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114-589: Approximately sixteen lists of censured theses were issued by the University of Paris during the 13th and 14th centuries. Most of these lists of propositions were put together into systematic collections of prohibited articles. Of these, the Condemnations of 1277 are considered particularly important by those historians who consider that they encouraged scholars to question the tenets of Aristotelian science . From this perspective, some historians maintain that

228-486: A cause that produces motion must precede its effect. God could be an instantaneous and motionless creator, and could have created the world without preceding it in time. To Aquinas, that the world began was an article of faith. The position of the Averroists was condemned by Stephen Tempier in 1277. Giordano Bruno , famously, believed in eternity of the world (and this was one of the heretical beliefs for which he

342-400: A concrete material substance, air, which could be altered by rarefaction and condensation. He adduced common observations (the wine stealer) to demonstrate that air was a substance and a simple experiment (breathing on one's hand) to show that it could be altered by rarefaction and condensation. Heraclitus of Ephesus (about 535–475 BC), then maintained that change, rather than any substance

456-456: A day. Aristarchus also estimated the sizes of the Sun and Moon as compared to Earth's size, and the distances to the Sun and Moon. His heliocentric model did not find many adherents in antiquity but did influence some early modern astronomers, such as Nicolaus Copernicus , who was aware of the heliocentric theory of Aristarchus. In the 2nd century BC, Hipparchus discovered precession , calculated

570-510: A dream of Asclepius , decided he should study medicine. After his father's death, Galen traveled widely searching for the best doctors in Smyrna , Corinth , and finally Alexandria . Galen compiled much of the knowledge obtained by his predecessors, and furthered the inquiry into the function of organs by performing dissections and vivisections on Barbary apes , oxen , pigs , and other animals. In 158 AD, Galen served as chief physician to

684-478: A fifth element, which he called aether . Aristotle used intuitive ideas to justify his reasoning and could point to the falling stone, rising flames, or pouring water to illustrate his theory. His laws of motion emphasized the common observation that friction was an omnipresent phenomenon: that any body in motion would, unless acted upon, come to rest . He also proposed that heavier objects fall faster, and that voids were impossible. Aristotle's successor at

798-541: A fundamental misunderstanding of Aristotelian physics: “To my mind I have demonstrated that when this man objected against these demonstrations he did not comprehend a thing of what Aristotle said.” Simplicius adhered to the Aristotelian doctrine of the eternity of the world and strongly opposed Philoponus, who asserted the beginning of the world through divine creation. Philoponus' arguments for temporal finitism were severalfold. Contra Aristotlem has been lost, and

912-529: A great deal of them have survived, in some cases the sole remnants of their kind of writing from antiquity. Two major themes that run through Ptolemy's works are mathematical modelling of physical phenomena and methods of visual representation of physical reality. Ptolemy's research program involved a combination of theoretical analysis with empirical considerations seen, for instance, in his systematized study of astronomy. Ptolemy's Mathēmatikē Syntaxis ( Ancient Greek : Μαθηματικὴ Σύνταξις ), better known as

1026-570: A major center of scientific research in the 3rd century BC. Two institutions established there during the reigns of Ptolemy I Soter (367–282 BC) and Ptolemy II Philadelphus (309–246 BC) were the Library and the Museum . Unlike Plato's Academy and Aristotle's Lyceum , these institutions were officially supported by the Ptolemies, although the extent of patronage could be precarious depending on

1140-401: A passive unmoved mover . The banned propositions included: Those who "knowingly" taught or asserted them as true would suffer automatic excommunication, with the implied threat of the medieval Inquisition if they persisted. It is not known which of these statements were "taught knowingly" or "asserted" by teachers at Paris, although Siger of Brabant and his radical Averroist colleagues at

1254-655: A subject. If an already existent matter must precede everything coming into existence, clearly nothing, including matter, can come into existence ex nihilo , that is, from absolute nothingness. An absolute beginning of the existence of matter is therefore impossible. The Aristotelian commentator Averroes supported Aristotle's view, particularly in his work The Incoherence of the Incoherence ( Tahafut al-tahafut ), in which he defended Aristotelian philosophy against al-Ghazali 's claims in The Incoherence of

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1368-497: A substratum it cannot occur" is equivalent to arguing that "because I cannot empirically observe eternity it does not exist." Maimonides himself held that neither creation nor Aristotle's infinite time were provable, or at least that no proof was available. (According to scholars of his work, he didn't make a formal distinction between unprovability and the simple absence of proof.) However, some of Maimonides' Jewish successors, including Gersonides and Crescas , conversely held that

1482-541: A summary of which is found in Pliny's Natural History . The legacy of Greek science in this era included substantial advances in factual knowledge due to empirical research (e.g., in zoology, botany, mineralogy, and astronomy), an awareness of the importance of certain scientific problems (e.g., the problem of change and its causes), and a recognition of the methodological significance of establishing criteria for truth (e.g., applying mathematics to natural phenomena), despite

