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30 Cards in this Set
- Front
- Back
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Euclid
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wrote Elements, father of geometry. Euclid's method of proving mathematical theorems by logical deduction from accepted principles remains the backbone of all mathematics.
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Thales
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earliest known Greek mathematician, sometimes called the father of modern philosophy, gave the first proof for a mathematical statement, proved the angles opposite the equal sides of an isosceles triangle are equal. Modern mathematics began with the thought that a mathematical statement might need a proof.
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Ptolemy
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was a Greek-speaking geographer, astronomer, and astrologer who lived in the Hellenistic culture of Roman Egypt. Came up with geocentricaq`1 orbits
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Archimedes
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Greek mathematician. Solved problems that require an understanding of calculus, used the method of exhaustion. Applied his skills in the construction of mechanical devices to protect the city-state of Syracuse from the invading Roman army.
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Pythagoreum theorem
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In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse). The Pythagoreans saw this fact as evidence that the universe had a numerical basis for it.
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Zeno's paradox
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In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead
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monist vs. pluralist
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The monists, such as Thales, believed in the underlying unity of nature, and sought some primal substance from which all others derived. Pluralists, such as Aristotle, recognized several primal or elemental substances. There are still monist present today, which are the cosmologists who are looking for a “theory of everything.” Present day pluralists doubt they will succeed.
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motion vs. rest
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the earth will not change unless someone changes it versus, the earth is always changing it and humans simply add on to this change. A defender of rest was Zeno, who illustrated this by the paradox of the foot race between Achilles and the tortoise. This paradox is frequently cited to show the inadequacies of Greek mathematics.
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materialist vs. idealist
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Materialists believed that atoms make up everything and Idealists believed that there is this perfect form and everything tries to reach that perfect form. Plato is an idealists because his Idel is realized only by logical thought, as seen in Meno, where Socrates and Meno attempt to define virtue logically.
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Four Causes: Material, Efficient, Formal, Final
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Aristotle believed that every phenomenon has 4 causes. Every effect has its cause, going right back to the first cause.
Material- is the thing itself Efficient- agent/action by which the event occurred Formal- is inherent in the nature of the thing Final- the goal toward which the phenomenon is directed |
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Socrates
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Socrates (and presumably Plato) says that Virtue is innate -- it is within us and can not be taught but, when it comes out, we recognize it as virtue (just as the slave boy could come to some conclusions about math even though he didn’t really know it. Socrates/Plato says it is an instinct and has gotten their by God's gift.
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Plato
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student of Socrates, famous of the cave allegory and meno. Meno illustrates Socrates’ idea of what virtue is. It also displays the Socratic method by Socrates questioning every answer that Meno gives.
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Meno
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The goal is a common definition that applies equally to all particular virtues. They decide that virtue is described as that that has come about in a virtuous way. Displays the Socratic method.
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virtue
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something done in a just and right way. virtue is something done in a virtuous way. Plato/Socrates and Aristotle differ in their views of virtue. Plato/Socrates believe virtue is innate, versus Aristotle who would say we have to work at it -- virtue is contextual -- we can only approximate it by trying to keep the middle road in that PARTICULAR context, we must have the knowledge/sense to know what that is.
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Aristotle
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was an ancient Greek philosopher, a student of Plato and teacher of Alexander the Great. Differs from Socrates’ idea of virtue by believing that virtue is something we have to work at it -- virtue is contextual -- we can only approximate it by trying to keep the middle road in that PARTICULAR context, we must have the knowledge/sense to know what that is.
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Doctrine of Mean
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A way according to confusious to gain perfect virtue. You must teach and learn and gain virtue by doing good.
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syllogism
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a general statement is followed by a more specific one, and an inevitable conclusion is drawn from the first two statements. For of argument is called deduction, and was the principle form of logic until the beginnings of modern science, which depends more extensively on induction.
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mayan calendar
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a calender of diffent combinations, that when put together, argues that time goes in a cycle
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Constantine
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Roman Emperor, converted to Christianity, made Christianity legal, aided in the growth of Chrisitanity. Gibbon’s idea that this was one of the reasons the Roman empire fell.
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Edict of Milan
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AD 313) declared that the Roman Empire would be neutral with regard to religious worship, officially ending all government-sanctioned persecution, especially of Christianity
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divine right
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It states that a monarch owes his rule to the will of God, not to the will of his subjects, parliament, the aristocracy or any other competing authority
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cyclic vs. linear time
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linear time is the thought that time does not repeat itself. It starts with creation, and ends with the second coming of Christ. Cyclic is the idea of the wheel of change and repeated events.
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Basilica
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originally used to describe a Roman public building (as in Greece, mainly a tribunal), usually located at the centre of a Roman town. After the Roman Empire became officially Christian, the term came by extension to refer to a large and important church that has been given special ceremonial rights by the Pope. Thus the word retains two senses today, one architectural and the other ecclesiastical.
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Flying buttresses
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In architecture, a flying buttress, or arc-boutant, is a butt, usually on a religious building, used to transmit the thrust of a vault across an intervening space (which might be an aisle, chapel or cloister), to a buttress outside the building. The employment of the flying buttress means that the load bearing walls can contain cut-outs, such as for large windows, that would otherwise seriously weaken the vault walls.
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Symbolic code of medieval art
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the symbolism of the church services familiarized the faithful with the symbolism of art. Church makes use of symbols to instruct and move the people. Relates to Jacques le Goff, and how our use of symbol change because our perception changes.
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definition of man in the middle ages
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The first view is the homo viator, man the voyager, always traveling the Earth and through his life span, the choices that he makes moves him toward eternal life or eternal death. The second view is the penitent. Medieval man, conditioned by the notion of sin that had been inculcated iin him, sought assurance of salvation in repentance.
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Islam
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is a monotheistic religion based upon the Qur'an, which adherents believe was sent by God (Arabic: الله Allāh) through Muhammad. Followers of Islam, known as Muslims (مسلم), believe Muhammad to have been God's final prophet. As a result, most of them see the actions and teachings of Muhammad as related in the Sunnah and Hadith to be indispensable tools for interpreting the Qur'an. Like Judaism and Christianity, Islam is an Abrahamic religion.
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Koran
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literally "the recitation"; also called al-qurʼān al-karīm "The Noble Qur'an"; also transliterated as Quran, Koran, and Al-Quran), is the central religious text of Islam. Muslims believe the Qur'an, in its original Arabic, to be the literal word of God that was revealed to Muhammad over a period of twenty-three years until his death. Mohammed said that this was his miracle when people criticized him being a prophet.
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Mutazilites vs. Asharites
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Mu'tazilis believed in the absolute unity and oneness of God. In this regard, they are no different from the overwhelming majority of Muslims. Asharites is a school of early Muslim speculative theology named after its founder, the theologian Abu l'Hasan al-Ash`ari (d. 945). The disciples of the school are known as Asharites, and the school is also referred to as Asharite school. It was instrumental in drastically changing the direction of Islamic theology, separating its development radically from that of theology in the Christian world
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Taqlid vs. Ijtihad
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referring to the acceptance of a religious ruling in matters of worship and personal affairs from someone regarded as a higher religious authority (e.g. an 'ālim) without necessarily asking for the technical proof. Ijtihad is a technical term of Islamic law that describes the process of making a legal decision by independent interpretation of the legal sources, the Qur'an and the Sunnah
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