Search Results - Philosophy of mathematics
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The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. Recurrent themes include The terms philosophy of mathematics and mathematical philosophy are frequently used as synonyms.[1] The latter, however, may be used to mean at least three other things. One sense refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of Scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another sense refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term mathematical philosophy to be an allusion to the approach taken by Bertrand Russell in his book Introduction to Mathematical Philosophy. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves that goes beyond simple interpretation to critical analysis. There are traditions of mathematical philosophy in both Western philosophy and Eastern philosophy. Western philosophies of mathematics go as far back as Plato, who studied the ontological status of mathematical objects, and Aristotle, who studied logic and issues related to infinity (actual versus potential). Greek philosophy on mathematics was strongly influenced by their study of geometry. At one time, the Greeks held the opinion that 1 (one) was not a number, but rather a unit of arbitrary length. A number was defined as a multitude. Therefore 3, for example, represented a certain multitude of units, and truly was not a number. At another point, a similar argument was made that 2 was not a number but a fundamental notion of a pair. These views come from the heavily geometric straight-edge-and-compass viewpoint of the Greeks just as lines drawn in a geometric problem are measured in proportion to the first arbitrarily drawn line, so too are the numbers on a number line measured in proportional to the arbitrary first "number" or "one." These earlier Greek ideas of number were later upended by the discovery of the irrationality of the square root of two. Hippasus, a disciple of Pythagoras, showed that the diagonal of a unit square was incommensurable with its (unit-length) edge in other words he proved there was no existing (rational) number that accurately depicts the proportion of the diagonal of the unit square to its edge. This caused a significant re-evaluation of Greek philosophy of mathematics. According to legend, fellow Pythagoreans were so traumatized by this discovery that they murdered Hippasus to stop him from spreading his heretical idea.
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Showing 1 to 4 of 4 Articles matching 'Philosophy of mathematics' in related articles. |
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1. Top Ten UK University - The University of Warwick
September 22, 2008
The university has 16,000 students, including 4,000 international students from over 120 countries. It offers a wide variety of subjects in Arts, Business, Computer Science, Education, Psychology, Politics, Engineering, Philosophy, Mathematics, Languages, Social Studies and Medicine. There are many excellent facilities in the university campus such as the post office, bank, restaurants, bars, pharmacy, sport centre, library, to name a few. The University of Warwick is consistently ranked in the Top 10 UK Universities on a number of league tables such as the Financial Times, Daily Telegra... (read more)
Author: Loke Yuen Wong
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2. Math Scholarships
September 03, 2008
Here is the information about various national scholarships available for math students. 1. The Davidson Fellows Scholarship gives$10,000, $25,000 and $50,000 scholarships to outstanding youth who have finished an important piece of work. Among application categories are Science, Mathematics, Music, Literature, Technology, Outside the Box and Philosophy. This scholarship is annually in Washington, with Congressional meetings and admission at the Congress’s Library. 2. The Fellowship Program and Homeland Security’s U.S. Department is designed for those students who are interested in following... (read more)
Author: Eliseo Rowntree
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3. The Bible On Reincarnation
July 23, 2008
A belief in reincarnation indicates a belief that people experience a series of rebirths until ultimately attaining oneness with God. The Bible's teachings on science, ancient history, and mathematics have been proven flawless. Also, it's a most unique book in that there's no doctrine, belief, or philosophy that has been, is, or ever will be on which the Bible is "silent". This fact alone attests to the amazing knowledge possessed by its numerous authors who wrote under divine inspiration, thing they should not have known by any natural means.
Many proponents of the theory of reincarn... (read more)
Author: Hannah Henderson
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4. Vedic Numerology IX
October 22, 2006
Vedic Numerology- Lesson 9
The Encyclopaedia of the Philosophic Sciences, the Vedas were the product of cognitions by Indian Seers in higher states of Consciousness. Astronomy, Mathematics. Astrology, Numerology, Logic, Philosophy, Gemology etc all derive from this mighty Encyclopaedia. Astronomy, Mathematics and Numerology evolved from the Wisdom of the Heavens, Astrology. Astro- Numerology was the perfect blend of the science of the Numbers and the Science of Time.
Effects of Fadic Number Nine
If the Nineian is YOU!
( Fadic Number is the number got after adding all... (read more)
Author: Govind Kumar
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