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Hellenistic Natural Philosophy

Hellenistic Natural Philosophy. The Hellenistic World Schools and Education Four Major Philosophies Mathematics Astronomy. Pre Alexander: Hellenic. Post Alexander: Hellenistic. Alexander the Great (356 – 323 BCE). Alexandria: the new cultural capital. Ptolemy’s Kingdom: Egypt.

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Hellenistic Natural Philosophy

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  1. Hellenistic Natural Philosophy • The Hellenistic World • Schools and Education • Four Major Philosophies • Mathematics • Astronomy Pre Alexander: Hellenic Post Alexander: Hellenistic Alexander the Great (356 – 323 BCE)

  2. Alexandria: the new cultural capital Ptolemy’s Kingdom: Egypt

  3. II. Schools and Education A. Elementary education: the gymnasium B. Sophists 1. Itinerant (travelling) teachers 2. Democracy demands educated citizenry 3. Sophists expand teaching subjects to include all knowledge

  4. C. Academy and Lyceum 1. Academy (388 – 83 BCE; 410 – 560 CE) 2. Lyceum (335 – 86 (?))

  5. Questions • Why is the Greek world after Alexander called “Hellenistic”? • After Alexander’s conquests living in Greece is like living in Hell • In tribute to Alexander’s wife, Helen • There was a mix of cultures from the countries Alexander conquered • Hellena in Egypt became the new cultural capital of Greece • Which of the following relates to why the Sophists were so popular? • They taught young girls how to become politicians • The Greeks valued all knowledge • The Greeks were very competitive • The Greeks rejected the authority of the gods • More than one of the answers above is possible • Which of the following is correct about events that occurred after • Alexander’s death? • Athens remained the cultural center of Greece • The Greek empire was stabilized into a single unit • Alexander’s general competed for prestige

  6. III. Four Major Philosophies A. Platonic and Aristotelian B. Epicureanism: ethics most important 1. Happiness (in moderation) • the way to happiness: eliminate fear of unknown and • supernatural through natural philosophy 2. Atomists (with some modification) • denial of • ruling mind • divine providence • destiny • life after death • final causes (purpose) • determinism Epicurus (341 – 270) • all is according to Chance

  7. 4. The Cosmos: Eternal cycle of expansion and contraction III. Four Major Philosophies C. Stoicism 1. Compared to Epicureans • Ethics number one • Happiness is the goal 2. Different from Epicureans • Achieve happiness by living in harmony with Nature • Cosmos is an organic being not mechanistic • Purpose exists • Divine rationality creates determinism 3. Pneuma (literally: breath) • Mix of air and fire • Three forms of pneuma Zeno of Citium (334 – 262 ) 1. Hexis: binds matter together 2. Physis: vital principle of plants and animals 3. Psyche: soul (organizing principle) • expansion: cosmos consumed in fire • contraction: cosmos reborn

  8. Questions • Which of the following philosophies taught that the Stuff was atoms? • Epicureanism • Stoicism • Both Epicureanism and Stoicism • Which of the following philosophies believed that the goal of life was • happiness? • Epicureanism • Stoicism • Both Epicureanism and Stoicism • Which of the following philosophies was atheistic? • Epicureanism • Stoicism • Both Epicureanism and Stoicism

  9. IV. Mathematics A. Application of mathematics to nature 1. Pythagoras: ultimate reality is numbers (geometric) 2. Plato: 4 elements reducible to geometry 3. Aristotle: there is a difference between Nature and numbers • Natural things are sensible and changeable • Geometry only one property of natural thing; also weight, color, etc. B. Greek math emphasizes geometry 1. Reason: problem with irrational numbers • Square with sides of 1 • Diagonal = √ 2 = 1.4142135623730950488016887240297 … 2. Euclid (325 – 270 BCE) father of mathematics (geometry)

  10. 3. Archimedes (287 – 212) • Method of exhaustion • Principle of the lever Eureka! • Water screw • Archimedes principle

  11. Questions • Which of the following Greeks was least interested in applying math to • Natural phenomena? • Plato • Archimedes • Pythagoras • Aristotle • What did the Greeks have against pure math (as opposed to geometry)? • Pure math had not yet been invented • They believed it played a minor role as simply one of many parts of form • They had problems with the aesthetics of irrational numbers • Their number system did not allow for complex calculations • An object floats in water when the weight of the water the object displaces • is equal to the weight of the object. • is less than the weight of the object. • is more than the weight of the object.

  12. V. Astronomy A. Final Cause 1. Observation and mapping of stars - astrology 2. Creating an accurate calendar • solar year (365.24 days) and lunar month (29.5 days) don’t match • 12 – 30 day months short by 5 days • Metonic calendar (425 BCE) • 19 solar years = 235 lunar months (off by 2 hours) • 12 years of 12 months followed by 7 years of 13 months • still in use: NASA and Hebrew calendar B. Plato and Eudoxus 1. Shift to planetary concentration 2. 2 sphere model 3. Ultimate goal to simplify 4. Aristotle further develops model and claims physical reality

  13. V. Astronomy C. Heliocentric universe Aristarchus (310 – 230 BCE) • Problem: it didn’t work 1. No stellar parallax observed (link) 2. Not common sense 3. Against authority and religion

  14. D. Size of the Earth Eratosthenes (276 – 194)

  15. E. Ptolemy (85 – 165 CE) Flat Earth Myth • Geographer • Astrologer • Astronomer

  16. Ptolemy's geocentric models Problem: how to reconcile circular (simplest) motion with erratic movement of planets (sun and moon included). 1. Simple circular motion doesn’t work to explain anything 2. Eccentric model: works well enough for sun and moon 3. Epicycle on deferent model for other planets • epicycle = small circle • deferent = large circle • Problem: not accurate enough to predict movement • or locations of planets

  17. Put all three together Ptolemy's geocentric models 4. Equant model • Earth off center • Planet orbits around central point (not Earth) • Planet sweeps out equal angles in equal times from a reference point (equant point) inside the circle. • Problem: still doesn’t work! Doh! 5. Solution! • Eccentric + (Deferent + epicycle) + Equant = • Physical Reality (almost!) • Simplicity? • The model of the Universe until 17th Century

  18. Questions • Which of the following was NOT a problem for Aristarchus’s heliocentric model of the universe? • Stellar parallax • Common sense • Retrograde motion of the planets • Accepted authority on the nature of the universe • Which of Ptolemy’s models worked well enough to explain the movement of • the sun? • Equant • Epicycle on deferent • Eccentric • A combination of equant and eccentric • Which of Ptolemy’s models worked well enough as a model of the universe? • Equant • Epicycle on deferent • Eccentric • A combination of equant, eccentric, and epicycle

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