1596-415: Is "broad in scope to the point of confusion." However, the order on the roll has been attributed to factors such as the order in which the errors appeared in the examined works. The list was reorganised shortly after 1277, possibly to facilitate its use in the academic community. In the 20th century, the articles were once again reorganised by Dominican historian Pierre Mandonnet , numbering and distinguishing

1710-399: Is a continuous substance. Two Greek philosophers, Leucippus (first half of the 5th century BC) and Democritus came up with the notion that there were two real entities: atoms , which were small indivisible particles of matter, and the void, which was the empty space in which matter was located. Although all the explanations from Thales to Democritus involve matter, what is more important

1824-540: Is chiefly known through the citations used by Simplicius of Cilicia in his commentaries on Aristotle's Physics and De Caelo . Philoponus' refutation of Aristotle extended to six books, the first five addressing De Caelo and the sixth addressing Physics , and from comments on Philoponus made by Simplicius can be deduced to have been quite lengthy. A full exposition of Philoponus' several arguments, as reported by Simplicius, can be found in Sorabji. One such argument

1938-504: Is especially interested in not just describing the occurrence of plants, animals and insects, but also their exploitation (or abuse) by man. The description of metals and minerals is particularly detailed, and valuable as being the most extensive compilation still available from the ancient world. Although much of the work was compiled by judicious use of written sources, Pliny gives an eyewitness account of gold mining in Spain , where he

2052-433: Is knowledge of necessary causes. He and his followers would not accept mere description or prediction as science. Most characteristic of Aristotle's causes is his final cause, the purpose for which a thing is made. He came to this insight through his biological researches , such as those of marine animals at Lesbos , in which he noted that the organs of animals serve a particular function: After Plato's death, Aristotle left

2166-531: Is necessarily eternal. Aristotle argued that a " vacuum " (that is, a place where there is no matter) is impossible. Material objects can come into existence only in place, that is, occupy space. Were something to come from nothing, "the place to be occupied by what comes into existence would previously have been occupied by a vacuum, inasmuch as no body existed." But a vacuum is impossible, and matter must be eternal. The Greek philosopher Critolaus (c. 200-c. 118 BC) of Phaselis defended Aristotle's doctrine of

2280-416: Is perfectly valid. Avicenna argued that prior to a thing's coming into actual existence, its existence must have been ' possible .' Were its existence necessary , the thing would already have existed, and were its existence impossible, the thing would never exist. The possibility of the thing must therefore in some sense have its own existence. Possibility cannot exist in itself, but must reside within

2394-472: Is precisely to be the substratum from which other things arise. Consequently, the underlying matter of the universe could have come into existence only from an already existing matter exactly like itself; to assume that the underlying matter of the universe came into existence would require assuming that an underlying matter already existed. As this assumption is self-contradictory, Aristotle argued, matter must be eternal. In Book VIII, his argument from motion

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2508-537: Is still not entirely clear. The Catholic Encyclopedia records that the theologians of the University of Paris had been very uneasy due to the antagonism that existed between Christian dogmas and certain Peripatetic doctrines . According to the historian Edward Grant , the theologians desired to condemn Aristotle's teachings on the eternity of the world and the unicity of the intellect. On 18 January 1277, Pope John XXI instructed Bishop Tempier to investigate

2622-446: Is that if an absolute beginning of motion should be assumed, the object to undergo the first motion must either: Option A is self-contradictory because an object cannot move before it comes into existence, and the act of coming into existence is itself a "movement," so that the first movement requires a movement before it, that is, the act of coming into existence. Option B is also unsatisfactory for two reasons: He concludes that motion

2736-461: Is that the condemnations allowed science "to consider possibilities that the great philosopher never envisioned." According to the historian of science Richard Dales, they "seem definitely to have promoted a freer and more imaginative way of doing science." Others point out that in philosophy, a critical and skeptical reaction followed on from the Condemnations 1277. Since the theologians had asserted that Aristotle had erred in theology, and pointed out

2850-429: Is the fact that these rival explanations suggest an ongoing process of debate in which alternate theories were put forth and criticized. Xenophanes of Colophon prefigured paleontology and geology as he thought that periodically the earth and sea mix and turn all to mud, citing several fossils of sea creatures that he had seen. The materialist explanations of the origins of the cosmos were attempts at answering

2964-689: Is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece ) and the 6th century AD (after which there was medieval science ). It is typically limited geographically to the Greco-Roman West , Mediterranean basin , and Ancient Near East , thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent . Ideas regarding nature that were theorized during classical antiquity were not limited to science but included myths as well as religion. Those who are now considered as

3078-538: The Almagest , sought to improve on the work of his predecessors by building astronomy not only upon a secure mathematical basis but also by demonstrating the relationship between astronomical observations and the resulting astronomical theory. In his Planetary Hypotheses , Ptolemy describes in detail physical representations of his mathematical models found in the Almagest , presumably for didactic purposes. Likewise,

3192-636: The Geography was concerned with the drawing of accurate maps using astronomical information, at least in principle. Apart from astronomy, both the Harmonics and the Optics contain (in addition to mathematical analyses of sound and sight, respectively) instructions on how to construct and use experimental instruments to corroborate theory. In retrospect, it is apparent that Ptolemy adjusted some reported measurements to fit his (incorrect) assumption that

