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What is the importance of Hesiod and Homer for understanding the Greek world-view?
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.)
What was the purpose of Homer and Hesiod's work?
to "instruct and entertain", not to be a philosophical and scientific interpretation of the world.
How did early Greek philosophy relate to Greek mythology? Did it? How was it reconciled?
-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)
Rather than explain the world as being the offspring of the gods, early philosophers such as Leucippus and Democritus posited what?
atoms and a primeval vortex
What did Aristotle call the philosophers that were concerned with nature?
physiologoi
Name four philosophers associated with Miletus.
Thales, Anaximander, Anaximenes, Leucippus
What were the Milesians, and what did they believe?
they were materialists and monists: they believed the world was made of something physical, and it was made of only one substance.
Why are the Milesians important? How did they compare to their immediate predecessors?
-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.
What kind of natural phenomena did the Milesians occupy themselves with?
those things that illustrated change, diversity, underlying reality
How did Leucippus and Democritus differ from their Milesian predecessors?
-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.
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?
-Their worldview is extremely mechanistic; only the atoms move according to their nature – there is no outside intervention (divine).
How did Immaterialist philosophers like Empedocles and Pythagoras feel about the world view of the atomists?
they rejected the cold, mechanical view of the world favored by the atomists
How did the Pythagoreans view the world? What was the fundamental nature of the world?
-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.
What was the fundamental question at the heart of change?
-How can the world be both stable and changeable?
Heraclitus was the first to address the issue of change. What was his interpretation?
Everything in a state of flux.
How did Parmenides and Zeno address the problem of change?
-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).
How do the explanations given by Parmenides correspond to experience? What does this say about their attitudes toward experience?
-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.
What was the Greek's answer to the problem of knowledge?
Most early Greek philosophy elevated reason in relation to sense experience. The senses could not get at the fundamental reality of things.
Why is Socrates so important in the history of Greek philosophy?
-With Socrates, there is a shift in emphasis away from cosmological matters to ethical and political ones.
How does Plato argue for the underlying reality of the world?
-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.
What are the implications of Plato’s ideas for the concerns of pre-Socratic philosophers?
-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.
Where can the bulk of Plato's cosmological ideas be found? What was the impact of this treatise?
-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.
Does Plato mean to suggest that the gods of Mount Olympus impose order on the world and interfere in it?
-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.
What is important about how Plato views the world through the geometrical solids?
-His ideas prefigure (to some extent) the mathematization of nature. He also fulfills the Pythagorean idea of reducing everything to mathematical first principles.
What can you say about the way that Plato viewed the heavens? How did he view them?
-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.
What is the fundamental question regarding the use of mathematics?
-Is nature mathematical?
Concerning mathematics, what did the Pythagoreans/Plato believe?
-For Plato, the fundamental reality of the world was mathematics (geometrical solids).
-Geometrical proportion bound the world together.
How did Aristotle feel about the nature of reality and mathematics?
-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.
Who was responsible for codifying the Greek mathematical achievement?
-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.
What was Archimedes' achievement to Greek mathematics?
-Archimedes built upon the work of Euclid, particularly his idea of “exhaustion.” He also calculated a more accurate value for pi.
What was Apollonius' achievement to Greek mathematics?
-Apollonius contributed greatly to work on conic sections.
What was the primary focus of early Greek astronomy?
-observation, mapping the stars, and determining the calendar (as well as solar and lunar motions).
-Metonic cycle (5th c. B.C.)
When did Greek astronomy begin to change?
-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.
How did Aristotle view Eudoxus’s system? How did he change it?
-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.
Plato and Eudoxus were not the only philosophers to develop cosmological schemes. How did Heraclides of Pontius contribute?
-Proposed that the earth rotates on its axis once every 24 hours.
Plato and Eudoxus were not the only philosophers to develop cosmological schemes. How did Aristarchus of Samoa contribute?
-Proposed a heliocentric system.
-Should not be seen as a precursor to Copernicus (judge by 3rd c. B.C. standards).
Why is Hipparchus’s approach to the use of mathematics important for his view of astronomy?
-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.
What did Ptolemy bring to Hellenistic Planetary Astronomy?
-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.
How did Ptolemy’s method differ from his predecessors?
-Ptolemy uses circles rather than spheres to attempt to explain the apparent positions of the planets (and the nonuniform motion of them).
Describe Ptolemy's Eccentric Model.
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.
