Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• A System of Logic
• A. J. Ayer
• Abstract object
• Abstraction
• Alan Turing
• Alexander Bain
• Alvin Goldman
• Ambiguity
• Analytic philosophy
• Aristotle
• Arthur Schopenhauer
• Averroes
• Baruch Spinoza
• Behaviorism
• Benjamin Lee Whorf
• Bertrand Russell
• C. D. Broad
• Carl Benjamin Boyer
• Carl Jung
• Categorization
• Category (Kant)
• Chinese room
• Class (philosophy)
• Cognition
• Cognitive science
• Concept
• Concept and object
• Concept learning
• Concept map
• Conceptual art
• Conceptual blending
• Conceptual framework
• Conceptual history
• Conceptual model
• Confucius
• Consciousness
• Contrastivism
• Conventionalism
• Conveyed concept
• Cratylism
• Cratylus (dialogue)
• Daniel Dennett
• Deconstruction
• Definitionism
• Derivative
• Dharmakirti
• Dog
• Dover Publications
• Dramatism
• Edmund Husserl
• Edward Sapir
• Emergent materialism
• Entity
• Epiphenomenalism
• Expressivism
• Franz Boas
• Fritz Mauthner
• Fuzzy concept
• G. E. Moore
• Gilbert Ryle
• Gottlob Frege
• Gustav Bergmann
• Hans-Georg Gadamer
• Henri Bergson
• Ibn Khaldun
• Idea
• Ideasthesia
• Immanuel Kant
• Information science
• Ingenuity
• Integral
• Intelligence
• Intension
• Intentionality
• Introspection
• J. L. Austin
• Jacques Derrida
• John Locke
• John Searle
• John Stuart Mill
• Kant
• Karl Popper
• Kurt Gödel
• Language
• Language of thought
• Leonard Bloomfield
• Lev Vygotsky
• Limit (mathematics)
• Limited Inc
• Linguistics
• Logic
• Logical atomism
• Logical form
• Logical positivism
• Ludwig Wittgenstein
• Martin Heidegger
• Marvin Minsky
• Materialism
• Meme
• Mental event
• Mental image
• Mental process
• Mental property
• Metalanguage
• Metaphors
• Metaphysics
• Mind
• Mind–body problem
• MIT Press
• Monism
• Naïve realism
• Ned Block
• Neutral monism
• Nietzsche
• Noam Chomsky
• Nominalism
• Non-cognitivism
• Notion (philosophy)
• Object (philosophy)
• Of Grammatology
• P. F. Strawson
• Pain (philosophy)
• Paul Grice
• Paul Ricœur
• Paul Tillich
• Perception
• Phallogocentrism
• Phenomenalism
• Philosophical logic
• Philosophy
• Philosophy of mind
• Philosophy of self
• Physicalism
• Plato
• Pragmatics
• Pragmatism
• Predicate (grammar)
• Property dualism
• Proposition
• Pyrrhonism
• Qualia
• Quality (philosophy)
• Quietism
• Recept
• Red
• Relevance theory
• René Descartes
• Rhetoric
• Richard Rorty
• Rudolf Carnap
• Saul Kripke
• Schema (Kant)
• Scholasticism
• Semantic externalism
• Semantic holism
• Semantics
• Semiotica
• Semiotics
• Sense and reference
• Set (mathematics)
• Sign (semiotics)
• Social construction
• Solipsism
• Speech act
• Statement (logic)
• Stoicism
• Structuralism
• Substance dualism
• Supposition theory
• Symbiosism
• Symbol
• Symbol grounding
• Søren Kierkegaard
• Tabula rasa
• Thomas Hobbes
• Thomas Nagel
• Truth-bearer
• Type physicalism
• Understanding
• Vasubandhu
• Verification theory
• Wikisource
• Wilhelm von Humboldt
• William James
• Xun Zi
• Zhuangzi
• 
  

• MIT Press
  The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States).
  The MIT Press traces its origins back to 1926 when MIT published under its own name a lecture series entitled Problems of Atomic Dynamics given by the visiting German physicist and later Nobel Prize winner, Max Born. Six years later, MIT's publishing operations were first formally instituted by the creation of an imprint called Technology Press in 1932. This imprint was founded by James R. Killian, Jr., at the time editor of MIT's alumni magazine and later to become MIT president.
  Technology Press published eight titles independently, then in 1937 entered into an arrangement with John Wiley & Sons in which Wiley took over marketing and editorial responsibilities. In 1962 the association with Wiley came to an end after a further 125 titles had been published. The press acquired its modern name after this separation, and has since functioned as an independent publishing house.
  
  wn.com/MIT_Press

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  Alan Turing
  Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence.
  During the Second World War, Turing worked for the Government Code and Cypher School (GCCS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
  After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s.
  
  wn.com/Alan_Turing
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  Alexander Bain
  Alexander Bain (11 June 1818 – 18 September 1903) was a Scottish philosopher and educationalist in the British school of empiricism who was a prominent and innovative figure in the fields of psychology, linguistics, logic, moral philosophy and education reform. He founded Mind, the first ever journal of psychology and analytical philosophy, and was the leading figure in establishing and applying applying the scientific method to psychology. Bain was the inaugural Regius Chair in Logic and Professor of Logic at the University of Aberdeen, where he also held Professorships in Moral Philosophy and English Literature and was twice elected Lord Rector of the University of Aberdeen.
  Alexander Bain was born in Aberdeen, Scotland to George Bain, a weaver and veteran soldier, and Margaret Paul. At age eleven he left school to work as a weaver hence the description of him as Weevir, rex philosophorum. He also took to lectures at the Mechanics' Institutes of Aberdeen and the Aberdeen Public Library.
  
  wn.com/Alexander_Bain
• Alvin Goldman
  Alvin Ira Goldman (born 1938) is an American professor of Philosophy at Rutgers University in New Jersey. He previously taught at the University of Michigan and at the University of Arizona. He earned his PhD from Princeton University and is married to Holly Smith, a well known ethicist, former administrator, and current professor at Rutgers University. He has done influential work on a wide range of philosophical topics, but his principal areas of research are epistemology, philosophy of mind, and cognitive science.
  Goldman's early book, A Theory of Human Action (a revised version of his Ph.D. thesis), presents a systematic way of classifying and relating the many actions we perform at any time. Its influence was broad and can be found in, among other writings, John Rawls' book A Theory of Justice. Goldman's early work in action theory soon gave way to work in other branches of philosophy, most influentially epistemology.
  
