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

• Abductive reasoning
• Alan Ross Anderson
• Alan Turing
• Alexander Bain
• Alfred Tarski
• Alonzo Church
• Ambiguity
• Analytic philosophy
• Antinomy
• Argument
• Argumentation theory
• Aristotelian logic
• Aristotle
• Arity
• Augustus De Morgan
• Averroes
• Avicenna
• Axiology
• Axiom
• Axiomatic system
• Belief
• Benjamin Lee Whorf
• Bertrand Russell
• Bias
• Boolean function
• Boolean logic
• Cantor's theorem
• Categorization
• Category Logic
• Chrysippus
• Church–Turing thesis
• Class (philosophy)
• Class (set theory)
• Classical logic
• Cogency
• Completeness
• Compound fact
• Computability theory
• Computable function
• Concatenation
• Concept
• Conclusions
• Confucius
• Consistency
• Contrastivism
• Conventionalism
• Countable set
• Cratylism
• Cratylus (dialogue)
• Credibility
• Critical thinking
• David Hilbert
• Decidability (logic)
• Decision problem
• Declarative sentence
• Deconstruction
• Deductive reasoning
• Deductive system
• Definition
• Degree of truth
• Deontic logic
• Description
• Description logic
• Dialetheism
• Domain of a function
• Doxastic logic
• Dramatism
• Duns Scotus
• Edward Sapir
• Effective method
• Empty set
• Entailment
• Entity
• Entscheidungsproblem
• Enumeration
• Ernst Schröder
• Ernst Zermelo
• Evidence
• Explanation
• Explanatory power
• Expressivism
• Extensionality
• Fact
• Fallacy
• Falsity
• Fictionalism
• Finitary relation
• Finite model theory
• Finite set
• Finitism
• First-order logic
• Folk psychology
• Formal language
• Formal proof
• Formal system
• Formation rule
• Franz Boas
• Fritz Mauthner
• Functional predicate
• Fuzzy finite element
• Fuzzy logic
• Fuzzy rule
• Fuzzy set
• Fuzzy set operations
• Georg Cantor
• George Boole
• George Boolos
• Gerhard Gentzen
• Gilbert Ryle
• Giuseppe Peano
• Gottlob Frege
• Gustav Bergmann
• Hans-Georg Gadamer
• Haskell Curry
• Henri Bergson
• Heyting arithmetic
• Hilary Putnam
• History of logic
• Ibn Khaldun
• Inductive reasoning
• Inference
• Informal logic
• Inquiry
• Intension
• Intentionality
• Internalism
• Intuitionism
• Intuitionistic logic
• J. L. Austin
• Jacques Derrida
• Jon Barwise
• Kurt Gödel
• Language
• Leonard Bloomfield
• Leopold Löwenheim
• Lev Vygotsky
• Limited Inc
• Linear logic
• Linguistics
• List of fallacies
• List of logicians
• List of paradoxes
• Logic
• Logical atomism
• Logical connective
• Logical form
• Logical positivism
• Logical truth
• Logicism
• Ludwig Wittgenstein
• Main contention
• Mathematical logic
• Mathematics
• Mental world
• Metalanguage
• Metalogic
• Metamathematics
• Metatheorem
• Modal logic
• Modal operator
• Model theory
• Name
• Natural deduction
• Noam Chomsky
• Nominalism
• Non-classical logic
• Non-cognitivism
• Non-standard model
• Of Grammatology
• Ontology
• Ontology language
• Open sentence
• Opinion
• Ordered pair
• Outline of logic
• P. F. Strawson
• Paraconsistent logic
• Paradox
• Parsimony
• Paul Bernays
• Paul Grice
• Paul Ricœur
• Paul Tillich
• Peter Geach
• Phallogocentrism
• Philosophical logic
• Philosophy
• Philosophy of logic
• Philosophy of mind
• Plato
• Platonic realism
• Portal Logic
• Portal Philosophy
• Possible world
• Power set
• Pragmatics
• Pragmatism
• Predicate (logic)
• Predicate logic
• Predicate variable
• Premise
• Preposition
• Presupposition
• Probability
• Proof theory
• Propaganda
• Proposition
• Prudence
• Psychology
• Pyrrhonism
• Quantification
• Question
• Quietism
• Range (mathematics)
• Raymond Smullyan
• Reason
• Recursion
• Recursive set
• Reference
• Relevance
• Relevance logic
• Relevance theory
• Rhetoric
• Rigour
• Rudolf Carnap
• Rule of inference
• Satisfiability
• Saul Kripke
• Scholasticism
• Second-order logic
• Semantic externalism
• Semantic holism
• Semantics
• Semiotics
• Sense and reference
• Set (mathematics)
• Set theory
• Sign (semiotics)
• Soundness
• Speech act
• Square of opposition
• Statement (logic)
• Stephen Cole Kleene
• Stoicism
• Strict implication
• Structural rule
• Structuralism
• Subject (grammar)
• Subject (philosophy)
• Subset
• Substitution (logic)
• Substructural logic
• Supposition theory
• Syllogism
• Symbiosism
• Symbol
• Symbol (formal)
• Syntax
• Syntax (logic)
• Template Logic
• Template talk Logic
• Temporal logic
• Term (logic)
• Term logic
• Theorem
• Thomas Hobbes
• Thoralf Skolem
• Truth
• Truth table
• Truth value
• Truth-bearer
• Truthbearer
• Type theory
• Uncountable set
• Vagueness
• Validity
• Valuation (logic)
• Venn diagram
• Verification theory
• W.V. Quine
• Well-formed formula
• Wilhelm von Humboldt
• William of Ockham
• Xun Zi
• Zhuangzi
• 
  