Describe Ptolemy's Epicycle on Deferent Model.
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).
Describe Ptolemy's Equant Model.
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.
How did Ptolemy use his models to describe the planetary motions?
Each of these models was used in unison to describe the breadth of planetary motions.
Why would astronomers like Ptolemy maintain the idea of uniform circular motion, despite the growing complication of their astronomical models?
-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.
The mathematical way was the only way to achieve any measure of certainty in astronomy. Ptolemy, however, does address physical concerns in his work
The mathematical way was the only way to achieve any measure of certainty in astronomy. Ptolemy, however, does address physical concerns in his work
What were the central concerns of optics?
-Light and vision.
Describe the atomist's view on optics.
Eye receives a thin film of atoms (simulacrum) from visible objects.
Describe Plato's view on optics.
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.
Describe Aristotle's view on optics.
Potentially transparent medium becomes actually transparent when illuminated by luminous body (e.g. sun); light = state of the medium.
Describe Euclid's view on optics.
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.
Describe Ptolemy's view on optics.
Combined Euclid’s geometrical approach with the physical and psychological effects of vision. He presented an analysis of the radiation issuing from the eye and its interaction with visible objects.
-He discusses reflection, building on the work of Euclid and others.
-His ideas concerning refraction differed. Analyzed refraction both mathematically and experimentally.
Was there a language barrier that the Romans had to face when confronted with Greek literature et al.? Why?
-The career of Cicero illustrates the connection that Romans had with Greek learning (in a similar way to Galen)
-Latin was only implemented in scholarly discourse when the audience’s linguistic ability was limited.
How did the Roman patrons engage Greek works of literature and philosophy? Were patrons interested in all of the subtleties of Aristotelian thought and the like? If not, what were they interested in?
-Romans knew little of serious scientific/philosophical treatises such as those by Hipparchus and Eudoxus. They preferred the more popularized versions of such knowledge.
-This is of little surprise given that learning was seen as a more or less leisurely pursuit.
What did Posidorius do for Roman and early Medieval science?
-Produced a great deal in Greek, covering a wide range of subjects from geography and history to natural philosophy. He wrote commentaries on Plato’s Timaeus and Aristotle’s Meteorology.
-His work was used a great deal by Lucretius in On the Nature of Things.
-His calculation of the Earth’s circumference was adopted by Ptolemy in his Geography and was later used by Christopher Columbus.
What did Varro contribute to Roman and early Medieval science?
-In his Nine Books of Disciplines, Varro provides a list of nine liberal arts important for Roman gentlemen to be familiar with. They were grammar, rhetoric, logic, arithmetic, geometry, astronomy, musical theory, medicine, architecture. These nine would eventually become the seven liberal arts of the medieval universities.
Cicero (d. 8 B.C.)
-Influenced by the skepticism in the Platonic school (probability was the most that could be achieved in philosophical matters). To achieve greater certainty, one must look back at past opinion (this would be used a great deal in the Middle Ages).
-In so doing, he managed to carry on the popularization of earlier works, particularly works concerning metaphysics (the fundamental nature of reality), the order of the universe, et al.
-His philosophy influenced by the Platonic and Stoic traditions, and he became a major source for the Middle Ages. His microcosm/macrocosm analogy was important in the medieval period and into the Renaissance.
Lucretius (d. 55 B.C.)
-His poem On the Nature of Things served to popularize a number of scientific questions, including the infinity of worlds, the creation and destruction of worlds, phases of the moon, the mortality of the soul, sense perception, et al.
Pliny the Elder (23/24-79 A.D.)
-wrote the Natural History – What was Pliny’s purpose in writing it?
-He wished to survey the universe and the natural objects in it. The contents range from the marvelous to the commonplace, including astronomy and cosmology.
-He did not seek to provide specialized knowledge of astronomy, cosmology, mathematics, and the like.
When did the commentary tradition really begin to start among the Romans?
-It began considerably later than the works described above.
-Macrobius (Commentary on the Dream of Scipio) and Martianus Capella (The Marriage of Philology and Mercury) were two of the earliest to do so.
How does Martianus Capella present his information on the seven liberal arts in The Marriage of Philology and Mercury?
-Bridesmaids representing the mathematical arts present information on their subject to a wedding audience.
-Geometry: highlights of Euclid’s Elements and a discussion of 5 Platonic solids
-Arithmetic: virtues and associations of first ten numbers, classifies the numbers, et al.