3306-502: The Averroist movement . The ground-breaking study by the historian Roland Hissette has shown that many of the censured propositions appear to have come from Aristotle, from Arab philosophers, or from "the philosophers" (i.e. other Greek philosophers). The role that Pope John XXI played in the lead up to the condemnations is a more recent point of discussion. Because the papal letter preceded Tempier's condemnation by only about six weeks,

3420-649: The Byzantine Empire and then in the Islamic world . Late Roman attempts to translate Greek writings into Latin had limited success (e.g., Boethius ), and direct knowledge of most ancient Greek texts only reached western Europe from the 12th century onwards. Pliny the Elder published the Naturalis Historia in 77 AD, one of the most extensive compilations of the natural world which survived into

3534-468: The Condemnations of 1210–1277 . The ancient Greek philosopher Aristotle argued that the world must have existed from eternity in his Physics as follows. In Book I, he argues that everything that comes into existence does so from a substratum . Therefore, if the underlying matter of the universe came into existence, it would come into existence from a substratum. But the nature of matter

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3648-525: The Eastern , Islamic , and Latin worlds and contributed to the birth of modern science . Their works covered many different categories including mathematics , cosmology , medicine , and physics . This subject inquires into the nature of things first began out of practical concerns among the ancient Greeks . For instance, an attempt to establish a calendar is first exemplified by the Works and Days of

3762-833: The Farnese Atlas . Science during the Roman Empire was concerned with systematizing knowledge gained in the preceding Hellenistic age and the knowledge from the vast areas the Romans had conquered. It was largely the work of authors active in this period that would be passed on uninterrupted to later civilizations. Even though science continued under Roman rule, Latin texts were mainly compilations drawing on earlier Greek work. Advanced scientific research and teaching continued to be carried on in Greek. Such Greek and Hellenistic works as survived were preserved and developed later in

3876-545: The Middle Ages . Pliny did not simply list materials and objects but also recorded explanations of phenomena. Thus he is the first to correctly describe the origin of amber as being the fossilized resin of pine trees. He makes the inference from the observation of trapped insects within some amber samples. Pliny's work is divided neatly into the organic world of plants and animals, and the realm of inorganic matter, although there are frequent digressions in each section. He

3990-414: The angle of refraction is proportional to the angle of incidence . Ptolemy's thoroughness and his preoccupation with ease of data presentation (for example, in his widespread use of tables ) virtually guaranteed that earlier work on these subjects be neglected or considered obsolete, to the extent that almost nothing remains of the works Ptolemy often refers. His astronomical work in particular defined

4104-453: The via moderna , in opposition to the via antiqua of the earlier scholastics, it has been seen as a forerunner of a modern age of analysis." Other, even more skeptical thinkers in the mid-14th century included John of Mirecourt and Nicholas of Autrecourt . It has been suggested that the new philosophy of nature that emerged from the rise of Skepticism following the Condemnations, contained "the seeds from which modern science could arise in

4218-440: The "argument from the impossibility of completing an actual infinite by successive addition", states: The first statement states, correctly, that a finite (number) cannot be made into an infinite one by the finite addition of more finite numbers. The second skirts around this; the analogous idea in mathematics, that the (infinite) sequence of negative integers "..-3, -2, -1" may be extended by appending zero, then one, and so forth;

4332-526: The 13th century, and is also of interest to modern philosophers and scientists. The problem became a focus of a dispute in the 13th century, when some of the works of Aristotle , who believed in the eternity of the world, were rediscovered in the Latin West . This view conflicted with the view of the Catholic Church that the world had a beginning in time. The Aristotelian view was prohibited in

4446-414: The 179 philosophical theses from the 40 theological ones. The list was summarised into groupings and further explained by John F. Wippel. The Stanford Encyclopedia of Philosophy also emphasised that "Tempier's theses express positions that cannot be maintained in light of revealed truth, and for this reason are each followed by the qualification 'error'." Another problem was that Tempier did not identify

4560-507: The Academy and traveled widely before returning to Athens to found a school adjacent to the Lyceum. As one of the most prolific natural philosophers of Antiquity, Aristotle wrote and lecture on many topics of scientific interest, including biology , meteorology , psychology , logic , and physics . He developed a comprehensive physical theory that was a variation of the classical theory of

4674-607: The Byzantine device was described by the scientist al-Biruni around 1000, and a surviving 13th-century astrolabe also contains a similar clockwork device. An important school of medicine was formed in Alexandria from the late 4th century to the 2nd century BC. Beginning with Ptolemy I Soter , medical officials were allowed to cut open and examine cadavers for the purposes of learning how human bodies operated. The first use of human bodies for anatomical research occurred in

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4788-634: The Eternity of the World in which he systematically argued against every proposition put forward for the eternity of the world. The intellectual battle against eternalism became one of Philoponus’ major preoccupations and dominated several of his publications (some now lost) over the following decade. Philoponus originated the argument now known as the Traversal of the infinite . If the existence of something requires that something else exist before it, then