• 
  Belize
  Belize ⁱ/bəˈliːz/ (formerly British Honduras) is a country located on the north eastern coast of Central America and it is the only country in the area where English is the official language, although Kriol and Spanish are more commonly spoken. Belize is bordered to the north by Mexico, south and west by Guatemala, and to the east by the Caribbean Sea. Its mainland is about 290 kilometres (180 mi) long and 110 kilometres (68 mi) wide.
  With 22,960 square kilometres (8,860 sq mi) of land and a population of only 333,200 inhabitants (2010 est.), Belize possesses the lowest population density in Central America. The country's population growth rate of 2.21% (2008 est.), however, is the highest in the region and one of the highest in the western hemisphere. Belize's abundance of terrestrial and marine species, and its diversity of ecosystems give it a key place within the globally significant Mesoamerican Biological Corridor.
  Belize has a diverse society, comprising many cultures and languages and it is the only nation in the region with a British colonial heritage but as a part of the Western Caribbean Zone, it also shares a common heritage with the Caribbean portions of other Central American countries. In general, Belize is considered to be a Central American nation with strong ties to both the Caribbean and Latin America. Belize is a member of the Caribbean Community (CARICOM), the Community of Latin American and Caribbean States (CELAC), and Sistema de la Integración Centroamericana (SICA).
  
  wn.com/Belize
• 
  Bradford
  Coordinates: 53°48′00″N 1°45′07″W / 53.8000°N 1.75206°W / 53.8000; -1.75206
  Bradford (ⁱ/ˈbrædfəd/) lies at the heart of the City of Bradford, a metropolitan borough of West Yorkshire, in Northern England. It is situated in the foothills of the Pennines, 8.6 miles (13.8 km) west of Leeds, and 16 miles (25.7 km) northwest of Wakefield. Bradford became a municipal borough in 1847, and received its charter as a city in 1897. Following local government reform in 1974, city status was bestowed upon the wider metropolitan borough.
  Bradford has a population of 293,717, making it the fourteenth-most populous settlement in the United Kingdom. Bradford forms part of the West Yorkshire Urban Area conurbation which in 2001 had a population of 1.5 million and is part of the Leeds-Bradford Larger Urban Zone (LUZ), the third largest in the UK after London and Manchester, with an estimated population in the 2004 Urban Audit of 2.4 million.
  Historically a part of the West Riding of Yorkshire, Bradford rose to prominence during the 19th century as an international centre of textile manufacture, particularly wool. It was a boomtown of the Industrial Revolution, and amongst the earliest industrialised settlements, rapidly becoming the "wool capital of the world". The area's access to a supply of coal, iron ore and soft water facilitated the growth of Bradford's manufacturing base, which, as textile manufacture grew, led to an explosion in population and was a stimulus to civic investment; Bradford has fine Victorian architecture including the grand Italianate City Hall.
  
