Knowledge (philosophy) - Knowledge (philosophy) In philosophy, Knowledge is usually defined as beliefs that are justified, true and actionable. Any description, hypothesis, concept, theory, or principle which fits this definition would be considered knowledge. Philosophy generally discusses propositional knowledge rather than know-how. The traditional way of gaining knowledge has been by accepting the teachings of generally recognized authorities of the past. These could be philosophical, religious or scientific teachings. A second way to derive knowledge is by observation and experiment: the scientific method. (Knowledge gained by observation was ignored or rejected by many classical religious authorities.) Knowledge is also be derived by reason and logic, and by mathematics. Table of contents showTocToggle("show","hide") 1 Defining knowledge 2 Inferential vs. factual knowledge 3 Ways to obtain knowledge 3.1 Practical limits for obtaining.
Greek philosophy - Greek philosophy Classical (or "early") Greek philosophy focused on the role of reason and inquiry. In many ways it paved the way both to modern science and to modern philosophy. Clear unbroken lines of influence lead from early Greek philosophers, through early Muslim philosophy to the Renaissance, the Enlightenment, and the secular sciences of the modern day. Table of contents showTocToggle("show","hide") 1 Pre-Socratic Philosophers 2 Socrates 3 Plato 4 Aristotle 5 Later Classical philosophers 6 The Neo-Platonists 7 Schools of thought in the Hellenistic period Pre-Socratic Philosophers The history of philosophy in the west begins with the Greeks, and particularly with a group of philosophers commonly called the pre-Socratics. This is not to deny the occurrence of other pre-philosophical rumblings in Egyptian, Semitic and Babylonian cultures. Certainly.
Universe (mathematics) - Universe (mathematics) In mathematics, and particularly in applications to set theory and the foundations of mathematics, a universe is, roughly speaking, a class that is large enough to contain (in some sense) all of the sets that one may wish to use. Table of contents showTocToggle("show","hide") 1 In a specific context 2 In ordinary mathematics 3 In set theory 4 In category theory In a specific context There are several precise versions of this general idea. Perhaps the simplest is that any set can be a universe, so long as you are studying that particular set. So if you're studying the real numbers, then the real line R, which is the set of all real numbers, could be your universe. Implicitly, this is the universe that Georg.
Foundations of mathematics - Foundations of mathematics The term "foundations of mathematics" is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory and model theory. The search for foundations of mathematics is however also the central question of the philosophy of mathematics: on what ultimate basis can mathematical statements be called "true"? The current dominant mathematical paradigm is based on axiomatic set theory and formal logic. Virtually all mathematical theorems today can be formulated as theorems of set theory. The truth of a mathematical statement, in this view, is then nothing but the claim that the statement can be derived from the axioms of set theory using the rules of formal logic. This formalistic approach does not explain several issues: why we should.
Foundations problem in mathematics - Foundations problem in mathematics The foundations problem in mathematics was the late 19th century and early 20th century term for the search for the simplest metamathematics. After several schools of the philosophy of mathematics met limitations one after the other in the 20th century, the assumption that any foundation could be successfully modelled within mathematics itself began to be heavily challenged. Today one refers more ambiguously to the foundations of mathematics to avoid giving the impression that there is a 'problem' that can be solved in the sense of a science or mathematics problem, with a single right answer that is checked by means describable in proof theory. The term 'foundations problem' only occurs in literature that makes the assumption that there is such a provable and single.
Ancient philosophy - Ancient philosophy Ancient Philosophy -- Western. Pre-Socratic Philosophers: The history of Philosophy in the west begins with the Greeks, and particularly with a group of philosophers commonly called the pre-Socratics. This is not to say that there were not other pre-philosophical rumblings in Egyptian, Semitic, and Babylonian cultures. Certainly there were great thinkers and writers in each of these cultures, and there is evidence that some of the earliest Greek philosophers may have had contact with at least some of the products of Egyptian and Babylonian thought. However, the early Greek thinkers add at least one element which differentiates their thought from all those who came before them. For the first time in history, we discover in their writings something more than dogmatic assertions about the way.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - The Unreasonable Effectiveness of Mathematics in the Natural Sciences The Unreasonable Effectiveness of Mathematics in the Natural Sciences, published by physicist Eugene Wigner in 1960, argues that the capacity of mathematics to successfully predict events in physics cannot be a coincidence, but must reflect some larger or deeper or simpler truth in both. Table of contents showTocToggle("show","hide") 1 The Miracle of Mathematics in the Natural Sciences 2 The Deep Connection between Science and Mathematics 2.1 References The Miracle of Mathematics in the Natural Sciences Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says “it is important to point out that the mathematical.