4902-616: The Faculty of Arts were targets. Evidently, the radical masters had taught that Aristotle put forward controversial propositions—which according to the Averroists would have been true at least in philosophy, even if rejected in theology—the doctrine of two truths —and questions such as free will and the immortality of the soul were doubtless subject to scholarly debate between masters and students. However, it seems "inconceivable" that any teacher would deny God's Providence. The chain of events leading up to Bishop Tempier's condemnation of 1277

5016-469: The Greek poet Hesiod , who lived around 700 BC. Hesiod's calendar was meant to regulate seasonal activities by the seasonal appearances and disappearances of the stars, as well as by the phases of the Moon, which were held to be propitious or ominous. Around 450 BC we begin to see compilations of the seasonal appearances and disappearances of the stars in texts known as parapegmata , which were used to regulate

5130-658: The Hellenistic age can be seen in the Antikythera mechanism (150–100 BC). It is a 37-gear mechanical computer which calculated the motions of the Sun, Moon, and possibly the other five planets known to the ancients. The Antikythera mechanism included lunar and solar eclipses predicted on the basis of astronomical periods believed to have been learned from the Babylonians . The device may have been part of an ancient Greek tradition of complex mechanical technology that

5244-414: The Lyceum was Theophrastus , who wrote valuable books describing plant and animal life. His works are regarded as the first to put botany and zoology on a systematic footing. Theophrastus' work on mineralogy provided descriptions of ores and minerals known to the world at that time, making some shrewd observations of their properties. For example, he made the first known reference to the phenomenon that

5358-480: The Philosophers ( Tahafut al-falasifa ). Averroes' contemporary Maimonides challenged Aristotle's assertion that "everything in existence comes from a substratum," on that basis that his reliance on induction and analogy is a fundamentally flawed means of explaining unobserved phenomenon. According to Maimonides, to argue that "because I have never observed something coming into existence without coming from

5472-482: The Pope's first letter. The Pope himself had not played any direct role in the condemnations, having merely requested an investigation, and one scholar has argued that there was "less than enthusiastic papal approval of the bishop of Paris' actions." Pierre Duhem considered that these condemnations "destroyed certain essential foundations of Peripatetic physics". Although the Aristotelian system viewed propositions such as

5586-574: The ban on Aristotle's natural philosophy was a dead letter. Nevertheless, the Bishop of Paris, Étienne Tempier , convened a meeting of conservative theologians and in December 1270 banned the teaching of certain Aristotelian and Averroist doctrines at Paris. Thirteen propositions were listed as false and heretical, some relating to Averroes' doctrine of the soul and the doctrine of monopsychism , and others directed against Aristotle's theory of God as

5700-497: The beliefs of the Church. In addition to the 219 errors, the condemnation also covered Andreas Capellanus 's De amore , and unnamed or unidentified treatises on geomancy , necromancy , witchcraft , or fortunetelling . The condemnation of 1277 was later partially annulled "insofar as the teachings of Thomas Aquinas would seem to be implied." The long list has often been labelled as not being particularly organised, and that it

5814-430: The birth of modern science." The condemnations certainly had a positive effect on science, but scholars disagree over their relative influence. Historians in the field no longer fully endorse his view that modern science started in 1277. Edward Grant's views on the subject perhaps approximate closest Duhem's, though Grant's are more refined and benefit from the greater materials available to him. What historians do agree upon

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5928-422: The branch of mechanical science known as dynamics . Pierre Duhem and Edward Grant state this caused a break from Aristotle's work and forced the teachers of the time to believe Aristotle's work imperfect. According to Duhem, "if we must assign a date for the birth of modern science, we would, without doubt, choose the year 1277 when the bishop of Paris solemnly proclaimed that several worlds could exist, and that

6042-466: The civil calendars of the Greek city-states on the basis of astronomical observations. Medicine is another area where practically oriented investigations of nature took place during this period. Greek medicine was not the province of a single trained profession and there was no accepted method of qualification of licensing. Physicians in the Hippocratic tradition, temple healers associated with

6156-429: The classic exposition is Bonaventure's argument in the second book of his commentary on Peter Lombard's sentences , where he repeats Philoponus' case against a traversal of the infinite. Thomas Aquinas , like Maimonides, argued against both the conservative theologians and the Averroists, claiming that neither the eternity nor the finite nature of the world could be proved by logical argument alone. According to Aquinas

6270-420: The complaints of the theologians. "Not only did Tempier investigate but in only three weeks, on his own authority, he issued a condemnation of 219 propositions drawn from many sources, including, apparently, the works of Thomas Aquinas , some of whose ideas found their way onto the list." The list published on 7 March condemned a great number of "errors", some of which emanated from the astrology , and others from

6384-464: The condemnations had positive effects on the development of science, perhaps even representing the beginnings of modern science. The Condemnation of 1210 was issued by the provincial synod of Sens , which included the Bishop of Paris as a member (at the time Pierre II de la Chapelle  [ fr ] ). The writings of a number of medieval scholars were condemned, apparently for pantheism , and it

