the following (as listed in Kirk/Raven [1962]):
(1) Plutarch (2nd C. CE), Academic philosopher, historian. Gave many quotes in his Moral Essays, Table Talk, The Principle of Cold.
(2) Sextus Empiricus (2nd-3rd C. CE), Skeptic philosopher and physicians: Against the Mathematicians
(3) Clement of Alexandria (2nd C. CE), head of the Catechetical school; many quotations in his Protrepticus and his Stromateis (Miscellanies).
(4) Hippolytus (3rd C. CE), theologian in Rome, quoted Presocratics in his attempt to link current Christian heresies to the pagans in his nine-volume Refutation of all Heresies.
(5) Diogenes Laertius (3rd C. CE) wrote his ten-volume Lives of the Philosophers — a vast compilation of gossip and misinformation, but also including short quotations.
(6) Simplicius (c.490-c.560 CE), Neoplatonist philosopher, the source of long extracts from Parmenides, Empedocles, Anaxagoras, and Diogenes of Apollonia: Commentary on Aristotle’s Physics.
(7) John Stobaeus (5th C. CE) wrote an Anthologium (Selections) consisting of numerous extracts, primarily of a moral nature.
Psyche: (sue-kay) mind, soul, spirit.
Ptolemaic Universe:
The Race Course: This is one of Zeno’s Paradoxes of motion. A runner cannot reach a goal, for she must first reach the midpoint (between the start and the finish). But before she can reach this new goal, she must reach the new midpoint, and on into infinity. Given this infinite number of acts that she must perform (points that she must pass through), she will never be able to reach her goal. [Aristotle, Physics (239b11-13, 263a4-6)]
How this works: If each act takes a discrete amount of time (given the assumption that time is atomic), and space is infinitely divisible, then it will take an infinite number of time-quanta to pass through the infinite number of lengths. If space is continuous, then the lengths can be infinitely small (there will be an infinite number of them in less than an inch); but an infinite number of temporal quanta will quickly add up to a very long time (namely, forever).
The initial assumption that “each act takes a discrete amount of time” appears reasonable, for if we could pass through two lengths of space within a single quantum of time, then we ought to be able to say how long it took to traverse the first length of space; but we would not be able to say that because the time-quantum (by definition) is not divisible; thus we require at least a quantum of time to traverse each distance of space, no matter how short the space.
Note that this paradox works only if time is atomic and space is continuous. If time is continuous, then the infinitely small distances could be traversed in infinitely short durations, so that presumably motion would be possible. Similarly, if both space and time are atomic, then there won’t be an infinite number of lengths to traverse — thus an infinite number of time-durations won’t be necessary to traverse them.
Seven Sages: Pausanias (10.24.1) lists the seven sages as follows: Solon of Athens, Chilon of Sparta, Thales of Miletus, Bias of Priene, Cleobulus of Lindos, Pittacus of Mytilene, and Periander of Corinth.
Theogony: An account of the origin of the gods, or a systematization (typically genetic) of the gods (from the Greek theogonia, from theos [god] + -gonia [-begetting]). The classic example from early Greek culture is Hesiod’s Theogony (second half of the 8th century BCE).
Writing: (language used)(material) Bernard Suzanne provides an image of how a passage of text from Plato's dialogues would have appeared. Written on papyrus scrolls, the letters were all upper-case, and there were no punctation marks, paragraph breaks, or even spaces between words. )
Zeno’s Paradoxes: Zeno of Elea [bio] was a younger contemporary of Parmenides [bio], and a disciple and champion of the latter’s views. Nearly all that we know of him comes from Plato’s dialogue, Parmenides, which depicts Zeno and Parmenides visiting Athens and in discussion with a much younger Socrates.
In defense of the Parmenidean philosophy, Zeno offered arguments against plurality (as many as forty arguments, according to Proclus; two of these survive), against place (described in Aristotle, Physics, 209a23-25), against our senses (the “millet seed”, an unsuccessful argument described in Aristotle, Physics, 250a19-21), and against motion.
Against Plurality: Take some object, such as a block of wood. We can divide this piece into ever smaller pieces; this may be difficult to do, but insofar as the piece has some size, then theoretically it can be cut in half. But this means that our block of wood has an infinite number of extended pieces, which would make it infinitely large. But of course our block of wood isn’t infinitely large, so we must have been wrong to say that it was infinitely divisible: after a number of divisions, we must find that no more divisions can be made. But this is possible only if the pieces have no size (since anything with size is divisible), in which case the block of wood is made of a finite number of pieces without size — thus the block also has no size. Therefore, either the block of wood is infinitely large or else it has no size at all; since it is neither of these things, then the block of wood is not divisible at all. This argument is generalizable to anything at all, with the consequence that plurality is impossible (since whatever is, cannot be divided).
Against Motion: The arguments against motion are the most famous, although none of these have survived in Zeno’s original wording. Our only source for them comes from Aristotle’s account in his Physics, where he describes four separate arguments or paradoxes. These arguments can be interpreted in a number of ways, one of which is to view them as a single complex argument against motion, where each paradox tackles one of four possible conceptions of motion, namely, where space and time are considered to be either continuous or discontinuous (atomic). Each paradox is avoidable by changing one’s conception of space or time from that assumed for the paradox; but since there is a paradox for each of these conceptions, the set of paradoxes taken as a whole presents an inescapable dilemma for the reality of motion. Either motion is illusory, or there is some conception of time or space that is neither continuous nor discontinuous; but since the law of excluded middle forbids there being some third alternative, we are left with the conclusion that motion is illusory.
The paradoxes of motion go by various names, but a fairly standard set are: The Achilles (here space and time are both understood to be continuous), The Race Course (space is continuous, time is atomic), The Arrow (space is atomic, time is continuous), and The Moving Blocks (both space and time are atomic).
Copyright ©2007 Steve Naragon (Manchester College)
Last modified: 8 Aug 2009
Please send comments and questions to:
ssnaragon@manchester.edu