Cognitive science of mathematics - Cognitive science of mathematics The cognitive science of mathematics is a term for the study of mathematical ideas using the techniques of cognitive science. Specifically, it is the search for foundations of mathematics in human cognition. This approach was long preceded by the study, in cognitive sciences proper, of human cognitive bias, especially in statistical thinking, most notably by Amos Tversky and Daniel Kahneman, including theories of measurement, risk and behavioral finance from these and other authors. These studies suggested that mathematical practice and perhaps even mathematics proper had little direct relevance to how people think about mathematical concepts. It seemed useful to ask where, if not from intuition, formal mathematics came from? One central claim that justifies a cognitive science of mathematics is that Euler's Identity reflects.
Karlheinz Brandenburg - 3, more commonly known as MP3. 1980 Master of Science in Electrical engineering 1982 Master of Science in Mathematics 1989 Doctor of Philosophy in Electrical engineering 1989 - 1990 worked at AT&T Bell Labs, USA 1990 returned to Erlangen to research on audio coding techniques 1993 appointed head at the Fraunhofer Institute für Integrierte Schaltungen (Fraunhofer IIS-A) He also authored a book called Applications of Digital Signal Processing to Audio and Acoustics. He currently holds 24 different patents on audio coding techniques, with several more pending..
Kurt Gödel - Publications 3 Further Reading 4 External Link Short Biography Childhood Kurt Gödel was born April 28, 1906, in Brno, Austria-Hungary (now Czech Republic) as the son of the manager of a textile factory. In his family little Kurt was known as Der Herr Warum (Mr. Why). He attended German-language primary and secondary school in Brno and completed them with honors in 1923. Although Kurt had first excelled in learning languages he later became more fond of history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for Vienna to go to Medical School at the University of Vienna (UV). Already during his teens Kurt studied Gabelsberger shorthand, Goethe's theory of colors and criticisms of Isaac Newton, and the writings of Kant. Studying in.
James Clerk Maxwell - to the fundamental models of nature. In 1931, on the centennial anniversary of Maxwell's birth, Einstein described Maxwell's work as the "most profound and the most fruitful that physics has experienced since the time of Newton." Algebraic mathematics with elements of geometry are a feature of much of Maxwell's work. Maxwell demonstrated that electric and magnetic forces are two complementary aspects of electromagnetism. He showed that electric and magnetic fields travel through space, in the form of waves, at a constant velocity of 3.0 × 108 m/s. He also proposed that light was a form of electromagnetic radiation. The scientific compound derived CGS unit measuring magnetic flux (commonly abbreviated as f ), the maxwell (Mx), was named in his honor. There is a mountain range on Venus, Maxwell Montes, named after.
Jacob Abbott - at Andover Theological Seminary in 1821, 1822, and 1824; was tutor in 1824-1825, and from 1825 to 1829 was professor of mathematics and natural philosophy at Amherst College; was licensed to preach by the Hampshire Association in 1826; founded the Mount Vernon School for young ladies in Boston in 1829, and was principal of it in 1829-1833; was pastor of Eliot Congregational Church (which he founded), at Roxbury, Massachusetts in 1834-1835; and was, with his brothers, a founder, and in 1843-1851 a principal of Abbott's Institute, and in 1845--1848 of the Mount Vernon School for boys, in New York City. He was a prolific author, writing juvenile stories, brief histories and biographies, and religious books for the general reader, and a few works in popular science. He died on the October.
Jakob Friedrich Fries - at Barby, Saxony. Having studied theology at the academy of the Moravian brethren at Niesky, and philosophy at theUniversities of Leipzig and Jena, he travelled for some time, and in 1806 became professor of philosophy and elementary mathematics at Heidelberg. Though the progress of his psychological thought compelled him to abandon the positive theology of the Moravians, he retained an appreciation of its spiritual or symbolic significance. His philosophical position with regard to his contemporaries had already been made clear in his critical work Reinhold, Fichte und Schelling (1803), and in the more systematic treatises System der Philosophie als evidente Wissenschaft (1804), Wissen, Glaube und Ahnung (1805). His most important treatise, the Neue oder anthropologische Kritik der Vernunft (2nd ed., 1828-1831), was an attempt to give a new foundation of psychological.
James Spedding - a country squire, and was educated at Bury St Edmunds and Trinity College, Cambridge; there he took a second class in the classical tripos, and was junior optime in mathematics in 1831. In 1835 he entered the colonial office, but he resigned this post in 1841. In 1842 he was secretary to Lord Ashburton on his Americann mission, and in 1855 he became secretary to the Civil Service Commission; but from 1841 onwards he was constantly occupied in his researches into Bacon's life and philosophy. On March 1 1881 he was knocked down by a cab in London, and on the 9th he died of erysipelas. Spedding's great edition of Bacon was begun in 1847 in collaboration with RE Ellis and DD Heath. In 1853 Ellis had to leave the work.