6498-402: The cult of Asclepius , herb collectors, drug sellers, midwives, and gymnastic trainers all claimed to be qualified as healers in specific contexts and competed actively for patients. This rivalry among these competing traditions contributed to an active public debate about the causes and proper treatment of disease, and about the general methodological approaches of their rivals. An example of

6612-410: The development of a scientific and rational approach to the world. Hero of Alexandria was a Greco-Egyptian mathematician and engineer who is often considered to be the greatest experimenter of antiquity. Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land, and a well-recognized description of a steam-powered device called an aeolipile, which

6726-506: The early seventeenth century." History of science in Classical Antiquity#Plato and Aristotle Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy . Classical antiquity

6840-454: The elements ( earth , water , fire , air , and aether ). In his theory, the light elements (fire and air) have a natural tendency to move away from the center of the universe while the heavy elements (earth and water) have a natural tendency to move toward the center of the universe, thereby forming a spherical Earth. Since the celestial bodies (i.e., the planets and stars ) were seen to move in circles, he concluded that they must be made of

6954-590: The entrance to the Academy the words "Let no man ignorant of geometry enter." Although the story is most likely a myth, it nonetheless testifies to Plato's interest in mathematics, which is alluded to in several of his dialogues. Plato's philosophy maintained that all material things are imperfect reflections of eternal unchanging ideas , just as all mathematical diagrams are reflections of eternal unchanging mathematical truths. Since Plato believed that material things had an inferior kind of reality, he considered that demonstrative knowledge cannot be achieved by looking at

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7068-459: The eternity of the world, and of the human race in general, against the Stoics . There is no observed change in the natural order of things; mankind recreates itself in the same manner according to the capacity given by Nature , and the various ills to which it is heir, though fatal to individuals, do not avail to modify the whole. Just as it is absurd to suppose that humans are merely earth-born, so

7182-493: The existence of a vacuum to be ridiculously untenable, belief in Divine Omnipotence sanctioned them as possible, whilst waiting for science to confirm them as true. From at least 1280 onward, many masters at Paris and Oxford admitted that the laws of nature are certainly opposed to the production of empty space, but that the realisation of such a space is not, in itself, contrary to reason. These arguments gave rise to

7296-410: The explanation is as short on specific evidence and the treatment as vague as that of his rivals. Nonetheless, observations of natural phenomena continued to be compiled in an effort to determine their causes, as for instance in the works of Aristotle and Theophrastus , who wrote extensively on animals and plants. Theophrastus also produced the first systematic attempt to classify minerals and rocks,

7410-419: The first scientists may have thought of themselves as natural philosophers , as practitioners of a skilled profession (e.g., physicians), or as followers of a religious tradition (e.g., temple healers). Some of the more widely known figures active in this period include Hippocrates , Aristotle , Euclid , Archimedes , Hipparchus , Galen , and Ptolemy . Their contributions and commentaries spread throughout

7524-523: The first books on the history of science , and Demetrius of Phalerum , who governed Athens for a time and later may have helped establish the Library of Alexandria . The military campaigns of Alexander the Great spread Greek thought to Egypt , Asia Minor , Persia , up to the Indus River . The resulting migration of many Greek speaking populations across these territories provided the impetus for

7638-410: The first in-depth descriptions of the cerebrum and cerebellum . For their contributions, Herophilos is often called the "father of anatomy ", while Erasistratus is regarded by some as the "founder of physiology ". Greek mathematics in the Hellenistic period reached a level of sophistication not matched for several centuries afterward, as much of the work represented by scholars active at this time

7752-457: The first thing cannot come into existence without the thing before it existing. An infinite number cannot actually exist, nor be counted through or 'traversed,' or be increased. Something cannot come into existence if this requires an infinite number of other things existing before it. Therefore, the world cannot be infinite. The Aristotelian commentator Simplicius of Cilicia and contemporary of Philoponus held that Philoponus’ arguments relied on

7866-525: The first to make use of prognosis and clinical observation, to categorize diseases, and to formulate the ideas behind humoral theory . However, most of the Hippocratic Corpus —a collection of medical theories, practices, and diagnoses—was often attributed to Hippocrates with very little justification, thus making it difficult to know what Hippocrates actually thought, wrote, and did. Despite their wide variability in terms of style and method,

7980-471: The foundation of several seats of learning, such as those in Alexandria , Antioch , and Pergamum . Hellenistic science differed from Greek science in at least two respects: first, it benefited from the cross-fertilization of Greek ideas with those that had developed in other non-Hellenic civilizations; secondly, to some extent, it was supported by royal patrons in the kingdoms founded by Alexander's successors . The city of Alexandria , in particular, became

8094-451: The gladiators in his native Pergamon , and was able to study all kinds of wounds without performing any actual human dissection. It was through his experiments, however, that Galen was able to overturn many long-held beliefs, such as the theory that the arteries contained air which carried it to all parts of the body from the heart and the lungs. This belief was based originally on the arteries of dead animals, which appeared to be empty. Galen