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  Aristotle
  Aristotle (Ancient Greek: Ἀριστοτέλης, Aristotélēs) (384 BC – 322 BC) was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. Together with Plato and Socrates (Plato's teacher), Aristotle is one of the most important founding figures in Western philosophy. Aristotle's writings were the first to create a comprehensive system of Western philosophy, encompassing morality, aesthetics, logic, science, politics, and metaphysics.
  Aristotle's views on the physical sciences profoundly shaped medieval scholarship, and their influence extended well into the Renaissance, although they were ultimately replaced by Newtonian physics. In the zoological sciences, some of his observations were confirmed to be accurate only in the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic. In metaphysics, Aristotelianism had a profound influence on philosophical and theological thinking in the Islamic and Jewish traditions in the Middle Ages, and it continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues (Cicero described his literary style as "a river of gold"), it is thought that the majority of his writings are now lost and only about one-third of the original works have survived.
  
  wn.com/Aristotle
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  Arthur Schopenhauer
  Arthur Schopenhauer (22 February 1788 – 21 September 1860) was a German philosopher known for his pessimism and philosophical clarity. At age 25, he published his doctoral dissertation, On the Fourfold Root of the Principle of Sufficient Reason, which examined the four separate manifestations of reason in the phenomenal world.
  Schopenhauer's most influential work, The World as Will and Representation, claimed that the world is fundamentally what humans recognize in themselves as their will. His analysis of will led him to the conclusion that emotional, physical, and sexual desires can never be fully satisfied. The corollary of this is an ultimately painful human condition. Consequently, he considered that a lifestyle of negating desires, similar to the ascetic teachings of Vedanta, Buddhism and the Church Fathers of early Christianity, was the only way to attain liberation.
  Schopenhauer's metaphysical analysis of will, his views on human motivation and desire, and his aphoristic writing style influenced many well-known thinkers, including Friedrich Nietzsche,Richard Wagner, Ludwig Wittgenstein, Erwin Schrödinger, Albert Einstein,Sigmund Freud, Otto Rank, Carl Jung, Joseph Campbell, Leo Tolstoy, Thomas Mann, and Jorge Luis Borges.
  
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  Averroes
  ʾAbū l-Walīd Muḥammad bin ʾAḥmad bin Rušd (Arabic: أبو الوليد محمد بن احمد بن رشد‎), better known just as Ibn Rushd (Arabic: ابن رشد‎), and in European literature as Averroes ( /əˈvɛroʊ.iːz/; April 14, 1126 – December 10, 1198), was an Andalusian Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy, geography, mathematics, physics and celestial mechanics. He was born in Córdoba, Al Andalus, modern-day Spain, and died in Marrakesh, Morocco. His school of philosophy is known as Averroism.
  Ibn Rushd was a defender of Aristotelian philosophy against claims from the influential Islamic theologian Ghazali who attacked philosophy so it would not become an affront to the teachings of Islam.
  Averroes' name is also seen as Averroës, Averroès or Averrhoës, indicating that the "o" and the "e" form separate syllables. Averroes is a Latinisation of a Hebrew transcription of the Arab name Ibn Rushd.
  
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  Baruch Spinoza
  Baruch Spinoza and later Benedict de Spinoza (24 November 1632 – 21 February 1677) was a Dutch philosopher. Revealing considerable scientific aptitude, the breadth and importance of Spinoza's work was not fully realized until years after his death. By laying the groundwork for the 18th century Enlightenment^{[citation needed]} and modern biblical criticism, he came to be considered one of the great rationalists of 17th-century philosophy. His magnum opus, the posthumous Ethics, in which he opposed Descartes's mind–body dualism, has earned him recognition as one of Western philosophy's most important contributors. In the Ethics, "Spinoza wrote the last indisputable Latin masterpiece, and one in which the refined conceptions of medieval philosophy are finally turned against themselves and destroyed entirely." Philosopher Georg Wilhelm Friedrich Hegel said of all contemporary philosophers, "You are either a Spinozist or not a philosopher at all."
  Spinoza's name in different languages is Hebrew: ברוך שפינוזה‎ Baruch Spinoza, Portuguese: Benedito or Bento de Espinosa and Latin: Benedictus de Spinoza; in all these languages, the given name means "the Blessed". Spinoza was raised in the Portuguese Jewish community in Amsterdam. He developed highly controversial ideas regarding the authenticity of the Hebrew Bible and the nature of the Divine. The Jewish religious authorities issued a cherem (Hebrew: חרם, a kind of ban, shunning, ostracism, expulsion, or excommunication) against him, effectively excluding him from Jewish society at age 23. His books were also later put on the Catholic Church's Index of Forbidden Books.
  
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  Benjamin Lee Whorf
  Benjamin Lee Whorf (April 24, 1897 in Winthrop, Massachusetts – July 26, 1941) was an American linguist. Whorf is widely known for his ideas about linguistic relativity, the hypothesis that language influences thought. An important theme in many of his publications, he has been credited as one of the fathers of this approach, often referred to as the "Sapir–Whorf hypothesis", named after him and his mentor Edward Sapir. Originally educated as a chemical engineer, he took up an interest in linguistics, studying with Sapir at Yale University. In the last ten years of his life he dedicated his spare time to linguistic studies, doing field work on Native American languages in the United States and Mexico. He managed to become one of the most influential linguists of his time, even while still working as a fire inspector for the Hartford Fire Insurance Company. He wrote a grammar of the Hopi language, studies of Nahuatl dialects, Maya hieroglyphic writing, and the first attempt at a reconstruction of Uto-Aztecan. He also published many articles in the most prestigious linguistic journals, many of them dealing with the ways in which he saw that different linguistic systems affected the thought systems and habitual behaviour of language users.
  
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  Bertrand Russell
  Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.
  Russell led the British "revolt against idealism" in the early 20th century. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his friend Ludwig Wittgenstein, and is widely held to be one of the 20th century's premier logicians. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science (see type theory and type system), and philosophy, especially philosophy of language, epistemology, and metaphysics.
  
  wn.com/Bertrand_Russell
• Carl Benjamin Boyer
  Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was a historian of sciences, and especially mathematics. David Foster Wallace called him the "Gibbon of math history". He wrote the books History of Analytic Geometry, The History of the Calculus and Its Conceptual Development, A History of Mathematics, and The Rainbow: From Myth to Mathematics. He served as book-review editor of Scripta Mathematica.
  Boyer was valedictorian of his high school class. He received an A.B. from Columbia College in 1928 and an M.A. in 1929. He received his Ph.D. in Mathematics from Columbia University in 1939.
  He was a full professor of Mathematics at Brooklyn College from 1952 until his death, although he had begun tutoring and teaching at Brooklyn College in 1928.
  Boyer was instrumental as an inspiration to the founding of The Metropolitan New York Section of the History of Science Society.
  He was a 1954 John Simon Guggenheim Memorial Foundation Fellow in History of Science & Technology.
  He died of a heart attack in New York in 1976.
  
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  Carl Jung
  Carl Gustav Jung (/ˈjʊŋ/ YUUNG; German: [ˈkarl ˈɡʊstaf ˈjʊŋ]; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, the founder of analytical psychology. Jung is considered the first modern psychiatrist to view the human psyche as "by nature religious" and make it the focus of exploration. Jung is one of the best known researchers in the field of dream analysis and symbolization. While he was a fully involved and practicing clinician, much of his life's work was spent exploring tangential areas, including Eastern and Western philosophy, alchemy, astrology, and sociology, as well as literature and the arts.
  Jung considered individuation, a psychological process of integrating the opposites including the conscious with the unconscious while still maintaining their relative autonomy, necessary for a person to become whole. Individuation is the central concept of analytical psychology.
  Many psychological concepts were first proposed by Jung, including the archetype, the collective unconscious, the complex, and synchronicity. Popular psychometric instruments like the Myers-Briggs Type Indicator (MBTI), have been principally developed from Jung's theories.
  