  wn.com/Bradford
• 
  Chesterfield
  Chesterfield is a market town and a borough of Derbyshire, England. It lies 24 miles (39 km) north of Derby, on a confluence of the rivers Rother and Hipper. Its population is 70,260 (2001), making it Derbyshire's largest town (the larger Derby being a city). It is located on the A61, 6 miles (9.7 km) from the M1, and forms part of the Sheffield City Region.
  Chesterfield received its market charter in the year 1204, and is currently home to one of the largest open air markets in Britain. The area around the town sits over a large coalfield, which was mined from many surrounding collieries until the 1980s. Little evidence of the mining industry remains today, and the town's economy has moved towards the tertiary sector. The town's most famous landmark, which is visible from many viewpoints outside the town, is the distinctive 'crooked' spire of its predominantly 14th century church.
  The town received its market charter in the year 1204 from King John and around 250 stalls can still be found in the town centre every Monday, Friday and Saturday. The charter constituted the town as a free borough, granting the burgesses of Chesterfield the same privileges as those of Nottingham.
  
  wn.com/Chesterfield
• 
  Cleethorpes
  Coordinates: 53°33′12″N 0°01′18″W / 53.5533°N 0.02155°W / 53.5533; -0.02155
  Cleethorpes is a town and unparished area in North East Lincolnshire, England, situated on the estuary of the Humber. It has a population of 31,853 and is a seaside resort.
  The name "Cleethorpes" is thought to come from joining the words "clee", an old word for clay, and "thorpes", an Old English/Old Norse word for villages, and is of comparatively modern origin. Before becoming a unified town, Cleethorpes was made up of three small villages, or "thorpes": Itterby, Oole and Thrunscoe, which were part of a wider parish called Clee (not to be confused with Old Clee).
  While there are neolithic and Bronze Age remains in the area, permanent occupation appears to date from the 6th century, when the Danes arrived, with substantial communities only appearing in the 9th century.
  The manor of Itterby was purchased in 1616 by the trustees of Peter Blundell's charity for the benefit of scholars and fellows at Sidney Sussex College, Cambridge from Blundell's School, Tiverton. This is reflected in many of the street and park names in the area.
  
  wn.com/Cleethorpes
• 
  Derby QUAD
  Derby QUAD also referred to as QUAD Derby or simply The QUAD is an arts centre in Derby, United Kingdom, first opened on 26 September 2008. It has a steel and glass design by Bath architects Feilden Clegg Bradley. When it was chosen over competing designs by Derby council cabinet in 2004 it was considered controversial. QUAD provides an art gallery, two cinemas, artists’ studios, and a cafe bar. The centre also has available spaces for people to create their own artwork.
  QUAD is a cinema, gallery, cafe and workshop space that anyone can use. QUAD connects people and businesses to art and film for entertainment, education and participation. There are artist studios you can hire and a BFI Médiathèque which you can use to watch various videos. QUAD runs creative courses for adults and children. The cinema shows a range of different movies from old subtitle movies to the latest movies.
  Coordinates: 52°55′24″N 1°28′32″W / 52.9232°N 1.4755°W / 52.9232; -1.4755
  
  wn.com/Derby_QUAD
• 
  Derbyshire
  Coordinates: 53°8′N 1°36′W / 53.133°N 1.6°W / 53.133; -1.6
  Derbyshire (ⁱ/ˈdɑrbɨʃə/ DAR-bi-shər or /ˈdɑrbɪʃɪər/ DAR-bi-sheer; abbreviated Derbys. or Derbs.) is a county in the East Midlands of England. A substantial portion of the Peak District National Park lies within Derbyshire. The southern extremity of the Pennine range of hills extends into the north of the county. The county contains within its boundary of approximately 225 miles part of the National Forest. It borders on Greater Manchester to the northwest, West Yorkshire to the north, South Yorkshire to the northeast, Nottinghamshire to the east, Leicestershire to the southeast, Staffordshire to the west and southwest and Cheshire also to the west. In 2003 the Ordnance Survey placed Church Flatts farm, near Coton in the Elms, as the furthest point from the sea in Great Britain.
  The city of Derby is now a unitary authority area, but remains part of the ceremonial county of Derbyshire. The non-metropolitan county contains 30 towns with between 10,000 and 100,000 inhabitants. There is a large amount of sparsely populated agricultural upland: 75% of the population live in 25% of the area.^{[citation needed]}
  