8208-406: The heart was the "seat of intelligence", arguing for the brain instead. Herophilos also wrote on the distinction between veins and arteries , and made many other accurate observations about the structure of the human body, especially the nervous system . Erasistratus differentiated between the function of the sensory and motor nerves , and linked them to the brain. He is credited with one of

8322-556: The imperfect material world. Truth is to be found through rational argumentation, analogous to the demonstrations of mathematicians. For instance, Plato recommended that astronomy be studied in terms of abstract geometrical models rather than empirical observations, and proposed that leaders be trained in mathematics in preparation for philosophy. Aristotle (384–322 BC) studied at the Academy and nonetheless disagreed with Plato in several important respects. While he agreed that truth must be eternal and unchanging, Aristotle maintained that

8436-497: The lack of universal consensus in any of these areas. The earliest Greek philosophers , known as the pre-Socratics , were materialists who provided alternative answers to the same question found in the myths of their neighbors: "How did the ordered cosmos in which we live come to be?" Although the question is much the same, their answers and their attitude towards the answers is markedly different. As reported by such later writers as Aristotle, their explanations tended to center on

8550-537: The latter appearing around the time of Hipparchus (190–120 BC). Advances in mathematical astronomy also took place during the Hellenistic age. Aristarchus of Samos (310–230 BC) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the known universe, with the Earth revolving around the Sun once a year and rotating about its axis once

8664-544: The material entities which embody the forms. He also played down (but did not negate) the importance of mathematics in the study of nature. The process of change took precedence over Plato's focus on eternal unchanging ideas in Aristotle's philosophy. Finally, he reduced the importance of Plato's forms to one of four causal factors. Aristotle thus distinguished between four causes : Aristotle insisted that scientific knowledge (Ancient Greek: ἐπιστήμη , Latin: scientia )

8778-633: The material source of things. Thales of Miletus (624–546 BC) considered that all things came to be from and find their sustenance in water. Anaximander (610–546 BC) then suggested that things could not come from a specific substance like water, but rather from something he called the "boundless". Exactly what he meant is uncertain but it has been suggested that it was boundless in its quantity, so that creation would not fail; in its qualities, so that it would not be overpowered by its contrary; in time, as it has no beginning or end; and in space, as it encompasses all things. Anaximenes (585–525 BC) returned to

8892-484: The method and subject matter of future research for centuries, and the Ptolemaic system became the dominant model for the motions of the heavens until the seventeenth century . Eternity of the world The eternity of the world is the question of whether the world has a beginning in time or has existed for eternity . It was a concern for ancient philosophers as well as theologians and philosophers of

9006-405: The mineral tourmaline attracts straws and bits of wood when heated, now known to be caused by pyroelectricity . Pliny the Elder makes clear references to his use of the work in his Natural History , while updating and making much new information available on minerals himself. From both these early texts was to emerge the science of mineralogy, and ultimately geology . Both authors describe

9120-557: The most important and original work was done in the three centuries from 600 to 300 BC". At the other end is the view of Italian physicist and mathematician Lucio Russo , who claims that the scientific method was actually born in the 3rd century BC, only to be largely forgotten during the Roman period and not revived again until the Renaissance. A good example of the level of achievement in astronomical knowledge and engineering during

9234-508: The most recognizable is the work of Euclid (325–265 BC), who presumably authored a series of books known as the Elements , a canon of geometry and elementary number theory for many centuries. Euclid's Elements served as the main textbook for the teaching of theoretical mathematics until the early 20th century. Archimedes (287–212 BC), a Sicilian Greek , wrote about a dozen treatises where he communicated many remarkable results, such as

9348-449: The negative consequences of uncritical acceptance of his ideas, scholastic philosophers such as Duns Scotus and William of Ockham (both Franciscan friars) believed he might also be mistaken in matters of philosophy. The Scotist and Ockhamist movements set Scholasticism on a different path from that of Albert the Great and Aquinas, and the theological motivation of their philosophical arguments can be traced back to 1277. They stressed

9462-536: The philosophy of the Peripatetics. These included: The penalty for anyone teaching or listening to the listed errors was excommunication, "unless they turned themselves in to the bishop or the chancellor within seven days, in which case the bishop would inflict proportionate penalties." The condemnation sought to stop the Master of Arts teachers from interpreting the works of Aristotle in ways that were contrary to

9576-412: The policies of the current ruler. Hellenistic scholars often employed the principles developed in earlier Greek thought in their scientific investigations, such as the application of mathematics to phenomena or the deliberate collection of empirical data. The assessment of Hellenistic science, however, varies widely. At one extreme is the view of English classical scholar Cornford, who believed that "all

9690-470: The possibility of their ultimate destruction is inconceivable. The world, as the manifestation of eternal order, must itself be eternal. The Neoplatonist philosopher Proclus (412 – 485 AD) advanced in his De Aeternitate Mundi (On the Eternity of the World) eighteen proofs for the eternity of the world, resting on the divinity of its creator. John Philoponus in 529 wrote his critique Against Proclus On