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  Confucius
  Confucius (551–479 BC) was a Chinese teacher, editor, politician, and philosopher of the Spring and Autumn Period of Chinese history.
  The philosophy of Confucius emphasized personal and governmental morality, correctness of social relationships, justice, and sincerity. His followers competed successfully with many other schools during the Hundred Schools of Thought era only to be suppressed in favor of the Legalists during the Qin Dynasty. Following the victory of Han over Chu after the collapse of Qin, Confucius's thoughts received official sanction and were further developed into a system known as Confucianism.
  Confucius is traditionally credited with having authored or edited many of the Chinese classic texts including all of the Five Classics, but modern scholars are cautious of attributing specific assertions to Confucius himself. Aphorisms concerning his teachings were compiled in the Analects, but only many years after his death.
  Confucius's principles had a basis in common Chinese tradition and belief. He championed strong family loyalty, ancestor worship, respect of elders by their children (and in traditional interpretations of husbands by their wives), and family as a basis for ideal government. He espoused the well-known principle "Do not do to others what you do not want done to yourself", an early version of the Golden Rule.
  
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  Daniel Dennett
  Daniel Clement Dennett (born March 28, 1942) is an American philosopher, writer and cognitive scientist whose research centers on the philosophy of mind, philosophy of science and philosophy of biology, particularly as those fields relate to evolutionary biology and cognitive science. He is currently the Co-director of the Center for Cognitive Studies, the Austin B. Fletcher Professor of Philosophy, and a University Professor at Tufts University. Dennett is a firm atheist and secularist, a member of the Secular Coalition for America advisory board, as well as an outspoken supporter of the Brights movement. Dennett is referred to as one of the "Four Horsemen of New Atheism," along with Richard Dawkins, Sam Harris, and the late Christopher Hitchens.
  Born in Boston, Massachusetts, Dennett spent part of his childhood in Lebanon, where, during World War II, his father was a covert counter-intelligence agent with the Office of Strategic Services posing as a cultural attaché to the American Embassy in Beirut. When he was five, his mother took him back to Massachusetts after his father died in an unexplained plane crash. His sister is the investigative journalist Charlotte Dennett.
  
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  Dharmakirti
  Dharmakīrti (ca. 7th century) also known as Serlingpa Dharmakīrti or Suvarnadvipi Dharmakīrti, was a Buddhist scholar of Srivijayan origin, Suvarnadvipa (Sumatra). He was one of the Buddhist founders of Indian philosophical logic. He was one of the primary theorists of Buddhist atomism, according to which the only items considered to exist are momentary states of consciousness.
  Born around the turn of the 7th century in Sumatra, Dharmakirti was a Srivijayan prince of Sailendra dynasty. He became a revered scholar monk in Srivijaya and moved to India to became a teacher at the famed Nalanda University, as well as a poet. He built on and reinterpreted the work of Dignaga, the pioneer of Buddhist Logic, and was very influential among Brahman logicians as well as Buddhists. His theories became normative in Tibet and are studied to this day as a part of the basic monastic curriculum.
  Collins (2000: p. 240) colourfully contextualized Dharmakirti and his experience of disaffection and collegiate misunderstanding at Nalanda:-
  
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  Edmund Husserl
  Edmund Gustav Albrecht Husserl (German pronunciation: [ˈhʊsɛʁl]; April 8, 1859, Proßnitz, Moravia, Austrian Empire – April 26, 1938, Freiburg, Germany) was a philosopher and mathematician and the founder of the 20th century philosophical school of phenomenology. He broke with the positivist orientation of the science and philosophy of his day, yet he elaborated critiques of historicism and of psychologism in logic. Not limited to empiricism, but believing that experience is the source of all knowledge, he worked on a method of phenomenological reduction by which a subject may come to know directly an essence.
  Although born into a Jewish family, Husserl was baptized as a Lutheran in 1886. He studied mathematics under Karl Weierstrass and Leo Königsberger, and philosophy under Franz Brentano and Carl Stumpf. Husserl himself taught philosophy as a Privatdozent at Halle from 1887, then as professor, first at Göttingen from 1901, then at Freiburg from 1916 until he retired in 1928. Thereafter he gave two notable lectures: at Paris in 1929, and at Prague in 1935. The notorious 1933 race laws of the Nazi regime took away his academic standing and privileges. Following an illness, he died at Freiburg in 1938.
  
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  Edward Sapir
  Edward Sapir (/səˈpɪər/; 1884–1939) was an American anthropologist-linguist, widely considered to be one of the most important figures in the early development of the discipline of linguistics.
  Born in German Pomerania, his parents emigrated to America when Sapir was a child. He studied Germanic linguistics at Columbia, where he came under the influence of Franz Boas who inspired him to work on Native American languages. While finishing his PhD he went to California to work with Alfred Kroeber documenting the indigenous languages there. He was employed by the Geological Survey of Canada for fifteen years, where he came into his own as one of the most influential and important linguists in North America. He was offered a professorship at the University of Chicago, and stayed for several years continuing to work for the professionalization of the discipline of linguistics. By the end of his life he was Professor of Anthropology at Yale, where he never really fit in. Among his many students were the linguists Mary Haas and Morris Swadesh, and anthropologists such as Fred Eggan and Hortense Powdermaker.
  
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  Franz Boas
  Franz Boas (/ˈfrɑːnz ˈboʊ.æz/; July 9, 1858 – December 21, 1942) was a German-American anthropologist and a pioneer of modern anthropology who has been called the "Father of American Anthropology" and "the Father of Modern Anthropology." Like many such pioneers, he trained in other disciplines; he received his doctorate in physics, and did post-doctoral work in geography. He applied the scientific method to the study of human cultures and societies; previously this discipline was based on the formulation of grand theories around anecdotal knowledge.
  Boas once summed up his approach to anthropology and folklore by saying: "In the course of time I became convinced that a materialistic point of view, for a physicist a very real one, was untenable. This gave me a new point of view and I recognized the importance of studying the interaction between the organic and inorganic, above all the relation between the life of a people and their physical environment."
  Franz Uri Boas was born in Minden, Westphalia. Although his grandparents were observant Jews, his parents embraced Enlightenment values, including their assimilation into modern German society. Boas’s parents were educated, well-to-do, and liberal; they did not like dogma of any kind. Due to this, Boas was granted the independence to think for himself and pursue his own interests. Early in life he displayed a penchant for both nature and natural sciences. Boas vocally opposed anti-Semitism and refused to convert to Christianity, he did not identify himself as a Jew; indeed, according to his biographer, "He was an 'ethnic' German, preserving and promoting German culture and values in America." In an autobiographical sketch, Boas wrote:
  
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• Fritz Mauthner
  Fritz Mauthner (22 November 1849 – 29 June 1923) was a journalist and philosopher from Horschitz, Bohemia.
  He became editor of the Berliner Tageblatt in 1895, but is best known for his Beiträge zu einer Kritik der Sprache (Contributions to a Critique of Language), published in three parts in 1901 and 1902. Ludwig Wittgenstein took several of his ideas from Mauthner, and acknowledges him in his Tractatus Logico-Philosophicus (1922).
  Mauthner died in Meersburg.
  
