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What is the importance of Hesiod and Homer for understanding the Greek world-view?
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From them, readers can see how phenomena in the Greek world were personified, as well as natural forces (earthquakes, storms, the sun and moon, etc.)
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What was the purpose of Homer and Hesiod's work?
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to "instruct and entertain", not to be a philosophical and scientific interpretation of the world.
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How did early Greek philosophy relate to Greek mythology? Did it? How was it reconciled?
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-Greek philosophy existed side-by-side with mythology. Philosophers sought to understand the very nature of the world-its composition, shape, etc.
-They sought to understand the process of change
-Sought universal explanations for natural phenomena like earthquakes
-The gods played no part in the explanations (see Heraditus and Anaximander)
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Rather than explain the world as being the offspring of the gods, early philosophers such as Leucippus and Democritus posited what?
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atoms and a primeval vortex
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What did Aristotle call the philosophers that were concerned with nature?
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physiologoi
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Name four philosophers associated with Miletus.
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Thales, Anaximander, Anaximenes, Leucippus
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What were the Milesians, and what did they believe?
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they were materialists and monists: they believed the world was made of something physical, and it was made of only one substance.
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Why are the Milesians important? How did they compare to their immediate predecessors?
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-They asked new kinds of questions-the origin of things, underlying reality, order in the world, etc.
-Answers were devoid of any presence by the gods.
-In addition to stating their theories, Milesians realized that they needed to be supported.
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What kind of natural phenomena did the Milesians occupy themselves with?
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those things that illustrated change, diversity, underlying reality
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How did Leucippus and Democritus differ from their Milesian predecessors?
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-Leucippus and Democritus were atomists. Each of them believed that the underlying reality of the world lay in the infinite atoms traveling in a void.
-Coming in different shapes and forms, they account for the diversity in the world.
-They also introduced the idea of vortices (flowing atoms) as an explanation for the formation of worlds.
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What is important about how Leucippus and Democritus viewed the world? How did it portray the world, and how was it different from their predecessors?
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-Their worldview is extremely mechanistic; only the atoms move according to their nature – there is no outside intervention (divine).
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How did Immaterialist philosophers like Empedocles and Pythagoras feel about the world view of the atomists?
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they rejected the cold, mechanical view of the world favored by the atomists
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How did the Pythagoreans view the world? What was the fundamental nature of the world?
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-The world was fundamentally numerical/mathematical in nature, not material.
-The nature of things, and their reality, are derived from numbers. For this reason, mathematics was a reliable way to ascertain the underlying reality of the world.
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What was the fundamental question at the heart of change?
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-How can the world be both stable and changeable?
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Heraclitus was the first to address the issue of change. What was his interpretation?
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Everything in a state of flux.
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How did Parmenides and Zeno address the problem of change?
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-Each denied the possibility of change. Parmenides suggested that something cannot move from existence to non-existence, or vice versa. Nothing creates nothing (you cannot create something out of nothing).
-Zeno addressed the question of motion (a particular kind of change).
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How do the explanations given by Parmenides correspond to experience? What does this say about their attitudes toward experience?
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-Each of them knew that their ideas flew in the face of experience, but the real question for them was whether experience could be trusted.
-For them, the rational process (logic) prevailed over the evidence of experience. The evidence of experience was an illusion.
-Atomists answered this claim by suggesting that there was fundamental stability in superficial change.
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What was the Greek's answer to the problem of knowledge?
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Most early Greek philosophy elevated reason in relation to sense experience. The senses could not get at the fundamental reality of things.
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Why is Socrates so important in the history of Greek philosophy?
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-With Socrates, there is a shift in emphasis away from cosmological matters to ethical and political ones.
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How does Plato argue for the underlying reality of the world?
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-He uses the example of a carpenter and his tables (equating the carpenter with the Demiurge). The limitations in the materials prevented the idea of the Demiurge to be perfectly realized.
-For this reason, there is the realm of forms/ideas, and the material realm.
-Forms/ideas are eternal and unchanging; while they are incorporeal, they exist in reality.
-Material world is transitory and changing. “Allegory of the Cave.”