9804-415: The possible eternity of the world and its creation would be contradictory if an efficient cause were to precede its effect in duration or if non-existence precedes existence in duration. But an efficient cause, such as God, which instantaneously produces its effect would not necessarily precede its effect in duration. God can also be distinguished from a natural cause which produces its effect by motion , for

9918-578: The prohibition had actually had an effect on the study of the physical texts in Paris is unclear. English scholars, including Robert Grosseteste and Roger Bacon , studied at Paris, when they could have chosen to study at the University of Oxford , where the works could still be discussed in public. It is assumed that at the least they continued to be read in Paris in private, and there are also signs that their discussion had become public by 1240. By 1270,

10032-413: The question of how an organized universe came to be; however, the idea of a random assemblage of elements (e.g., fire or water) producing an ordered universe without the existence of some ordering principle remained problematic to some. One answer to this problem was advanced by the followers of Pythagoras (c. 582–507 BC), who saw number as the fundamental unchanging entity underlying all the structure of

10146-515: The question was decidable, philosophically. In the West, the 'Latin Averroists' were a group of philosophers writing in Paris in the middle of the thirteenth century, who included Siger of Brabant , Boethius of Dacia . They supported Aristotle's doctrine of the eternity of the world against conservative theologians such as John Pecham and Bonaventure . The conservative position is that the world can be logically proved to have begun in time, of which

10260-549: The search for causal explanations is found in the Hippocratic text On the Sacred Disease , which deals with the nature of epilepsy. In it, the author attacks his rivals (temple healers) for their ignorance in attributing epilepsy to divine wrath, and for their love of gain. Although the author insists that epilepsy has a natural cause, when it comes to explain what that cause is and what the proper treatment would be,

10374-430: The size and distance of the Moon and invented the earliest known astronomical devices such as the astrolabe . Hipparchus also created a comprehensive catalog of 1020 stars, and most of the constellations of the northern hemisphere derive from Greek astronomy . It has recently been claimed that a celestial globe based on Hipparchus's star catalog sits atop the broad shoulders of a large 2nd-century Roman statue known as

10488-431: The sources of the minerals they discuss in the various mines exploited in their time, so their works should be regarded not just as early scientific texts, but also important for the history of engineering and the history of technology . Other notable peripatetics include Strato , who was a tutor in the court of the Ptolemies and who devoted time to physical research, Eudemus , who edited Aristotle's works and wrote

10602-463: The sum of 1 + 2 + 3 + 4 gives the perfect number 10. Thus, the Pythagoreans were some of the first to apply mathematical principles to explain the rational basis of an orderly universe—an idea that was to have immense consequences in the development of scientific thought. According to tradition, the physician Hippocrates of Kos (460–370 BC) is considered the "father of medicine" because he was

10716-758: The sum of an infinite geometric series in Quadrature of the Parabola , an approximation to the value π in Measurement of the Circle , and a nomenclature to express very large numbers in the Sand Reckoner . The most characteristic product of Greek mathematics may be the theory of conic sections , which was largely developed in the Hellenistic period, primarily by Apollonius (262–190 BC). The methods used made no explicit use of algebra, nor trigonometry,

10830-519: The targets of his condemnation, merely indicating that it was directed against unspecified members of the Arts Faculty in Paris. Siger of Brabant and Boethius of Dacia have been singled out as the most prominent targets of the 1277 censure, even though their names are not found in the document itself, appearing instead in the rubrics of only two of the many manuscripts that preserve the condemnation. These two scholars were important proponents of

10944-418: The titles of which were not even specified. Alexander of Aphrodisias was probably among the Aristotelian commentators whose influence was targeted. The University of Toulouse (founded in 1229) tried to capitalise on the situation by advertising itself to students: "Those who wish to scrutinize the bosom of nature to the inmost can hear the books of Aristotle which were forbidden at Paris." However, whether

11058-402: The traditional Franciscan themes of Divine Omnipotence and Divine Freedom, which formed part of Ockham's first thesis. Ockham's second thesis was the principle of parsimony: also known as Ockham's razor . This developed a new form of logic, based on an empiricist theory of knowledge. "While Scholastic in setting," as David Lindberg writes, it was "thoroughly modern in orientation. Referred to as

11172-401: The traditional assumption was that Tempier had acted on papal initiative, and in an overzealous and hasty way. However, more than forty days after Tempier produced his list, another papal letter gives no indication that the Pope was as yet aware of Tempier's action, and seems to suggest otherwise. It is therefore possible that Tempier had already been preparing his condemnations prior to receiving

11286-411: The universe is eternal. The first premise is defended by a reductio ad absurdum where Philoponus shows that actual infinites can not exist in the actual world because they would lead to contradictions albeit being a possible mathematical enterprise. Since an actual infinite in reality would create logical contradictions, it can not exist including the actual infinite set of past events. The second argument,

11400-450: The universe. Although it is difficult to separate fact from legend, it appears that some Pythagoreans believed matter to be made up of ordered arrangements of points according to geometrical principles: triangles, squares, rectangles, or other figures. Other Pythagoreans saw the universe arranged on the basis of numbers, ratios, and proportions, much like musical scales. Philolaus , for instance, held that there were ten heavenly bodies because