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• Gilbert Ryle
  Gilbert Ryle (19 August 1900, Brighton – 6 October 1976, Oxford), was a British philosopher, a representative of the generation of British ordinary language philosophers that shared Wittgenstein's approach to philosophical problems, and is principally known for his critique of Cartesian dualism, for which he coined the phrase "the ghost in the machine". Some of his ideas in the philosophy of mind have been referred to as "behaviourist." Ryle's best known book is The Concept of Mind (1949), in which he writes that the "general trend of this book will undoubtedly, and harmlessly, be stigmatised as 'behaviourist'." Ryle, having engaged in detailed study of the key works of Bernard Bolzano, Franz Brentano, Alexius Meinong, Edmund Husserl, and Martin Heidegger, himself suggested instead that the book "could be described as a sustained essay in phenomenology, if you are at home with that label."
  Ryle was born in Brighton, England in 1900 and grew up in an environment of learning. His father was a Brighton doctor, a generalist who had interests in philosophy and astronomy, and passed on to his children an impressive library. Ryle was educated at Brighton College, and in 1919, he went up to Queen's College at Oxford, initially to study Classics but was quickly drawn to Philosophy. He would graduate with first class honours in 1924 and was appointed to a lectureship in Philosophy at Christ Church, Oxford. A year later, he was to become a tutor. Ryle remained at Christ Church until World War II.
  
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  Gottlob Frege
  Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925, pronounced [ˈɡɔtloːp ˈfreːɡə ]) was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on the philosophy of language and mathematics. While he was mainly ignored by the intellectual world when he published his writings, Giuseppe Peano (1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of logicians and philosophers.
  Frege was born in 1848 in Wismar, in the state of Mecklenburg-Schwerin (the modern German federal state Mecklenburg-Vorpommern). His father Carl (Karl) Alexander Frege (3 August 1809 – 30 November 1866) was the co-founder and headmaster of a girls' high school until his death. After Carl's death, the school was led by Frege's mother Auguste Wilhelmine Sophie Frege (née Bialloblotzky, 12 January 1815 – 14 October 1898).
  
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• Gustav Bergmann
  Gustav Bergmann (May 4, 1906, Vienna – April 21, 1987, Iowa City) was a philosopher born in Vienna, Austria. He studied at the University of Vienna and was a member of the Vienna Circle. In the United States, he was a professor of philosophy and psychology at the University of Iowa.
  Bergmann earned his Ph.D. in mathematics at the University of Vienna in 1928. While studying for his doctorate, he was invited to join the Vienna Circle, a group of philosophers, mathematicians, scientists, and others committed to a scientific worldview under the name of logical positivism. In 1930-31, he worked with Albert Einstein in Berlin. Unable as a Jew to find academic employment, Bergmann obtained a law degree from the University of Vienna in 1935, and practiced corporation law until he and his family fled to the United States in 1938. Settling at the University of Iowa in Iowa City in 1939, Bergmann eventually became professor of both philosophy and psychology.
  
  
  
  
  
  
  
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• Henri Bergson
  Henri-Louis Bergson (French pronunciation: [bɛʁksɔn] 18 October 1859 – 4 January 1941) was a major French philosopher, influential especially in the first half of the 20th century. Bergson convinced many thinkers that immediate experience and intuition are more significant than rationalism and science for understanding reality.
  He was awarded the 1927 Nobel Prize in Literature "in recognition of his rich and vitalizing ideas and the brilliant skill with which they have been presented".
  Bergson was born in the Rue Lamartine in Paris, not far from the Palais Garnier (the old Paris opera house) in 1859 (the year in which France emerged as a victor in the Second Italian War of Independence, and in the month before the publication of Charles Darwin's On the Origin of Species). His father, the pianist Michał Bergson, was of a Polish Jewish family background (originally bearing the name Bereksohn). His mother, Katherine Levison, daughter of a Yorkshire doctor, was from an English and Irish Jewish background. The Bereksohns were a famous^{[citation needed]} Jewish entrepreneurial family of Polish descent. Henri Bergson's great-great-grandfather, Szmul Jakubowicz Sonnenberg, called Zbytkower, was a prominent banker and a protégé of Stanisław August Poniatowski, King of Poland from 1764 to 1795.
  
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  Ibn Khaldun
  Ibn Khaldūn or Ibn Khaldoun (full name, Arabic: أبو زيد عبد الرحمن بن محمد بن خلدون الحضرمي ‎, Abū Zayd ‘Abdu r-Raḥmān bin Muḥammad bin Khaldūn Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the forerunners of modern historiography,sociology and economics.
  He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world.
  Ibn Khaldun's life is relatively well-documented, as he wrote an autobiography (التعريف بابن خلدون ورحلته غربا وشرقا; Al-Taʻrīf bi Ibn-Khaldūn wa Riħlatuhu Gharbān wa Sharqān) in which numerous documents regarding his life are quoted word-for-word. However, the autobiography has little to say about his private life, so little is known about his family background. Generally known as "Ibn Khaldūn" after a remote ancestor, he was born in Tunis in AD 1332 (732 A.H.) into an upper-class Andalusian family, the Banū Khaldūn. His family, which held many high offices in Andalusia, had emigrated to Tunisia after the fall of Seville to Reconquista forces around the middle of the 13th century. Under the Tunisian Hafsid dynasty some of his family held political office; Ibn Khaldūn's father and grandfather however withdrew from political life and joined a mystical order. His brother, Yahya Ibn Khaldun, was also a historian who wrote a book on the Abdalwadid dynasty, and who was assassinated by a rival for being the official historiographer of the court.
  
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  Immanuel Kant
  Immanuel Kant (German pronunciation: [ɪˈmaːnu̯eːl ˈkant]; 22 April 1724 – 12 February 1804) was a German philosopher from Königsberg (today Kaliningrad of Russia), who researched, lectured, and wrote on philosophy and anthropology during the Enlightenment at the end of the 18th century. At the time, there were major successes and advances in the sciences (for example, Isaac Newton, Carl Friedrich Gauss, and Robert Boyle) applying reason and logic.
  Kant’s major work, the Critique of Pure Reason (Kritik der reinen Vernunft, 1781), aimed to unite reason with experience to move beyond what he took to be failures of traditional philosophy and metaphysics. He hoped to end an age of speculation where objects outside experience were used to support what he saw as futile theories, while opposing the skepticism of thinkers such as Descartes, Berkeley and Hume.
  He stated:
  Kant proposed a ‘Copernican Revolution’ in reverse, saying that:
  Kant published other important works on ethics, religion, law, aesthetics, astronomy, and history. These included the Critique of Practical Reason (Kritik der praktischen Vernunft, 1788) and the Metaphysics of Morals (Die Metaphysik der Sitten, 1797), which dealt with ethics. And the Critique of Judgment (Kritik der Urteilskraft, 1790), which looks at aesthetics and teleology. He aimed to resolve disputes between empirical and rationalist approaches. The former asserted that all knowledge comes through experience; the latter maintained that reason and innate ideas were prior. Kant argued that experience is purely subjective without first being processed by pure reason. He also said that using reason without applying it to experience only leads to theoretical illusions. The free and proper exercise of reason by the individual was both a theme of the Enlightenment, and of Kant's approaches to the various problems of philosophy.
  