-To access the greater reality of forms/ideas, we need to escape the shackles of sense experience.
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What are the implications of Plato’s ideas for the concerns of pre-Socratic philosophers?
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-Forms = underlying reality.
-Change and Stability can both occur; stability in the realm of forms, and change in the material world.
-Plato puts observation (sense experience) and true knowledge in opposition. The senses are chains that tie us down. The senses, however, could be useful in a very limited sense.
-To perceive the material world, the senses are useful; however, to pursue an understanding of the realm of ideas/forms, reason unaided by the senses must be used.
-Plato’s concerns foreshadow the discussion of universals and individuals. This is a feature of modern science.
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Where can the bulk of Plato's cosmological ideas be found? What was the impact of this treatise?
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-The bulk of Plato’s cosmological and natural ideas are found in his Timaeus.
-The Timaeus formed the core of early medieval natural philosophy, before Aristotle’s thought became more commonplace.
-In the Timaeus, Plato denies the atomists’ claims that the world is fundamentally mechanical in nature. Order for Plato is extrinsic, not intrinsic.
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Does Plato mean to suggest that the gods of Mount Olympus impose order on the world and interfere in it?
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-Plato does not go that far; he merely asserts that an outside mind had to be responsible for the world. Enter the Demiurge. The Demiurge is the personification of reason. This is not creation ex nihilo.
-Demiurge also not omnipotent; he is limited by the nature of the material he finds.
-Plato also posits the “five Platonic solids.” He associates them with the four elements, and the dodecahedron with the cosmos as a whole.
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What is important about how Plato views the world through the geometrical solids?
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-His ideas prefigure (to some extent) the mathematization of nature. He also fulfills the Pythagorean idea of reducing everything to mathematical first principles.
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What can you say about the way that Plato viewed the heavens? How did he view them?
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-The earth was round, moved around the celestial sphere approximately once a year; he also outlined the orbits of the sun, moon, and the other planets.
-Plato conceived of an animistic world, rejecting the idea of a lifeless cosmos (atomists).
-Divinity accounted for the order and rationality of the cosmos.
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What is the fundamental question regarding the use of mathematics?
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-Is nature mathematical?
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Concerning mathematics, what did the Pythagoreans/Plato believe?
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-For Plato, the fundamental reality of the world was mathematics (geometrical solids).
-Geometrical proportion bound the world together.
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How did Aristotle feel about the nature of reality and mathematics?
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-Aristotle believed that the world went beyond what geometry/mathematics could explore.
-He, however, did not overlook the power of mathematics. He argues that physics is different than mathematics.
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Who was responsible for codifying the Greek mathematical achievement?
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-In his Elements, Euclid lays out the definitions commonly associated with geometry.
-Definitions of lines, points, surface, angles (right, acute, obtuse), et al.
-He also outlines the rules which govern them.
-five postulates (lines connect any two points, straight lines can be extended, all right angles are equal, a circle can be drawn about any point, etc.
-axioms (self-evident truths) (things equal to same thing are equal to each other, whole greater than the part, etc.)
-With Aristotle, Euclid’s rigorous approach influenced scientific demonstration for centuries.
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What was Archimedes' achievement to Greek mathematics?
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-Archimedes built upon the work of Euclid, particularly his idea of “exhaustion.” He also calculated a more accurate value for pi.
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What was Apollonius' achievement to Greek mathematics?
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-Apollonius contributed greatly to work on conic sections.
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What was the primary focus of early Greek astronomy?
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-observation, mapping the stars, and determining the calendar (as well as solar and lunar motions).
-Metonic cycle (5th c. B.C.)
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When did Greek astronomy begin to change?
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-Plato and Eudoxus of Cnidus (4th c. B.C.)
-Shift on 3 fronts:
1.From stellar to planetary concerns.
2.Creation of geometrical model (“two-sphere model” – heaven and earth as concentric spheres, where the celestial sphere rotates around the terrestrial sphere)
-- celestial equator = earth’s equator; planets, et al. move along the ecliptic (which intersects the equator at the equinoxes).
3.Establishment of criteria governing theories designed to account for planetary observations.
