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Greek contributions to modern mathematics
Greek contributions to modern mathematics
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A Notion of Zero in the Philosophy of Aristotle
ABSTRACT: This article shows that Aristotle created the first notion of a zero in the history of human thought. Since this notion stood in evident contradiction to the basic principles of his metaphysics and logic, he rejected it.
The origin and development of mathematical symbols was closely connected with the development of mathematics itself and development of philosophy. It resulted from the fact that philosophy provided the motivation for investigations and creation of adequate and good mathematical symbols. Moreover, being one of the cultural factors, (1) it played a significant role in the process of accepting or rejecting certain notions.
This article aims at producing evidence that particular ideas of Hellenic philosophy made it impossible for Hellenic thinkers to accept notion of a zero. The following considerations will be preceded by brief information on the ancient notations.
The ancient numeric systems aimed at ascribing to a singular whole number or written symbol (up to a point determined by practical needs). This symbol was a combination of a limited number of signs, produced on the basis of more or less regular laws. (2) Three ancient groups of people: the Babylonians, the Chinese and the Mayas discovered a position principle, that is one of the prerequisites leading to discovering a zero and considering it a number. (3) The first appeared in the Babylonian numeration in the 3rd century BC as a result of overcoming ambiguity in the notation of numbers. The sign for a zero that is the so-called diagonally drafted double nail ( ) indicated, first of all, a lack of units of some "sixty" order. It was also treated as kind of an arithmetic operator, since adding it at the end meant multiplication by "sixty". But neither the Babilonian mathematicians nor astronomers treated zero as a number. A diagonally drafted double nail was conceived of as an empty place, that is a lack of unites of a respective order.
Hellenes people used two systems of denoting numbers. The Athenian system was mathematically equal to the Roman system, whereas the Ionic system, just like the Hebrew system, was a system of an alphabetic type. In both systems, just like in the Egyptian hieroglyphic system or the Hebrew numeration, numbers had their established values regardless of the place they were put in. (4) None of the Hellenic system was based on a position principle, none of them used a symbol of zero, either.
in this paper, I will dispute the ancient analization of the facts that show a
Logan, Jenkins. “Twelfth Night: The Limits of Festivity.” Studies in English Literature, 1500-1900 22.2 (1982): 223-38. Print.
ABSTRACT: At issue is the reliability of Heidegger’s contention that Greek thinking, especially Plato’s, was constricted by an unthought "pre-ontology." "The meaning of being" supposedly guiding and controlling Greek ontology is "Being = presence." This made "the question of the meaning of ousia itself" inaccessible to the Greeks. Heidegger’s Plato’s Sophist is his most extensive treatment of a single dialogue. To test his own reliability, he proposes "to demonstrate, by the success of an actual interpretation of [the Gigantomachia], that this sense of Being [as presence] in fact guided [Plato’s] ontological questioning . . .". I will show Heidegger’s strategy in connecting what he takes to be Plato’s naive pre-ontology — Being = Presence — to the ontology of the Gigantomachia — Being = Power. I will show that Heidegger blatantly misreads the text to make the connection: he completely misses the distinction between bodies and bodiless things. The text makes sense, I will show, if and only if its explicit ontology — Being = Power — is its implicit pre-ontology. Plato wrote his text not to discuss, but to exemplify, Heidegger’s ontology-preontology distinction. He wrote the Gigantomachia for Heidegger, but Heidegger missed it.
The Ancient Greeks for many years in history have been critically acclaimed as a culture that emphasizes significantly on executing and maintaining perfection within its society. It is a culture popularly known for its significant advancements in areas such as; art, architecture, math, and philosophy. This constant need to improve seemed to be a trait that heavily lied within the Ancient Greeks and this is shown through their embodiment of perfectionism. All throughout history, the Greeks have been praised and looked upon greatly due to their significant lifestyle and historical achievement. Through extensive research of the Greeks, including the analyzation of their art, architecture, math and philosophy, I will be able to depict the true
This paper is an initial attempt to develop a dynamic conception of being which is not anarchic. It does this by returning to Aristotle in order to begin the process of reinterpreting the meaning of ousia, the concept according to which western ontology has been determined. Such a reinterpretation opens up the possibility of understanding the dynamic nature of ontological identity and the principles according to which this identity is established. The development of the notions of energeia, dynamis and entelecheia in the middle books of Aristotle’s Metaphysics will be discussed in order to suggest that there is a dynamic ontological framework at work in Aristotle’s later writing. This framework lends insight into the dynamic structure of being itself, a structure which does justice as much to the concern for continuity through change as it does to the moment of difference. The name for this conception of identity which affirms both continuity and novelty is "legacy." This paper attempts to apprehend the meaning of being as legacy.
Lewis, Jone Johnson. "A history of the abortion controversy in the United States." Women's History. 2004. 23 Feb. 2005
Archibald, Zofia. Discovering the World of the Ancient Greeks. New York: Facts On File, 1991. Print.
A tumultuous event that still lives on as a debate in our country today was the Roe V. Wade Supreme Court case. It began on January 22, 1973, when the Supreme Court ruled that women have a right protected by the Fourteenth Amendment to choose whether they terminate a pregnancy or not. A steamy debate on morals and personal rights spread like wildfire across the country. As explained by Sarah Weddington, “This overturned a Texas law making all abortions (except those performed to save the life of the woman) illegal. . .” (Weddington par. 1).
Aristotle believes that before the concept of time there were three kinds of substances, two of them being physical and one being the unmovable. The three substances can be described as one being the “sensible eternal”, the second being the “sensible perishable” and the third substance being the immovable. To further this theory the sensible perishable can be seen as matter, the sensible eternal as potential, and the immovable can be seen as that which is Metaphysical and belongs to another science. According to Aristotle, the immovable is God. It is the immovable that sets the sensible perishable into motion and therefore turns the potential into the actual.
"Ancient Greek Philosophy." Ancient Greek Philosophy. The Academy of Evolutionary Metaphysics, 2005. Web. 26 Feb. 2014.
The. The "Aristotle". Home Page English 112 VCCS Litonline. Web. The Web.
“Laws against abortion have been around for approximately two hundred years though they have varied by state,” (Laws Against Abortion par. 1). In 1973, however, abortion was legalized as a result of the U.S. Supreme Court rule in Roe v. Wade. In this court case, the Supreme Court held that “the word ‘person,’ as used in the Fourteenth Amendment, does not include the unborn,” (McCuen 106). The ruling created a fundamental right for a woman to choose to have an abortion, no matter t...
Shields, Jon A. "Roe's Pro-Life Legacy." First Things: A Monthly Journal Of Religion & Public
Zeno of Elea was a mathematician who is known for introducing a number of intelligent and original paradoxes. A paradox is a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. Zeno was not only a Greek mathematician but also a Greek philosopher and wrote books about the paradoxes that he discovered. His paradoxes continue to stump intelligent people from Aristotle done to people in the present day. Not only did Zeno’s paradoxes contribute to him being considered a mathematician but also his rich background. Little is known about Zeno himself but the information we do know comes from either the manuscript “Parmenides” written by Plato or Aristotle.
In the Roman civilization there was no symbol for zero. Romans used the word “nulla” for an empty space. The word nulla meant “nothing”; what our common day zero means. Romans had a very unorganized number system. It was full of flaws. With no use of zero, there was absolutely no way for counting above several thousand units. When the Roman Empire fell in 300 A.D., the introduction and adaptation of Arabic numerals, today's decimal numbers, took place. Thus, the invention of zero, nothing, was a huge leap forward in Roman history.