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• Jacques Derrida
  Jacques Derrida ( /ʒɑːk ˈdɛrɨdə/; French pronunciation: [ʒak dɛʁida]; July 15, 1930 – October 9, 2004) was a French philosopher, born in French Algeria. He developed the critical theory known as deconstruction and his work has been labeled as post-structuralism and associated with postmodern philosophy.
  His more than 40 published books, together with essays and public speaking, has had a significant impact upon the humanities, particularly on Anthropology, Sociology, Semiotics, Jurisprudence, Literary Theory and Cultural Studies in general. His influence in the academe in Continental Europe, South America and all countries where continental philosophy is predominant, is enormous; becoming crucial in debates around Ontology, Epistemology (especially concerning Social Sciences), Ethics, Esthetics, Hermeneutics and Philosophy of Language.
  His work also influenced architecture (in the form of deconstructivism), music and plastic arts. and art critics. Particularly in his later writings, he frequently addressed ethical and political themes, and his work influenced various activist and other political movements.
  
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  John Locke
  John Locke FRS ( /ˈlɒk/; 29 August 1632 – 28 October 1704), widely known as the Father of Classical Liberalism, was an English philosopher and physician regarded as one of the most influential of Enlightenment thinkers. Considered one of the first of the British empiricists, following the tradition of Francis Bacon, he is equally important to social contract theory. His work had a great impact upon the development of epistemology and political philosophy. His writings influenced Voltaire and Rousseau, 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.
  Locke's theory of mind is often cited as the origin of modern conceptions of identity and the self, figuring prominently in the work of later philosophers such as Hume, Rousseau and Kant. Locke was the first to define the self through a continuity of consciousness. He postulated that the mind was a blank slate or tabula rasa. Contrary to pre-existing Cartesian philosophy, he maintained that we are born without innate ideas, and that knowledge is instead determined only by experience derived from sense perception.
  
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  John Searle
  John Rogers Searle (born July 31, 1932, in Denver, Colorado) is an American philosopher and currently the Slusser Professor of Philosophy at the University of California, Berkeley. Widely noted for his contributions to the philosophy of language, philosophy of mind and social philosophy, he began teaching at Berkeley in 1959, where, among his many distinctions, he was the first tenured professor to join the Free Speech Movement. He received the Jean Nicod Prize in 2000, and the National Humanities Medal in 2004. Among his notable concepts are the "Chinese Room" argument against artificial intelligence.
  Searle's father, G. W. Searle, an electrical engineer, was employed by AT&T, while his mother, Hester Beck Searle, was a physician. John Searle began his college education at the University of Wisconsin-Madison, and subsequently became a Rhodes Scholar at Oxford University, where he earned an undergraduate degree and a doctorate in philosophy and ethics.
  In the 1950s, as an undergraduate at the University of Wisconsin, Searle was the secretary of "Students against Joseph McCarthy" (McCarthy was then the junior Senator from Wisconsin).
  
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  John Stuart Mill
  John Stuart Mill, FRSE (20 May 1806 – 8 May 1873) was a British philosopher, political economist and civil servant. He was an influential contributor to social theory, political theory, and political economy. He has been called "the most influential English-speaking philosopher of the nineteenth century". Mill's conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of utilitarianism, an ethical theory developed by Jeremy Bentham. Hoping to remedy the problems found in an inductive approach to science, such as confirmation bias, he clearly set forth the premises of falsification as the key component in the scientific method. Mill was also a Member of Parliament and an important figure in liberal political philosophy.
  John Stuart Mill was born on Rodney Street in the Pentonville area of London, the eldest son of the Scottish philosopher, historian and economist James Mill, and Harriet Burrow. John Stuart was educated by his father, with the advice and assistance of Jeremy Bentham and Francis Place. He was given an extremely rigorous upbringing, and was deliberately shielded from association with children his own age other than his siblings. His father, a follower of Bentham and an adherent of associationism, had as his explicit aim to create a genius intellect that would carry on the cause of utilitarianism and its implementation after he and Bentham had died.
  
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  Karl Popper
  Sir Karl Raimund Popper, CH FRSFBA (28 July 1902 – 17 September 1994) was an Austro-Britishphilosopher and professor at the London School of Economics. He is generally regarded as one of the greatest philosophers of science of the 20th century; he also wrote extensively on social and political philosophy.
  Popper is known for his attempt to repudiate the classical observationalist/inductivist form of scientific method in favour of empirical falsification. He is also known for his opposition to the classical justificationist account of knowledge which he replaced with critical rationalism, "the first non justificational philosophy of criticism in the history of philosophy". In political discourse, he is known for his vigorous defence of liberal democracy and the principles of social criticism that he came to believe made a flourishing "open society" possible.
  Karl Popper was born in Vienna (then in Austria-Hungary) in 1902, to upper middle-class parents. All of Karl Popper's grandparents were Jewish, but the Popper family converted to Lutheranism before Karl was born. Karl's father Simon Siegmund Carl Popper was a lawyer from Bohemia, and mother Jenny Schiff was of Silesian and Hungarian descent. After establishing themselves in Vienna, the Poppers made a rapid social climb in Viennese society: Simon Siegmund Carl became a legal partner^{[clarification needed]} of Vienna's liberal mayor Raimond Grübl and, after his death in 1898, took over the firm (Karl received his middle name from the mayor).
  
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  Kurt Gödel
  Kurt Friedrich Gödel (/ˈkɜrt ɡɜrdəl/; German pronunciation: [ˈkʊʁt ˈɡøːdəl] ( listen); April 28, 1906 – January 14, 1978) was an Austrian/American logician, mathematician, and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.
  Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
  
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• Leonard Bloomfield
  Leonard Bloomfield (April 1, 1887 – April 18, 1949) was an American linguist who led the development of structural linguistics in the United States during the 1930s and the 1940s. His influential textbook Language, published in 1933, presented a comprehensive description of American structural linguistics. He made significant contributions to Indo-European historical linguistics, the description of Austronesian languages, and description of languages of the Algonquian family.
  Bloomfield's approach to linguistics was characterized by its emphasis on the scientific basis of linguistics, adherence to behaviorism especially in his later work, and emphasis on formal procedures for the analysis of linguistic data. The influence of Bloomfieldian structural linguistics declined in the late 1950s and 1960s as the theory of Generative Grammar developed by Noam Chomsky came to predominate.
  Bloomfield was born in Chicago, Illinois on April 1, 1887. His father Sigmund Bloomfield immigrated to the United States as a child in 1868; the original family name Blumenfeld was changed to Bloomfield after their arrival in the United States. In 1896 his family moved to Elkhart Lake, Wisconsin, where he attended elementary school, but returned to Chicago for secondary school. His uncle Maurice Bloomfield was a prominent linguist at Johns Hopkins University, and his aunt Fannie Bloomfield Zeisler was a well-known concert pianist.
  
