Assignment 5 (Early Greek Astronomy) Flashcards
In his account of the farmer’s year in Works and Days (lines 381-617), which of the following celestial phenomena does Hesiod NOT mention?
The rising of Venus (or other planetary movements)
Equinox
equal night
Constellation
collection of stars
Planet
wandering star
solstice
sun at standstill
What evidence is there to suggest awareness of solstices before time of Hesiod?
Ancient monuments like Stonehenge in England and Newgrange in Ireland.
Why was Babylonian astronomical tradition more highly developed than Greek tradition at earlier date? (3)
- Babylonians believed celestial phenomena provided signs of welfare for king and city (motivation)
- Centralized political system and state temples provided infrastructure and organization for astronomical records.
- Babylonians were literate centuries earlier than the Greeks.
What does Hesiod treat as a god?
Night, The Moon, The Sun, The Sky, Dawn, etc.
What is NOT treated by Hesiod as a god?
The planet Mars
What best describes Hesiod’s Theogany?
A genealogy of the gods, narrative about succession of ruling gods, account of origins of the world
What is the worldview that Hesiod presents in Theogony?
Mythic worldview, order imposed by will of Zeus (king of the gods)
Outline some key episodes from Hesiod’s Theogony in chronological order.
Castration of Sky
Rhea’s deception of Cronus
Battle between Titans and gods of Olympus
Battle between Zeus and Typhoeus
Zeus swallowing Metis
archē
First principle
to apeiron
the unlimited
physis
nature
stoicheion
element
ouranos
sky or heaven
What was Anaximander’s view on divinity in the world?
Anaximander declared the unlimited heavens are gods. He believed gods are born, appear/disappear at long intervals, innumerable worlds
What did Thales, Anaximenes, and Anaxmiander believe were the first principle?
Thales: Water
Anaximenes: Air
Anaximander: The Unlimited
Who wrote the lines “One god, among both gods and humans the greatest, Neither in bodily frame similar to mortals nor in thought.”
Xenophanes
Where does the English word ‘mathematics’ derive from?
Greek “mathein”: ‘to learn’
In the following passage (Metaphysics 1.5, 986a), to whom does Aristotle refer?
“They assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion or number.”
Pythagoreans
Describe the Greek numerical system.
Alphabet of 27 letters: the first nine letters represented the units from 1 to 9, the second nine represented the tens from 10 to 90, and the third nine represented the hundreds from 100 to 900.
State what language the terms are originally derived from: Geometry, Algebra, Arithmetic, Astronomy
Geometry: Greek
Algebra: Arabic
Arithmetic: Greek
Astronomy: Greek
Greeks generally expressed their math more through _______ than through _________.
area/volume (geometry), than through numbers (arithmetic)
In Plato’s dialogue Meno, Socrates demonstrates the immortality of the soul by leading one of Meno’s slaves through the solution of a problem in geometry. Which problem is it?
Doubling the area of a square
Place the following thinkers and writers in chronological order, from earliest to latest. (Plato, Euclid, Hesiod, Anaximander, Pythagoras)
Hesiod, Anaximander, Pythagoras, Plato, Euclid
Hesiod’s major contribution
Poet who wrote ‘Theogony’, a mythic account of the cosmos and ‘Works and Days’
Anaximander major contribution
Ionian physicist who identified the unlimited as the first principle of the world
Pythagoras known as
Philosopher portrayed in later sources both as an important mathematician and as a shaman-like religious leader
Plato is a
Philosopher who regarded mathematics as the standard of what real knowledge should be
Euclid is a
Mathematician whose work ‘The Elements’ summarized Greek mathematical learning
Greek worlds
kosmoi
What did Anaximander mean by the unlimited?
- not water or air or anything we experience
- some abstract substratum that can take on different forms, but in it of itself is unchanging
What did Anaximander think about the heavenly bodies?
They are not anthropomorphic beings.
What is Anaximander’s view on divinity?
To apeiron is the gods. The gods are born, innumerable in the world. appear and disappear at great intervals
Unlimited heaven in Greek
apeiron ouranous
Compare Hesiod and Anaximander’s view of the divinity cosmos?
They both believe cosmos is divine but Hesiod anthropormophic beings while Anaximander thinks to aperion (the unlimited) is gods and they are more abstract and impersonal.
What were Xenophenes thoughts?
He criticized anthropomorphic mythic worldviews as based on sloppy thinking. He believed the cosmos was divine but pure mind.
In moving from Hesiod to thinkers such as Anaximander and Xenophanes, are we moving from a pre-rational to a rational worldview?
Not necessarily because Hesiod was rational in believing cosmos was orderly.
What is the key difference in early philosophers conception of the cosmos?
While Hesiod relied on anthropomorphic beings, Anaximander and Xenophenes explained through abstract principles. Did not deny divine, but more impersonal and abstract then anthropomorphic beings.
Greek astronomy
law of the stars
Define astronomy and important underlying ideas that developed in the early Greece.
The idea that we can use math to analyze and express underlying order (‘laws’) of the movements of the celestial bodies.
Pythagoras contribution
the first principle (arche) is numbers
Plato contribution to early mathematics
mathematics is the definitive standard of what real knowledge should be
Eculid contribution to early math
culmination of early Greek mathematics in Elements (300 BCE)
Greek mathematics and meaning
mathematika: things to do with ‘mathein’ to learn
Pythagoras
mid 6th century BCE, left no writings, Early writings: emphasized fate of soul after death. Later writings: Pythagoras as a religious leader and some say he was mathetmatician and philosopher
Greek numbers
arithmoi
Etymology of geometry
Earth measuring; gē (earth), metria (measuring)
Etymology of arithmetic
things to do with arithmos (numbers); arithmetika
Etymology of algebra
Arabic al-jabr, ‘the restoration’ (of what is missing):
an extension and generalization of arithmetic using variables as well as numbers
Plato lived when? Who was he a follower of?
~ 400 BCE, Socrates
Describe Plato’s Meno. Who are the main characters and what is the premise?
The main characters are Meno and Socrates. They are trying to determine: What is virtue?
What does Socrates argue about virtue in Meno and what is his evidence?
We in fact do know what virtue is, but have forgotten: bc the soul is immortal. We already have knowledge of everything; what we call learning is in fact remembering. Meno’s slave is able to double the area of a square.
Why did Plato choose a geometrical proof as the most
persuasive example he could think of to justify his
argument about the immortality of the soul and its
prior knowledge? What, for Plato, made mathematics
so special?
The force of deductive (as opposed to inductive)
reasoning; deductive reasoning has an absolute and
inevitable quality that inductive reasoning cannot
achieve.
What did Plato argue the standard of true knowledge should be?
Mathematics, some absolute and inevitable quality of a mathetmatical proof
It was during ______ lifetime that Greek mathematics underwent rapid development as a distinctive intellectual discipline.
Plato (4th century BCE)