James McKeen Cattell - picture of the family's success one could add political power as well, as James' uncle Alexander Gilmore Cattell represented New Jersey in the United States Senate. By all accounts, Cattell had a happy childhood. He entered Lafayette College in 1876 at the age of sixteen, and graduated in four years with the highest honors. In 1883 the faculty at Lafayette awarded him a M.A., again with highest honors. Despite his later renoun as a scientist, he spent most of his time devouring English literature, although he showed a remarkable gift for mathematics as well. Cattell did not find his calling until after he arrived in Germany for graduate studies, where he met Wilhelm Wundt at the University of Leipzig. Cattell left Germany in 1882 to study at Johns Hopkins University, but.
Jan Lukasiewicz - axiomatizations of classical propositional logic; it has just three axioms and is one of the most used axiomatizations today. He also pursued philosophy, approaching the human aspects of scientific theory-making with ideas similar to those of Karl Popper. Łukasiewicz's Polish Notation of 1920 was at the root of the idea of the recursive stack a last-in, first-out computer memory store invented by Charles Hamblin of the New South Wales University of Technology (NSWUT), and first implemented in 1957. This design led to the English Electric multi-programmed KDF9 computer system of 1963, which had two such hardware register stacks. A similar concept underlies the Reverse Polish Notation (or postfix notation) of Hewlett Packard calculators. Table of contents showTocToggle("show","hide") 1 Life Events 2 External Links 3 Reading Life Events 1878 Born 1890-1902 Studies.
Jean le Rond d'Alembert - Destouches secretly pays for the education of Jean le Rond because he does not want his parentage officially recognised. Studies D'Alembert first visited a private school. The chevalier Destouches left d'Alembert an annuity of 1'200 livres at his death in 1726. Due to the influence of the Destouches family, at the age of twelve d'Alembert entered the Quatre-Nations jansenist collčge (the institution was also known under the name Mazarin). Here he studied philosophy, law, and art, receiving bachelier in 1735. In his later life d'Alembert scorned the Cartesian principles he had been taught by the Jansenists: "physical premotion, innate ideas and the vortices". The Jansenists steered d'Alembert toward an ecclesiastical career, attempting to deter him from pursuits such as poetry and mathematics. Theology was, however, "rather unsubstantial fodder" to d'Alembert. He.
Jef Raskin - The Humane Interface, which in large part builds on his earlier work with the Canon Cat. Raskin received a B.S. Mathematics and B.A. in Philosophy from the State University of New York and an M.S. in Computer Science from the Pennsylvania State University. As an assistant professor at the University of California, San Diego (UCSD), he taught classes ranging from computer science to photography. Raskin joined Apple in January 1978 as the 31st employee. He later hired his former student Bill Atkinson from UCSD to work at Apple, and began the Macintosh project. At the beginning of the new millenium Raskin undertook the building of a system incarnating his concepts of the humane interface, by using Open source elements within his rendition of a ZUI or Zooming User Interface. Links: Jef.
John Wyclif - Early Life 2 Early Career 3 Bases of his Reformatory Activities 4 Political Career 5 Public Declaration of his Ideas 6 Conflict with the Church. 7 Statement Regarding Royal Power 8 Wyclif and the Papacy 9 Attack on Monasticism 10 Relation to the English Bible 11 Activity as a Preacher 12 Anti-Wyclif Synod 13 Last Days 14 Wyclif's Doctrines 15 Basal Positions in Philosophy 16 Attitude toward Speculation 17 Doctrine of Scripture 18 Theology and Christology Realistic 19 Further reading Early Life His family was of early Saxon origin, long settled in Yorkshire. In his day the family was a large one, covering a considerable territory, and its principal seat was Wycliffe-on-Tees, of which Ipreswell was an outlying hamlet. (1324 is the year usually given for Wyclif's birth; Rashdall in the.
John Dalton - himself started teaching. This youthful venture was not successful, the amount he received in fees being only about five shillings a week, and after two years he took to farm work. But he had received some instruction in mathematics from a distant relative, Elihu Robinson, and in 1781 he left his native village to become assistant to his cousin George Bewley, who kept a school at Kendal. There he passed the next twelve years, becoming in 1785, through the retirement of his cousin, joint manager of the school with his elder brother Jonathan. About 1790 he seems to have thought of taking up law or medicine, but his projects met with no encouragement from his relatives and he remained at Kendal till, in the spring of 1793, he moved to Manchester..