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• Lev Vygotsky
  Lev Semyonovich Vygotsky (Russian: Лев Семёнович Вы́готский or Выго́тский, born Лев Симхович Выгодский (Lev Simkhovich Vygodsky), November 17 [O.S. November 5] 1896 – June 11, 1934) was a Soviet psychologist, the founder of cultural-historical psychology, and the leader of the Vygotsky Circle. In the early 1920s, his birth name was changed from Vygodskii (with "d") into Vygotskii (with middle "t").
  Lev Vygotsky was born in Orsha, Byelorussia, in the Russian Empire (present-day Belarus) into a nonreligious Jewish family. He was raised in the city of Gomel, where he obtained both public and private education. He was influenced by his cousin, David Vygodsky. Vygotsky was eventually admitted to the Moscow State University through a “Jewish Lottery” to meet a three percent Jewish student quota for entry in Moscow and Saint Petersberg universities. There he studied law, but his thirst for knowledge pushed him to enroll in the “unofficial” “Shanyavskii People’s University”. Upon graduation in 1917, Vygotsky returned to Gomel to teach, “a profession he was now able to practice due to the abolition of the anti-Semitic legislation after the October Socialist Revolution”, and publish "copies of great literary works".
  
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  Ludwig Wittgenstein
  Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947. In his lifetime, he published just one book review, one article, a children's dictionary, and the 75-page Tractatus Logico-Philosophicus (1921). In 1999, his posthumously published Philosophical Investigations (1953) was ranked as the most important book of 20th-century philosophy, standing out as "...the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".Bertrand Russell described him as "the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating".
  Born in Vienna into one of Europe's wealthiest families, he gave away his entire inheritance. Three of his brothers committed suicide, with Ludwig contemplating it too. He left academia several times: serving as an officer on the frontline during World War I, where he was decorated a number of times for his courage; teaching in schools in remote Austrian villages, where he encountered controversy for hitting children when they made mistakes in mathematics; and working during World War II as a hospital porter in London, where he told patients not to take the drugs they were prescribed, and where no-one knew he was one of the world's most famous philosophers. He described philosophy, however, as "the only work that gives me real satisfaction."
  
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  Martin Heidegger
  Martin Heidegger (September 26, 1889 – May 26, 1976); German pronunciation: [ˈmaɐ̯tiːn ˈhaɪdɛɡɐ]) was a German philosopher known for his existential and phenomenological explorations of the "question of Being."
  Heidegger argues that philosophy is preoccupied with what exists and has forgotten the question of the "ground" of being. We find ourselves "always already" fallen into a world that already existed; but he insists that we have forgotten the basic question of what being itself is. This question defines our central nature. He argues that we are practical agents, caring and concerned about our projects in the world, and allowing it to reveal, or "unconceal" itself to us. He also says that our manipulation of reality is often harmful and hides our true being as essentially limited participants, not masters, of the world which we discover.
  Heidegger wrote about these issues in his best-known book, Being and Time (1927), which is considered to be one of the most important philosophical works of the 20th century. Heidegger's influence is far reaching, from philosophy to deconstructionism and literary theory, theology, architecture, and artificial intelligence.
  
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  Marvin Minsky
  Marvin Lee Minsky (born August 9, 1927) is an American cognitive scientist in the field of artificial intelligence (AI), co-founder of Massachusetts Institute of Technology's AI laboratory, and author of several texts on AI and philosophy.
  Marvin Lee Minsky was born in New York City to a Jewish family, where he attended The Fieldston School and the Bronx High School of Science. He later attended Phillips Academy in Andover, Massachusetts. He served in the US Navy from 1944 to 1945. He holds a BA in Mathematics from Harvard (1950) and a PhD in mathematics from Princeton (1954). He has been on the MIT faculty since 1958. In 1959 he and John McCarthy founded what is now known as the MIT Computer Science and Artificial Intelligence Laboratory. He is currently the Toshiba Professor of Media Arts and Sciences, and Professor of electrical engineering and computer science.
  Isaac Asimov described Minsky as one of only two people he would admit were more intelligent than he was, the other being Carl Sagan.Patrick Winston has also described Minsky as the smartest person he has ever met. Ray Kurzweil has referred to Minsky as his mentor.
  
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• Ned Block
  Ned Block (born 1942) is an American philosopher working in the field of the philosophy of mind who has made important contributions to matters of consciousness and cognitive science. In 1971, he obtained his Ph.D. from Harvard University under Hilary Putnam. He went to Massachusetts Institute of Technology (MIT) as an assistant professor of philosophy (1971-1977), worked as associate professor of philosophy (1977-1983), professor of philosophy (1983-1996) and served as chair of the philosophy section (1989-1995). He has, since 1996, been a professor in the departments of philosophy and psychology and at the Center for Neural Science at New York University (NYU).
  Block is noted for presenting the Blockhead argument against the Turing Test as a test of intelligence in a paper entitled Psychologism and Behaviourism (1981). He is also known for his criticism of functionalism, arguing that a system with the same functional states as a human is not necessarily conscious. In his more recent work on consciousness, he has made a distinction between phenomenal consciousness and access consciousness, where phenomenal consciousness consists of subjective experience and feelings and access consciousness consists of that information globally available in the cognitive system for the purposes of reasoning, speech and high-level action control. He has argued that access consciousness and phenomenal consciousness might not always coincide in human beings.
  
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  Noam Chomsky
  Avram Noam Chomsky (/ˈnoʊm ˈtʃɒmski/; born December 7, 1928) is an American linguist, philosopher,cognitive scientist, historian, and activist. He is an Institute Professor and Professor (Emeritus) in the Department of Linguistics & Philosophy at MIT, where he has worked for over 50 years. Chomsky has been described as the "father of modern linguistics" and a major figure of analytic philosophy. His work has influenced fields such as computer science, mathematics, and psychology.
  Ideologically identifying with anarcho-syndicalism and libertarian socialism, Chomsky is known for his critiques of U.S. foreign policy and contemporary capitalism, and he has been described as a prominent cultural figure. His media criticism has included Manufacturing Consent: The Political Economy of the Mass Media (1988), co-written with Edward S. Herman, an analysis articulating the propaganda model theory for examining the media.
  According to the Arts and Humanities Citation Index in 1992, Chomsky was cited as a source more often than any other living scholar from 1980 to 1992, and was the eighth most cited source overall. Chomsky is the author of over 100 books. He is credited as the creator or co-creator of the Chomsky hierarchy, the universal grammar theory, and the Chomsky–Schützenberger theorem.
  