-Astronomy: Ptolemy, Hipparchus, Eratosthenes; celestial spheres, the zodiac, the major constellations; his discussion of the motion of Mercury and Venus is particularly interesting.
Boethius (480-524)
-Boethius set out to translate as much Plato and Aristotle as he could find (and to reconcile their thought with Christianity), in addition to Euclid’s Elements.
What was the attitude of Christian writers toward Greek sources (Plato? Aristotle?)?
-Tertullian (ca. 155-230) did not see philosophy as necessary or helpful for Christianity. It should be avoided at all costs.
-St. Augustine (354-430) believed that natural philosophy should be cultivated as the “handmaiden” of religion (this idea is not restricted to just this period).
Where was Roman education generally conducted?
-elementary education (provided by parent or tutor)
-grammarian (approx. 12 years of age)
-rhetorician (approx. 15 years of age)
-philosopher (only for those of great means; conducted entirely in Greek)
How did the coming of the Germanic tribes to Rome affect education? Did the change occur overnight?
-Germanic tribes cared little for formal education
-The support of the affluent who could afford to patronize education began to deteriorate, and the educational structure likewise began to deteriorate.
-Roman learning deteriorated more quickly in the farther provinces, but it continued on in Rome itself, as well as in southern Gaul, Spain, and North Africa.
Where does Christianity fit into this picture? Why did the Church fathers do what they did?
-While it would seem logical to suppose that the Church fathers would seize the opportunity to install a more Christian educational system, supplanting the older pagan one, they thought instead of appropriating it and building upon it (reconciling its content with Christianity).
-This would serve as the official position throughout the Middle Ages.
-This is not to say that the Church was extremely dependent on the Roman schools. They would not go out of their way to save them, if they were threatened.
St. Benedict (d. ca. 550)
-Established a monastery at Monte Cassino in the sixth century and drew up a rule to govern the lives of the monks there (and eventually elsewhere)
-First among these rules is that the monks should be literate, because they were to copy texts required by the monastic community, and worship including reading the Bible and devotional literature
-For this reason (and others), there seems to have been very little contact with classical literature in monasteries (since it was not emphasized in the educational program)
What was the largest contribution to the history of science during the early Middle Ages?
-preservation and transmission of earlier knowledge
Isidore of Seville (ca. 560-636)
-wrote two book of particular interest in the history of science, On the Nature of Things and Etymologies.
-On the Nature of Things: a superficial account of Greek natural philosophy.
-Etymologies: encyclopedic accounts of things by way of their names (etymologies of them).
-He provides a basic account of astronomy, including planetary motions, the seasons, et al.
Venerable Bede (d. 735)
-Wrote on the range of monastic concerns, including natural philosophy, calendrics/timekeeping, but also history.
-Like Isidore of Seville, Bede did not provide tremendous depth in his discussions of different subjects, but he does manage to preserve and transmit knowledge in a usable form.
How did the experience of Byzantine education differ from that in Rome? Why?
-Byzantine education did not experience the same kind of decline, because many of the factors present in Rome were not important in Byzantium.
-Religious leaders seemed to have the same priorities as those in Rome, so it was more a question of desire to discuss pagan sources rather than lacking the opportunity to do so.
-Authors focused on writing commentaries of classical works, particularly of Aristotle and Plato and also attempting to address their work critically.
Neoplatonists and Aristotle
-One of the most consistent interests for Neoplatonists in this period was writing commentaries on various works of Aristotle, particularly On the Soul, Physics, On the Heavens, On Generation and Corruption, et al.
Simplicius (d. aft. 533)
-determined to reconcile Aristotelianism and Platonism
John Philoponus (d. ca. 570)
-attempted to show the errors in Aristotle’s thought, including his argument for the fall of bodies and for the eternity of the universe.
Both Simplicius and John Philoponus marked the course that Aristotle would take during the Middle Ages, particularly the areas of criticism against Aristotle and the need to reconcile his thought with Christianity.
Both Simplicius and John Philoponus marked the course that Aristotle would take during the Middle Ages, particularly the areas of criticism against Aristotle and the need to reconcile his thought with Christianity.
Which religious group was most responsible for transmitting Greek knowledge to the East? How?
-The Nestorians (Christians) who were expelled in 431 eventually set up a school in Nisibis (focused on theology and Biblical studies, but also on Aristotelian logic and other aspects of Greek philosophy).