-Eudoxus proposes an answer to the complexity of planetary motion
-he proposes a series of concentric spheres for each planet (the number of which differs according to the complexity of the motion – see Mars vs. the sun/moon (fig. 5.5)
-Eudoxus’s is a purely mathematical/geometrical model; it was not meant to represent the physical reality of the heavens. In addition, they would yield qualitative, but not quantitative results.
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How did Aristotle view Eudoxus’s system? How did he change it?
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-He made the spheres proposed physically real.
-While very complicated, Aristotle’s system (and Aristotle himself) poses the question of whether astronomy is a mathematical science, or a physical one.
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Plato and Eudoxus were not the only philosophers to develop cosmological schemes. How did Heraclides of Pontius contribute?
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-Proposed that the earth rotates on its axis once every 24 hours.
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Plato and Eudoxus were not the only philosophers to develop cosmological schemes. How did Aristarchus of Samoa contribute?
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-Proposed a heliocentric system.
-Should not be seen as a precursor to Copernicus (judge by 3rd c. B.C. standards).
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Why is Hipparchus’s approach to the use of mathematics important for his view of astronomy?
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-He was a believer in quantitative prediction in astronomy; he developed methods for assigning numerical values to geometrical models.
-Brought about demand for quantitative match between theory and observation.
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What did Ptolemy bring to Hellenistic Planetary Astronomy?
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-Unlike his predecessors, who lived centuries before him, Ptolemy had access to the theoretical advances made during the intervening centuries.
-Ptolemy brought mathematical power to astronomy that was previously unimaginable.
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How did Ptolemy’s method differ from his predecessors?
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-Ptolemy uses circles rather than spheres to attempt to explain the apparent positions of the planets (and the nonuniform motion of them).
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Describe Ptolemy's Eccentric Model.
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1.If planet P is observed from C, the center, it will not only move uniformly, it will also appear to do so.
2.If planet P is observed from E, the position of the earth, it will appear to slow at A, and it will speed up at D.
3.Simple way to explain nonuniform motions.
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Describe Ptolemy's Epicycle on Deferent Model.
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1.The motion of planet P moves along an epicycle, whose center moves uniformly around the deferent.
2.When the planet P is on the outside of the epicycle, it will be at its maximum speed.
3.When the planet P is on the near side of the epicycle, it will slow and begin a period of retrograde motion (if motion of P is greater than the earth).
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Describe Ptolemy's Equant Model.
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1.Built on eccentric model. Instead of E, a point Q (the equant) is placed as the vantage point for observing planetary motion.
2.Over a given arc, the planet P carves out a right angle. Not all arcs are the same distance, so the speed of the planet P increases.
3.Uniform motion does not occur around the center C, but through Q. Viewing the motion from E, the variable motion seems more variable.
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How did Ptolemy use his models to describe the planetary motions?
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Each of these models was used in unison to describe the breadth of planetary motions.
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Why would astronomers like Ptolemy maintain the idea of uniform circular motion, despite the growing complication of their astronomical models?
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-Tradition (other astronomers stuck with it).
-Uniform circular motion is the simplest motion.
-For quantitative predictability, uniform circular motion was necessary on geometrical grounds.
-Special character of the heavens demanded the most perfect of motions.
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The mathematical way was the only way to achieve any measure of certainty in astronomy. Ptolemy, however, does address physical concerns in his work
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The mathematical way was the only way to achieve any measure of certainty in astronomy. Ptolemy, however, does address physical concerns in his work
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What were the central concerns of optics?
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-Light and vision.
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Describe the atomist's view on optics.
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Eye receives a thin film of atoms (simulacrum) from visible objects.
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Describe Plato's view on optics.
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Fire issues from the observer’s eye and coalesces with sunlight to form a medium; “motions” originating in the visible object are passed to the eye and ultimately to the soul.
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Describe Aristotle's view on optics.
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Potentially transparent medium becomes actually transparent when illuminated by luminous body (e.g. sun); light = state of the medium.
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Describe Euclid's view on optics.
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Rectilinear rays emerge from the observer’s eye in the form of a cone. One sees only that on which the rays fall. His theory is entirely geometrical (not satisfactory for philosophers such as Aristotle.
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