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• Paul Grice
  Herbert Paul Grice (March 13, 1913, Birmingham, England – August 28, 1988, Berkeley, California), usually publishing under the name H. P. Grice, H. Paul Grice, or Paul Grice, was a British-educated philosopher of language, who spent the final two decades of his career in the United States.
  Born and raised in Harborne (now a suburb of Birmingham), in the United Kingdom, he was educated at Clifton College and then at Corpus Christi College, Oxford. After a brief period teaching at Rossall School, he went back to Oxford where he taught until 1967. In that year, he moved to the United States to take up a professorship at the University of California, Berkeley, where he taught until his death in 1988. He returned to the UK in 1979 to give the John Locke lectures on Aspects of Reason. He reprinted many of his essays and papers in his valedictory book, Studies in the Way of Words (1989).
  He was married and had two children. He and his wife lived in an old Spanish style house in the Berkeley Hills.^{[citation needed]}
  
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  Paul Ricœur
  Paul Ricœur (27 February 1913 – 20 May 2005) was a French philosopher best known for combining phenomenological description with hermeneutic interpretation. As such his thought is situated within the same tradition as other major hermeneutic phenomenologists, Martin Heidegger and Hans-Georg Gadamer.
  Ricœur was born in Valence, Drôme, France to a devout Protestant family, making him a member of a religious minority in Catholic France.
  Ricœur's father died in a 1915 World War I battle when Ricœur was only two years old. He was raised by his paternal grandparents and an aunt in Rennes, France, with a small stipend afforded to him as a war orphan. Ricœur, whose penchant for study was fueled by his family's Protestant emphasis on Bible study, was bookish and intellectually precocious. Ricœur received his bachelor's degree' in 1933 from the University of Rennes and began studying philosophy at the Sorbonne in 1934, where he was influenced by Gabriel Marcel. In 1935, he was awarded the second-highest agrégation mark in the nation for philosophy, presaging a bright future.
  
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  Paul Tillich
  Paul Johannes Tillich (August 20, 1886 – October 22, 1965) was a German-American theologian and Christian existentialist philosopher. Tillich was one of the most influential Protestant theologians of the 20th century. Among the general public, he is best known for his works The Courage to Be (1952) and Dynamics of Faith (1957), which introduced issues of theology and modern culture to a general readership. Theologically, he is best known for his major three-volume work Systematic Theology (1951–63), in which he developed his "method of correlation": an approach of exploring the symbols of Christian revelation as answers to the problems of human existence raised by contemporary existential philosophical analysis.
  Tillich was born on August 20, 1886, in the small village of Starzeddel Silesia which was then part of Germany. He was the oldest of three children, with two sisters: Johanna (b. 1888, d. 1920) and Elisabeth (b. 1893). Tillich’s Prussian father Johannes Tillich was a conservative Lutheran pastor of the Evangelical State Church of Prussia's older Provinces; his mother Mathilde Dürselen was from the Rhineland and was more liberal. When Tillich was four, his father became superintendent of a diocese in Schönfliess, a town of three thousand, where Tillich began elementary school. In 1898, Tillich was sent to Königsberg Chojna to begin gymnasium. At Königsberg, he lived in a boarding house and experienced loneliness that he sought to overcome by reading the Bible. Simultaneously, however, he was exposed to humanistic ideas at school.
  
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  Plato
  Plato ( /ˈpleɪtoʊ/; Greek: Πλάτων, Plátōn, "broad"; 424/423 BC – 348/347 BC) was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the foundations of Western philosophy and science. In the words of A. N. Whitehead:
  The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings. I allude to the wealth of general ideas scattered through them.
  Plato's sophistication as a writer is evident in his Socratic dialogues; thirty-six dialogues and thirteen letters have been ascribed to him. Plato's writings have been published in several fashions; this has led to several conventions regarding the naming and referencing of Plato's texts. Plato's dialogues have been used to teach a range of subjects, including philosophy, logic, ethics, rhetoric, and mathematics.
  
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  René Descartes
  René Descartes (French pronunciation: [ʁəne dekaʁt]; Latinized form: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system — allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius.
  
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  Richard Rorty
  Richard McKay Rorty (October 4, 1931 – June 8, 2007) was an American philosopher. He had a long and diverse academic career, including positions as Stuart Professor of Philosophy at Princeton University, Kenan Professor of Humanities at the University of Virginia, and Professor of Comparative Literature at Stanford University. His complex intellectual background gave him a comprehensive and nuanced understanding of the traditional analytic philosophy, which he would later famously reject in favor of his own brand of pragmatism.
  The philosophical program he developed included a rejection of a representationalist account of knowledge, that is, "mirror of nature", which he reviewed as a holdover from Plato and pervasive throughout the history of western philosophy. In response to these visual theorists, which he drew as embodied by modern analytic philosophy, Rorty advocated for a novel form of American pragmatism, sometimes called neopragmatism, in which scientific and philosophical methods are merely a set of contingent "vocabularies" which were abandoned or adopted over time according to social conventions and usefulness.
  
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• Rudolf Carnap
  Rudolf Carnap (May 18, 1891 – September 14, 1970) was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism.
  Carnap was born to a west German family that had been humble until his parents' generation. He began his formal education at the Barmen Gymnasium. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. But he also studied carefully Kant's Critique of Pure Reason during a course taught by Bruno Bauch, and was one of very few students to attend Gottlob Frege's courses in mathematical logic. After serving in the German army during World War I for three years, he was given permission to study physics at the University of Berlin, 1917–18, where Albert Einstein was a newly appointed professor. Carnap then attended the University of Jena, where he wrote a thesis defining an axiomatic theory of space and time. The physics department said it was too philosophical, and Bruno Bauch of the philosophy department said it was pure physics. Carnap then wrote another thesis, with Bauch's supervision, on the theory of space in a more orthodox Kantian style, and published as Der Raum (Space) in a supplemental issue of Kant-Studien (1922). In it he makes the clear distinction between formal, physical and perceptual (e.g., visual) spaces.
  
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  Saul Kripke
  Saul Aaron Kripke (born November 13, 1940) is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center. Since the 1960s Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape-recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy. A recent poll conducted among philosophers ranked Kripke among the top ten most important philosophers of the past 200 years.
  Kripke has made influential and original contributions to logic, especially modal logic, since he was a teenager. Unusual for a professional philosopher, his only degree is an undergraduate degree from Harvard, in mathematics. His work has profoundly influenced analytic philosophy, with his principal contribution being a semantics for modal logic, involving possible worlds as described in a system now called Kripke semantics. Another of his most important contributions is his argument that necessity is a 'metaphysical' notion, which should be separated from the epistemic notion of a priori, and that there are necessary a posteriori truths, such as "Water is H₂O." He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein." His most famous work is Naming and Necessity (1980).
  
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  Søren Kierkegaard
  Søren Aabye Kierkegaard (/ˈsɔrən ˈkɪərkəɡɑrd/ or /ˈkɪərkəɡɔr/; Danish: [ˈsɶːɐn ˈkiɐ̯ɡəɡɒːˀ] ( listen)) (5 May 1813 – 11 November 1855) was a Danish philosopher, theologian and religious author. He was a critic of idealist intellectuals and philosophers of his time, such as Georg Wilhelm Friedrich Hegel, Friedrich Wilhelm Joseph Schelling and Karl Wilhelm Friedrich Schlegel. He was also critical of the state and practice of Christianity, primarily that of the Church of Denmark. He is widely considered to be the first existentialist philosopher.
  Much of his philosophical work deals with the issues of how one lives as a "single individual", giving priority to concrete human reality over abstract thinking, and highlighting the importance of personal choice and commitment.
  His theological work focuses on Christian ethics, on the institution of the Church, and on the differences between purely objective proofs of Christianity. He wrote of the individual's subjective relationship to Jesus Christ, the God-Man, which came through faith. Much of his work deals with the art of Christian love.
  