  wn.com/Derbyshire
• 
  Ethiopia
  Ethiopia ( /ˌiːθiˈoʊpiə/) (Ge'ez: ኢትዮጵያ ʾĪtyōṗṗyā), officially known as the Federal Democratic Republic of Ethiopia, is a landlocked country located in the Horn of Africa. It is the second-most populous nation in Africa, with over 82 million inhabitants, and the tenth largest by area, occupying 1,100,000 km². Ethiopia is bordered by Eritrea to the north, Djibouti and Somalia to the east, Sudan and South Sudan to the west, and Kenya to the south. With its capital at Addis Ababa, it is also the most populous landlocked nation in the world.
  Ethiopia was a monarchy for most of its history, and the Ethiopian dynasty traces its roots to the 2nd century BC. Ethiopia is also one of the oldest sites of human existence known to scientists today, having yielded some of humanity's oldest traces. It may be the region from which Homo sapiens first set out for the Middle East and points beyond. Alongside Rome, Persia, China and India, the Ethiopian Aksum Empire was considered one of the great world powers of the 3rd century. During the Scramble for Africa, Ethiopia was the only African country beside Liberia that retained its sovereignty as a recognized independent country, and was one of only four African members of the League of Nations. After a brief period of Italian occupation, Ethiopia became a charter member of the United Nations. When other African nations received their independence following World War II, many of them adopted the colors of Ethiopia's flag, and Addis Ababa became the location of several international organizations focused on Africa.
  
  wn.com/Ethiopia
• 
  Grimsby
  Coordinates: 53°33′34″N 0°04′05″W / 53.5595°N 0.0680°W / 53.5595; -0.0680
  Grimsby (or archaically Great Grimsby) is a seaport on the Humber Estuary in Lincolnshire, England. It has been the administrative centre of the unitary authority area of North East Lincolnshire since 1996. According to legend, Grimsby was first founded by Grim, a Danish fisherman, 'By' means 'village' in Old Norse and modern Swedish and 'city' or 'town' in modern Danish and Norwegian.
  The town was previously titled "Great Grimsby" to distinguish it from Little Grimsby, a village about 14 miles (22 km) to the south, near Louth. People from Grimsby are called Grimbarians.
  The town itself has a population of 87,574. It is physically linked to the adjoining town of Cleethorpes, and 11,000 of its inhabitants live in the village of Scartho which was absorbed into Grimsby before laws on the green belt were put in place. All three areas come under the jurisdiction of the same council, North East Lincolnshire. It is close to the main terminus of the A180, which ends in Cleethorpes. 22 January is Great Grimsby Day.
  
  wn.com/Grimsby
• 
  Holborn
  Coordinates: 51°31′02″N 0°07′06″W / 51.5172°N 0.1182°W / 51.5172; -0.1182
  Holborn ( /ˈhoʊbərn/ HOH-bərn) is an area of central London and also the name of the area's principal street, known as High Holborn between St. Giles's High Street and Gray's Inn Road (the junction being roughly where Holborn Bar — the entrance to the City of London — once was) and then Holborn Viaduct between Holborn Circus and Newgate Street. The street since boundary changes in 1994 runs along the boundary between the London Borough of Camden and the City of London; previously the boundary was less obvious in the area and crossed the street at Holborn Bar.
  The area's first mention is in a charter of Westminster Abbey, by King Edgar, dated to 959. This mentions "the old wooden church of St Andrew" (St Andrew, Holborn). The name Holborn may be derived from the Middle English "hol" for hollow, and bourne, a brook, referring to the River Fleet as it ran through a steep valley to the east. Historical cartographer William Shepherd in his Plan of London about 1300 labels the Fleet as "Hole Bourn" where it passes to the east of St Andrew's church. However, the 16th century historian John Stow attributes the name to the Old Bourne ("old brook"), a small stream which he believed ran into the Fleet at Holborn Bridge, a structure lost when the river was culverted in 1732. The exact course of the stream is uncertain, but according to Stow it started in one of the many small springs near Holborn Bar, the old City toll gate on the summit of Holborn Hill. This is supported by a map of London and Westminster created during the reign of Henry VIII that clearly marks the street as 'Oldbourne' and 'High Oldbourne'. Other historians, however, find the theory implausible, in view of the slope of the land.
  
  wn.com/Holborn
• 
  Otford
  Coordinates: 51°18′35″N 0°11′12″E / 51.30969°N 0.18657°E / 51.30969; 0.18657
  Otford is a village and civil parish in the Sevenoaks District of Kent known for its classically English (Kentish) countryside. The village is located on the River Darent, flowing north down its valley from its source on the North Downs. The name is a contraction of Otterford, possibly derived from Offa, the King of Mercia who fought a battle at Otford against the Kentish Saxons in 776 at the Battle of Otford.
  Notable landmarks are the Archbishop's Palace, the duck-pond roundabout, and the scale model of the Solar System which claims to be "the largest scale model in the world".
  The parish church is dedicated to St Bartholomew.
  According to the 2001 Census, the population of the Otford and Shoreham ward was 4,381, Otford's population being 3,528.
  Otford lies on the A225, a main road between Dartford and Sevenoaks. The presence of the site of a Roman villa, in addition to the remains of an ancient trackway, suggests that this road has a long history. The M26 motorway uses the valley here as part of its route.
  
