Chapter 5.

Intellectual World of the Greeks

5.1. Greek Science

• Periods
  • Ionian (Pre-Socratic): 600 B.C. - 400 B.C.
  • Plato and Aristotle: 400 B.C. - 300 B.C.
  • Hellenistic Period: 300 B.C. - 100 B.C.
  • Greco-Roman Period: 100 B.C. - 600 A.D.
• Information Sources
  • Original works; none for pre-Socratics
  • Commentaries by later writers, such as Plato, Aristotle, Theophrastus
  • Literary sources
  • Doxographers; summaries, opinions, and summaries of summaries, particularly summaries of multivolume history of philosophy by Theophrastus
  • Chronologies, catalogs, similar materials

5.2. Character of Greek Science

• Drew generalizations from empirical experience
• Systematized and organized scientific knowledge
• Created logic
  • Deduction, reasoning from general to draw conclusion about specifics
  • Induction, reasoning from specific to draw conclusions about generalities
• Developed new mathematical techniques, primarily geometry
• Greek natural philosophy used
  • Empirical observations
  • Conclusions base on empirical evidence
  • Analogies
  • Experiments and rigorous observations sometimes, not always
  • Inductive-deductive logic, emphasized the deductive elements
• Greek science was
  • Critical
  • Naturalistic
  • Rational
  • Secular
• Greek natural philosophers sought to define physics, i.e. to define nature of natural world
• Greek science produced three influential views of natural world
  • Physical-material view of Ionian Materialists or Monists
  • "Most of the first philosophers thought that principles in the form of matter were the only principles of all things: for the original source of all existing things, that from which a thing first comes into being and into which it is finally destroyed, the substance persisting but changing in its qualities, this they declare is the element and first principle of existing things, and for this reason they consider that there is no absolute coming-to-be or passing away, on the ground that such a nature is always preserved...for there must be some natural substance, either one or more than one, from which the other things come-into-being, while it is preserved." Aristotle, Metaphysics
  • Formal-mathematical view of Pythagorean-Platonic Formalists
  • Material-formal view of Aristotelian Dynamists

5.3. Ionians (Pre-Socratics)

• Thales of Miletus (624-546 B.C.)
• Second Web Site for Thales
  • Geometer, astronomer, and engineer
  • Possibly of Phoenician descent; first of Ionian natural philosophers; no original works survive; little is known except from Aristotle (384 - 322 B.C.)
  • Original style of thought; learned geometry from Egyptians; developed proofs of some simple geometric notions; said to have predicted solar eclipse of 585 B.C. (unlikely)
  • Reputed to be the wisest of 7 wise men or sages of Greece
  • World floats in a primordial sea; world composed of water manifesting in many forms; water is primary element and ultimate constituent of all things
  • Water in this context is not exactly water of our senses, but is a unifying principle
  • Possibly aware of water cycle, biological cycles involving water, Aristotle suggests influenced by physiology
  • World can be discussed as processes governed by natural laws; concept of unity underlying diversity
• Anaximander of Miletus (ca. 550 B.C.)
  • Disciple of Thales
  • Drew some of first maps
  • No single substance may be regarded as primary, for the ultimate (aperion) is unbounded and its nature indefinable
  • All is "according to necessity...and the assessment of time"
  • World consists of intermingled opposites - hot and cold, dry and wet, light and dark - and is animated by their interplay
• Anaximenes of Miletus (ca. 525 B.C.)
  • Disciple of Anaximander
  • Ultimate substance is air; air is pervasive and forever restless; air is flame and fire when rarefied, cloud and water when condensed, earth and rock when more condensed
  • Stars are fiery rarefaction's high above the atmosphere
  • Motion is eternal and change comes about through it
• Heraclitus (ca. 500 B.C.) of Ephesus in Ionia
  • Apparently influenced by Pythagoras
  • Taught that Logos - Mind or Reason expressed in words or things - was unifying principle
  • Fire is primary element; world "was ever, is now, and ever shall be an ever-living fire"
  • System of perpetual flux; "all things change and nothing remains at rest"
  • Reality is a unity of process; being is forever becoming; wisdom consists of knowing how things change; only change is changeless
• Xenophanes (ca. 500 B.C.) of Colophon in Ionia
  • All things are made of water and earth
  • Innumerable Suns and Moons
  • Earth is infinite, neither enclosed by air nor by heaven
• Anaxagoras of Clazomenae (ca. 450 B.C.)
  • Among last of Ionian natural philosophers of note; taught in Athens
  • "Nothing comes into being or perishes, but is compounded from or dissolved into things that are"
  • Inspired atomists by arguing that all things are compounded from numberless minute portions of an elemental an universal substance
  • Universe is unlimited in extent, similarly composed, and subject to similar laws
  • Universe is ruled by Mind - the Logos - not by whims of gods
  • Moon shines by reflected sunlight (lunar eclipse) and has mountains on its surface
  • Stars are fiery bodies so distant that we cannot feel their warmth as we do the Sun's
  • Universe is of unlimited extension in which things are similarly composed and subject to similar laws (contrary to general belief among Greeks)
• Empedocles of Agrigentum (ca. 450 B.C.)
  • Born on south coast of Sicily; not only a natural philosopher, but poet, seer, physician, social reformer, person of great enthusiasm; considered by some as charlatan, as hero by others
  • Postulates four elements--fire, air, water, earth--and two moving forces--love and strife
  • Actually performed some experiments; showed air was material substance
  • Observations concerning light and vision; argues vision caused by both emission by luminous bodies and rays issuing from eyes
  • Argued light had finite velocity
  • Two hemispheres revolve around earth, one composed of fire (day), and second of air with a little fire (night)
  • Sun is not made of fire, but stars are fiery elements, while Moon is air and receives its light from the Sun

