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Chiliagon
In geometry, a chiliagon () or 1000-gon is a polygon with 1,000 sides. Philosophers commonly refer to chiliagons to illustrate ideas about the nature and workings of thought, meaning, and mental representation. Regular chiliagon A ''regular chiliagon'' is represented by Schläfli symbol and can be constructed as a truncated 500-gon, t, or a twice-truncated 250-gon, tt, or a thrice-truncated 125-gon, ttt. The measure of each internal angle in a regular chiliagon is 179°38'24"/\fracrad. The area of a regular chiliagon with sides of length ''a'' is given by :A = 250a^2 \cot \frac \simeq 79577.2\,a^2 This result differs from the area of its circumscribed circle by less than 4 parts per million. Because 1,000 = 23 × 53, the number of sides is neither a product of distinct Fermat primes nor a power of two. Thus the regular chiliagon is not a constructible polygon. Indeed, it is not even constructible with the use of an angle trisector, as the number of sides is neither a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its ''edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. General properties ''These properties apply to all regular polygons, whether convex or star.'' A regular ''n''-sided polygon has rotational symmetry of order ''n''. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Problem Of The Speckled Hen
In the theory of empirical knowledge, the problem of the speckled hen is whether a single immediate observation of a speckled hen provides a certain knowledge of the number of speckles observed. Clearly, this is not an isolated example, and therefore it is of fundamental nature.Roderick Chisholm, "The Problem of the Speckled Hen", ''Mind'' 51 (1942): pp. 368–373. Philosophically, this problem probes the limits of knowledge by acquaintance: one is unable to know with certainty the existence of determinate things in one's experience merely by the virtue of the experience. Roderick Chisholm attributes it to Gilbert Ryle suggesting to A. J. Ayer. It is viewed as a criticism of the view expressed by C. I. Lewis that there can never be "positive bafflement in the presence of the immediate, because there is here no question which fails to find an answer".C. I. Lewis, Mind and the World-Order, p. 128, As cited by Chisholm (1942). Joseph Heath remarks that this problem is one of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meditations On First Philosophy
''Meditations on First Philosophy, in which the existence of God and the immortality of the soul are demonstrated'' ( la, Meditationes de Prima Philosophia, in qua Dei existentia et animæ immortalitas demonstratur) is a philosophical treatise by René Descartes first published in Latin in 1641. The French translation (by the Duke of Luynes with Descartes' supervision) was published in 1647 as ''Méditations Métaphysiques''. The title may contain a misreading by the printer, mistaking ''animae immortalitas'' for ''animae immaterialitas'', as suspected by A. Baillet. The book is made up of six meditations, in which Descartes first discards all belief in things that are not absolutely certain, and then tries to establish what can be known for sure. He wrote the meditations as if he had meditated for six days: each meditation refers to the last one as "yesterday". (In fact, Descartes began work on the ''Meditations'' in 1639.) One of the most influential philosophical texts ever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Locke
John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Enlightenment thinkers and commonly known as the "father of liberalism". Considered one of the first of the British empiricists, following the tradition of Francis Bacon, Locke is equally important to social contract theory. His work greatly affected the development of epistemology and political philosophy. His writings influenced Voltaire and Jean-Jacques Rousseau, and many Scottish Enlightenment thinkers, as well as the American Revolutionaries. His contributions to classical republicanism and liberal theory are reflected in the United States Declaration of Independence. Internationally, Locke’s political-legal principles continue to have a profound influence on the theory and practice of limited representative government and the protection of basic rights and freedoms under the rule of law. Locke's theory of mind is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meditations On First Philosophy/Meditation VI
''Meditations'' () is a series of personal writings by Marcus Aurelius, Roman Emperor from AD 161 to 180, recording his private notes to himself and ideas on Stoic philosophy. Marcus Aurelius wrote the 12 books of the ''Meditations'' in Koine Greek as a source for his own guidance and self-improvement. It is possible that large portions of the work were written at Sirmium, where he spent much time planning military campaigns from 170 to 180. Some of it was written while he was positioned at Aquincum on campaign in Pannonia, because internal notes tell us that the first book was written when he was campaigning against the Quadi on the river Granova (modern-day Hron) and the second book was written at Carnuntum. It is unlikely that Marcus Aurelius ever intended the writings to be published. The work has no official title, so "Meditations" is one of several titles commonly assigned to the collection. These writings take the form of quotations varying in length from one sentence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Gassendi
Pierre Gassendi (; also Pierre Gassend, Petrus Gassendi; 22 January 1592 – 24 October 1655) was a French philosopher, Catholic priest, astronomer, and mathematician. While he held a church position in south-east France, he also spent much time in Paris, where he was a leader of a group of free-thinking intellectuals. He was also an active observational scientist, publishing the first data on the transit of Mercury in 1631. The lunar crater Gassendi is named after him. He wrote numerous philosophical works, and some of the positions he worked out are considered significant, finding a way between skepticism and dogmatism. Richard Popkin indicates that Gassendi was one of the first thinkers to formulate the modern "scientific outlook", of moderated skepticism and empiricism. He clashed with his contemporary Descartes on the possibility of certain knowledge. His best known intellectual project attempted to reconcile Epicurean atomism with Christianity. Biography Early l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hume
David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999br>David Hume" ''Encyclopædia Britannica''. Retrieved 18 May 2020. was a Scottish Enlightenment philosopher, historian, economist, librarian, and essayist, who is best known today for his highly influential system of philosophical empiricism, scepticism, and naturalism. Beginning with '' A Treatise of Human Nature'' (1739–40), Hume strove to create a naturalistic science of man that examined the psychological basis of human nature. Hume argued against the existence of innate ideas, positing that all human knowledge derives solely from experience. This places him with Francis Bacon, Thomas Hobbes, John Locke, and George Berkeley as an Empiricist. Hume argued that inductive reasoning and belief in causality cannot be justified rationally; instead, they result from custom and mental habit. We never actually perceive that one eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roderick Chisholm
Roderick Milton Chisholm (; November 27, 1916 – January 19, 1999) was an American philosopher known for his work on epistemology, metaphysics, free will, value theory, and the philosophy of perception. The ''Stanford Encyclopedia of Philosophy'' remarks that he "is widely regarded as one of the most creative, productive, and influential American philosophers of the 20th Century." Life and career Chisholm graduated from Brown University in 1938 and received his Ph.D. at Harvard University in 1942 under Clarence Irving Lewis and D. C. Williams. He was drafted into the United States Army in July 1942 and did basic training at Fort McClellan in Alabama. Chisholm administered psychological tests in Boston and New Haven. In 1943 he married Eleanor Parker, whom he had met as an undergraduate at Brown. He spent his academic career at Brown University and served as president of the Metaphysical Society of America in 1973. He was editor of ''Philosophy and Phenomenological Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and aesthetics have made him one of the most influential figures in modern Western philosophy. In his doctrine of transcendental idealism, Kant argued that space and time are mere "forms of intuition" which structure all experience, and therefore that, while " things-in-themselves" exist and contribute to experience, they are nonetheless distinct from the objects of experience. From this it follows that the objects of experience are mere "appearances", and that the nature of things as they are in themselves is unknowable to us. In an attempt to counter the skepticism he found in the writings of philosopher David Hume, he wrote the '' Critique of Pure Reason'' (1781/1787), one of his most well-known works. In it, he developed his theory of expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