-They were patronized by Persian kings, giving them greater influence in the court. Khusraw I also seems to have had Greek works translated into Syriac for his use.
How were Greek works translated into Arabic?
-Many times, works would be translated from Greek to Syriac to Arabic (or in various combinations thereof).
When did patronage for translations of Greek works into Arabic begin? To flourish?
-Under al-Mansur (754-775); under his son, Harun ar-Rashid, translation flourished, peaking under Al-Ma’mun.
Hunayn ibn Ishaq (808-73)
-Early in his life, he went to Byzantium in search of manuscripts, and he would spend the greater part of his life translating them.
How would you describe Hunayn ibn Ishaq’s translation methods? Why is this important? Which authors did he translate most?
-He collaborated with his son and nephew, but he also checked more than one version of a given manuscript to weed out errors.
-Hunayn tended to focus his attention of Hippocrates and Galen (mostly Galen), being that he himself was a physician, but he also translated Plato’s Timaeus and various works by Aristotle.
-His son, Ishaq, translated more Aristotle, but also Euclid and Ptolemy.
“By the year 1000, almost the entire corpus of Greek medicine, natural philosophy, and mathematical science had been rendered into usable Arabic versions”(170).
“By the year 1000, almost the entire corpus of Greek medicine, natural philosophy, and mathematical science had been rendered into usable Arabic versions”(170).
What purpose did Greek learning serve in the Islamic world, given the Islamic view of knowledge and knowledge acquisition?
-Knowledge, regardless of its origin, needed to demonstrate a degree of utility.
-Medicine (immediately useful), but the utility of astronomy, astrology, mathematics could also be demonstrated to a degree.
-Translation of mathematical, astronomical, and astrological works (and philosophical and logical works that would aid in understanding them) was patronized to a degree (at least on an individual level).
What factors affected the broad dissemination of Greek learning in the Islamic world? Are scholars agreed on the measure of Islamic acceptance of Greek learning? If so, how? If not, how not?
-The question of utility remains fundamental, but it is easier for knowledge to be useful to a single patron than it would be for a culture at large.
-Division of knowledge (traditional: oral, based on the Koran; foreign: written, based on Greek learning)
-As in the medieval west, there seemed to have been a tension between traditional and foreign knowledge. For this reason, foreign knowledge, particularly if its methodology penetrated traditional knowledge, would be viewed as dangerous.
-Marginality Thesis: Greek learning and its use in the Islamic world remained on the fringes due to pressure from the orthodoxy of Islam. Science in Islam was a marginal pursuit.
-Appropriation Thesis: Greek learning was welcomed in Islam to some degree, as it was some was taught (on occasion in the madrasahs), but it never reached to point where it became a force in the Islamic world. Greek learning served as a “handmaiden” to Islamic traditional knowledge (as with logic).
-As in everything, a more satisfying conclusion lies somewhere in the middle. Greek learning was never as marginal as the “Marginality Thesis” would contend, but it never enjoyed the level of acceptance that the “Appropriation Thesis” maintains.
What effect did this have on the pursuit of Greek learning in the Islamic world?
-There was greater freedom to pursue whatever knowledge scholars wanted to pursue. Islamic institutions were generally ambivalent to Greek learning. This could have contributed to the deterioration of Islamic learning in the thirteenth and fourteenth centuries.
How would you characterize the Islamic scientific achievement? Is Pierre Duhem right?
-Reflecting on the purpose of Islamic science (compiling, studying, and building on the Greek achievement), it is clear that Islamic scientists made a significant contribution to science.
-In astronomy, Islamic scientists studied and endeavored to improve on the Ptolemaic system (improving the calculations possible in the system). Al-Battani, Al-Farghani, and Thibat ibn Qurra were among the scientists who dedicated themselves to this venture.
-In optics, it was the work of Ibn al-Haytham (Alhazen) who contributed the most. He developed an intromission theory of vision which carried on through the Middle Ages and into the early modern period (until Kepler).
What two factors may have contributed to the decline of Islamic science?
-Conservative orthodox Islamic element which distrusted and failed to see the utility of the foreign sciences (science remained a primarily marginal enterprise in Islam).
-Continuous wars both in the west (the Reconquista in Spain) and in the east (Mongols sacking Baghdad in 1258) did not allow for great stability in the educational enterprise.
-The apathy of educational institutions toward foreign learning (Greek) on hastened its demise in the Islamic world.