11514-522: The uses of the parts of the body of man . The information in these tracts became the foundation of authority for all medical writers and physicians for the next 1300 years until they were challenged by Vesalius and Harvey in the 16th century. Claudius Ptolemy (c. 100–170 AD), living in or around Alexandria , carried out a scientific program centered on the writing of about a dozen books on astronomy , astrology , cartography , harmonics , and optics . Despite their severe style and high technicality,

11628-412: The whole of heavens could, without contradiction, be moved with a rectilinear motion." Duhem's view has been extremely influential in the historiography of medieval science , and opened it up as a serious academic discipline. "Duhem believed that Tempier, with his insistence of God's absolute power, had liberated Christian thought from the dogmatic acceptance of Aristotelianism , and in this way marked

11742-447: The work of Herophilos (335–280 BC) and Erasistratus (c. 304 – c. 250 BC), who gained permission to perform live dissections, or vivisections , on condemned criminals in Alexandria under the auspices of the Ptolemaic dynasty . Herophilos developed a body of anatomical knowledge much more informed by the actual structure of the human body than previous works had been. He also reversed the longstanding notion made by Aristotle that

11856-448: The world cannot have existed for infinite time. Philoponus's works were adopted by many; his first argument against an infinite past being the "argument from the impossibility of the existence of an actual infinite", which states: This argument defines event as equal increments of time. Philoponus argues that the second premise is not controversial since the number of events prior to today would be an actual infinite without beginning if

11970-434: The world is knowable through experience and that we come to know the truth by what we perceive with our senses. For him, directly observable things are real; ideas (or as he called them, forms) only exist as they express themselves in matter, such as in living things, or in the mind of an observer or artisan. Aristotle's theory of reality led to a different approach to science. Unlike Plato, Aristotle emphasized observation of

12084-604: The writings of the Hippocratic Corpus had a significant influence on the medical practice of Islamic and Western medicine for more than a thousand years. The first institution of higher learning in Ancient Greece was founded by Plato (c. 427 – c. 347 BC), an Athenian who — perhaps under Pythagorean influence — appears to have identified the ordering principle of the universe as one based on number and geometry. A later account has it that Plato had inscribed at

12198-415: Was able to demonstrate that living arteries contain blood, but his error, which became the established medical orthodoxy for centuries, was to assume that the blood goes back and forth from the heart in an ebb-and-flow motion. Anatomy was a prominent part of Galen's medical education and was a major source of interest throughout his life. He wrote two great anatomical works, On anatomical procedure and On

12312-435: Was based upon Aristotle's own theorem that there were not multiple infinities, and ran as follows: If time were infinite, then as the universe continued in existence for another hour, the infinity of its age since creation at the end of that hour must be one hour greater than the infinity of its age since creation at the start of that hour. But since Aristotle holds that such treatments of infinity are impossible and ridiculous,

12426-425: Was fundamental, although the element fire seemed to play a central role in this process. Finally, Empedocles of Acragas (490–430 BC), seems to have combined the views of his predecessors, asserting that there are four elements (Earth, Water, Air and Fire) which produce change by mixing and separating under the influence of two opposing "forces" that he called Love and Strife. All these theories imply that matter

12540-452: Was further stated that: "Neither the books of Aristotle on natural philosophy or their commentaries are to be read at Paris in public or secret, and this we forbid under penalty of excommunication ." However, this had only local force, and its application was further restricted to the Arts faculty at the University of Paris . Theologians were therefore left free to read the prohibited works,

12654-477: Was later, at least in part, transmitted to the Byzantine and Islamic worlds, where mechanical devices which were complex, albeit simpler than the Antikythera mechanism, were built during the Middle Ages . Fragments of a geared calendar attached to a sundial, from the fifth or sixth century Byzantine Empire , have been found; the calendar may have been used to assist in telling time. A geared calendar similar to

12768-698: Was of a very advanced level. There is also evidence of combining mathematical knowledge with high levels of technical expertise, as found for instance in the construction of massive building projects (e.g., the Syracusia ), or in Eratosthenes ' (276–195 BC) measurement of the distance between the Sun and the Earth and the size of the Earth . Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues. Among

12882-504: Was stationed as an officer. Pliny is especially significant because he provides full bibliographic details of the earlier authors and their works he uses and consults. Because his encyclopaedia survived the Dark Ages , we know of these lost works , even if the texts themselves have disappeared. The book was one of the first to be printed in 1489, and became a standard reference work for Renaissance scholars, as well as an inspiration for

12996-583: Was the first-recorded steam engine. The greatest medical practitioner and philosopher of this era was Galen , active in the 2nd century AD. Around 100 of his works survive—the most for any ancient Greek author—and fill 22 volumes of modern text. Galen was born in the ancient Greek city of Pergamon (now in Turkey ), the son of a successful architect who gave him a liberal education. Galen was instructed in all major philosophical schools (Platonism, Aristotelianism, Stoicism and Epicureanism) until his father, moved by

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