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  Thomas Hobbes
  Thomas Hobbes of Malmesbury (5 April 1588 – 4 December 1679), in some older texts Thomas Hobbs of Malmsbury, was an English philosopher, best known today for his work on political philosophy. His 1651 book Leviathan established the foundation for most of Western political philosophy from the perspective of social contract theory.
  Hobbes was a champion of absolutism for the sovereign but he also developed some of the fundamentals of European liberal thought: the right of the individual; the natural equality of all men; the artificial character of the political order (which led to the later distinction between civil society and the state); the view that all legitimate political power must be "representative" and based on the consent of the people; and a liberal interpretation of law which leaves people free to do whatever the law does not explicitly forbid.
  He was one of the founders of modern political philosophy. His understanding of humans as being matter and motion, obeying the same physical laws as other matter and motion, remains influential; and his account of human nature as self-interested cooperation, and of political communities as being based upon a "social contract" remains one of the major topics of political philosophy.
  
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  Thomas Nagel
  Thomas Nagel (born July 4, 1937) is an American philosopher, currently University Professor of Philosophy and Law at New York University, where he has taught since 1980. His main areas of philosophical interest are philosophy of mind, political philosophy and ethics. He is well known for his critique of reductionist accounts of the mind in his essay "What Is It Like to Be a Bat?" (1974), and for his contributions to deontological and liberal moral and political theory in The Possibility of Altruism (1970) and subsequent writings.
  Nagel was born July 4, 1937, in Belgrade, Yugoslavia (now Serbia) to a Jewish family. He received a BA from Cornell University in 1958, a BPhil from the University of Oxford in 1960, and a PhD from Harvard University in 1963 under the supervision of John Rawls. Before settling in New York, Nagel taught briefly at the University of California, Berkeley (from 1963 to 1966) and at Princeton University (from 1966 to 1980), where he trained many well-known philosophers including Susan Wolf, Shelly Kagan, and Samuel Scheffler, who is now his colleague at NYU. In 2006, he was made a member of the American Philosophical Society.
  
  wn.com/Thomas_Nagel
• 
  Vasubandhu
  Vasubandhu (Sanskrit: वसुबन्दु; traditional Chinese: 世親; pinyin: Shìqīn; Tibetan: དབྱིག་གཉེན་, Wylie: dbyig gnyen) (fl. 4th c.) was an Indian Buddhist monk, and along with his half-brother Asanga, one of the main founders of the Indian Yogācāra school. However, some scholars consider Vasubandhu to be two distinct people. Vasubandhu is one of the most influential figures in the entire history of Buddhism. In the Jodo Shinshu branch of Buddhism, he is considered the Second Patriarch. In Zen, he is the 21st Patriarch.
  Born a brahmin Vasubandhu was said to have been the half brother of Asanga, another key personage in the founding of the Yogacara School. He was also, as well as his elder half brother Asanga, one of the ‘Six Ornaments’(i.e. six great commentators on the Buddha’s teachings). He resided at Kausambhi (near modern Allahabad) where he was trained in the orthodox Sarvastivada Order of Buddhism, which had its seat at Kausambhi. He was contemporaneous with King Chandragupta I, the father of Samudragupta. This information temporally places this Vasubandhu in the fourth century CE.
  
  wn.com/Vasubandhu
• 
  Wilhelm von Humboldt
  Friedrich Wilhelm Christian Karl Ferdinand Freiherr von Humboldt (22 June 1767 – 8 April 1835) was a Prussian philosopher, government functionary, diplomat, and founder of the University of Berlin, which was named after him (and his brother, naturalist Alexander von Humboldt) in 1949. He is especially remembered as a linguist who made important contributions to the philosophy of language and to the theory and practice of education. In particular, he is widely recognized as having been the architect of the Prussian education system which was used as a model for education systems in countries such as the United States and Japan.
  Humboldt was born in Potsdam, Margraviate of Brandenburg, and died in Tegel, Province of Brandenburg. His younger brother, Alexander von Humboldt, was equally famous, as a geographer.
  Humboldt was a philosopher and wrote On the Limits of State Action in 1791-2 (though it was not published until 1850, after Humboldt's death), one of the boldest defences of the liberties of the Enlightenment. It influenced John Stuart Mill's essay On Liberty through which von Humboldt's ideas became known in the English-speaking world. Humboldt outlined an early version of what Mill would later call the "harm principle".
  
  wn.com/Wilhelm_von_Humboldt
• 
  William James
  William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher who was trained as a physician. He was the first educator to offer a psychology course in the U.S. He wrote influential books on the young science of psychology, educational psychology, psychology of religious experience and mysticism, and on the philosophy of pragmatism. He was the brother of novelist Henry James and of diarist Alice James. In the summer of 1878, James married Alice Gibbens.
  William James was born at the Astor House in New York City. He was the son of Henry James Sr., a noted and independently wealthy Swedenborgian theologian well acquainted with the literary and intellectual elites of his day. The intellectual brilliance of the James family milieu and the remarkable epistolary talents of several of its members have made them a subject of continuing interest to historians, biographers, and critics.
  James interacted with a wide array of writers and scholars throughout his life, including his godfather Ralph Waldo Emerson, his godson William James Sidis, as well as Charles Sanders Peirce, Bertrand Russell, Josiah Royce, Ernst Mach, John Dewey, Macedonio Fernández, Walter Lippmann, Mark Twain, Horatio Alger, Jr., Henri Bergson and Sigmund Freud.
  
  wn.com/William_James
• 
  Zhuangzi
  Zhuangzi (simplified Chinese: 庄子; traditional Chinese: 莊子; pinyin: Zhuāng Zǐ; Wade–Giles: Chuang Tzŭ) was an influential Chinese philosopher who lived around the 4th century BCE during the Warring States Period, a period corresponding to the philosophical summit of Chinese thought — the Hundred Schools of Thought, and is credited with writing—in part or in whole—a work known by his name, the Zhuangzi. His name Zhuangzi (English "Master Zhuang", with Zi being an honorific) is sometimes spelled Zhuang Tze, Zhuang Zhou, Chuang Tsu, Chuang Tzu, Chouang-Dsi, Chuang Tse, or Chuangtze.
  The only account of the life of Zhuangzi is a brief sketch in chapter 63 of Sima Qian's Records of the Grand Historian, where he is described as a minor official from the town of Meng (in modern Anhui) in the state of Song, living in the time of King Hui of Liang and King Xuan of Qi (late 4th century BCE). Sima Qian writes:
  The validity of his existence has been questioned by some, including himself (See below) and Russell Kirkland, who writes:
  
  wn.com/Zhuangzi

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