5.4. Pythagorean Philosophy

• Pythagoras and the Pythagorean school of Croton (ca. 529 B.C.)
  • Born on island of Samos off Ionian coast
  • Possibly studied in Miletus under Thales
  • Apparently spent some 22 years in Egypt studying astronomy and geometry; some 12 years in Babylon studying arithmetic and music
  • Around age 56 (ca. 510 B.C.), he settled in Croton, one of many Greek colonies in southern Italy, founded there his famous Pythagorean school, died in Metapontion
  • Pythagoras found a basic relation between musical harmony and mathematics
  • Pythagoras pioneered linking of geometry with numbers
• Pythagorean theorem says that square of hypotenuse of a right triangle is equal to sum of squares of its two sides,
  a[E(2)] + b[E(2)] = c[E(2)]
  • Right angle: gravity is vertical and horizon stands at right angles to it
  • Rotate right angle through four successive 90o turns and we return to cross of gravity and horizon; fourfold symmetry of plane space
  • Pythagorean theorem most important single theorem in mathematics; fundamental characterization of the space in which we exist
• Pythagoreans argued that ultimate reality is number
  • "since all other things seemed in their whole nature to be modeled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number." Aristotle
  • "Most people say that the earth lies at the center of the Universe...but the Italian philosophers known as Pythagoreans take the contrary view. At the center, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the center." Aristotle, De caleo
  • "Also, when the Sun and the Moon, they say, and all the stars, so great in number and in size, are moving with so rapid a motion, how should they not produce a sound immensely great? Starting from this argument and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony." Aristotle
  • Pythagorean emphasis on number as the principle of all existence changed history of cosmological thought
  • Doctrine of musical harmonies influenced Kepler and are in part responsible for Kepler's three laws of planetary motion

5.5. Parmenidian and Atomist Philosophy

• Parmenides of Elea (ca. 480 B.C.)
  • Born in Elea on western coast of southern Italy; founder of Eleatic school of natural philosophy; departed for Athens at age 56
  • Founder of metaphysics; concerned not with appearances, but with means of reaching the truth beyond them
  • Necessary means of seeking truth is not observational or experimental, but purely logical
  • Tried to develop Ionian monism as rigorously as possible against pluralism or Pythagorean dualism
  • Being fills totality of space; non-Being is pure space, emptiness, but can not exist, yet it can be thought and expressed
  • Concludes that Universe must be one, and limited, yet must fill whole of space; for reasons of symmetry must be spherical; universe of Being is eternal, changeless, motionless; change and motion are unreal
• Zeno of Elea (ca. 450 B.C.)
  • Born in Elea; disciple of Parmenides and accompanied him to Athens in 444 B.C.
  • Assumed that plurality and change lead to logical absurdities
  • Systematic use of reductio ad absurdum for which Aristotle called him discoverer of dialectics
• Leucippus of Miletus (ca. 440 B.C.)
  • Little definitive knowledge of his origins, even his birthplace
  • Disciple of Eleatic school and student of Zeno
  • Probably developed atomic ideas as reaction to Parmenides ideas about matter
  • Said to have written a book called The Great World System, however no trace of writings remain
  • Most famous saying: "Nothing happens in vain (without reason), everything has a cause and is the result of necessity"
• Democritus of Abdera (ca. 410 B.C.)
  • Much more known about Democritus than Leucippus; born in Abdera in Thrace on northern end of Aegean Sea
  • He traveled widely and for much of his life; five years in Egypt learning mathematics, traveled through Asia Minor, went to Babylon, Persia, and even possibly India; study and conversed with learned men and studied under their direction
  • Knowledge of philosophy, mathematics, astronomy, medicine, and ethics
  • Devised atomic theory from Leucippus; world divided in two parts, full composed of atoms, and empty or vacuum
  • Atoms are indivisible, infinite in number, eternal, absolutely simple; they are alike in quality but differ in shape, order, and position
  • Every material object composed of atoms in varying combinations; material reality is a continual aggregating and disaggregating of atoms

5.6. Pre-Socratics Contributions in Review

• Identifying features of Milesian view
  • Universal substance from which all else is made
• Identifying features of Pluralist View
  • Several substances or "atoms" from which all is composed
  • Between atoms lies the void
• Significant Pre-Socratic concepts:
  • Unity principle: unity underlying diversity of our experiences with nature and nature's behavior
  • Transformation (or conservation) principle: universal substance (or substances) are not destroyed or created, but only changed in form and condition to produce multiplicity of material objects we encounter in natural world
  • Pythagorean concept of number: number (or mathematics) underlies all of nature and is tool or path by which we interpret the world
  • Natural law principle: world operates under rational rules through natural laws rather than through arbitrary and capricious actions of gods