  wn.com/Otford
• 
  Shirebrook
  Coordinates: 53°12′17″N 1°13′11″W / 53.2048°N 1.2197°W / 53.2048; -1.2197
  Shirebrook is a town in the Bolsover district of north-east Derbyshire on the border with Nottinghamshire, England. At the 2001 UK Census it had a population of 9,291 (civil parish), 10,412 (urban area). It is on the B6407, and close to the A632 road, between Mansfield and Bolsover.
  The town is served by Shirebrook railway station.
  Shirebrook is a small market town with a market square (Market days are Tuesdays, Wednesdays, Fridays and Saturdays) surrounded by several shops. There is a large Co-operative food, 2 butchers, carpet shops, a photographers, 2 card shops, 4 cake shops, 3 Tattooists, 2 furniture shops, a baby shop, 2 pet shops, 3 cafes, 4 pubs, a lock smith, 1 solicitors, 2 DIY stores, multiple take-aways and 2 pharmacists. Shirebrook is home to many small local businesses. Much of the growth and prosperity of the town was built around coal mining. Shirebrook Colliery opened in 1896 and closed in 1993. Like many former 'pit towns' in the area this led to high unemployment and other social problems. The former site of the colliery is currently being redeveloped. The Kissingate Leisure Centre is on Park Road. It has no swimming pool, but it does have an indoor five-a-side football area and a skate park. The Kissingate Leisure Centre itself was closed after being heavily damaged by fire on Friday 7 November, 2008, but reopened almost 12 months later.
  
  wn.com/Shirebrook

• Alan Ross Anderson
  Alan Ross Anderson (1925 – 1973) was an American logician and professor of philosophy at Yale University and the University of Pittsburgh.
  A frequent collaborator with Nuel Belnap, Anderson was instrumental in the development of relevance logic and deontic logic.
  Anderson died of cancer in 1973.
  Anderson believed that the conclusion of a valid inference ought to have something to do with (i.e. be relevant to) the premises. Formally, he captured this "relevance condition" with the principle that
  As simple as this idea appears, implementing it in a formal system requires a radical departure from the semantics of classical logic. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine, Alasdair Urquhart, Robert K. Meyer, Anil Gupta (logician), and others) explored the formal consequences of the relevance condition in great detail in their influential Entailment books (see references below), which are the most frequently cited works in the field of relevance logic.
  Anderson and Belnap were quick to observe that the concept of relevance had been central to logic since Aristotle, but had been unduly neglected since Gottlob Frege and George Boole laid the foundations for what would come to be known, somewhat ironically, as "classical" logic. (For an example of classical logic's failure to satisfy the relevance condition, see the article on the principle of explosion.)
  
  wn.com/Alan_Ross_Anderson
• 
  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
• 
  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
• 
  Alfred Tarski
  Alfred Tarski (January 14, 1901 – October 26, 1983) was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death.
  A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.
  His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."
  Alfred Tarski was born Alfred Teitelbaum (Polish spelling: "Tajtelbaum"), to parents who were Polish Jews in comfortable circumstances. He first manifested his mathematical abilities while in secondary school, at Warsaw's Szkoła Mazowiecka. Nevertheless, he entered the University of Warsaw in 1918 intending to study biology.
  
  wn.com/Alfred_Tarski
• Alonzo Church
  Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, solving the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem.
  Alonzo Church was born on June 14, 1903 in Washington, D.C. where his father, Samuel Robbins Church, was the judge of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position because of failing eyesight. With help from his uncle, also named Alonzo Church, he was able to attend the Ridgefield School for Boys in Ridgefield, Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformations, and graduating in 1924 with a degree in mathematics. He stayed at Princeton, earning a Ph.D. in mathematics in three years under Oswald Veblen.
  
  wn.com/Alonzo_Church
• 
  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
• 
  Augustus De Morgan
  Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him.
  Augustus De Morgan was born in 1806. His father was Col. Augustus De Morgan, who held various appointments in the service of the East India Company. His mother descended from James Dodson, who computed a table of anti-logarithms, that is, the numbers corresponding to exact logarithms. Augustus De Morgan became blind in one eye a month or two after he was born. The family moved to England when Augustus was seven months old. As his father and grandfather had both been born in India, De Morgan used to say that he was neither English, nor Scottish, nor Irish, but a Briton "unattached", using the technical term applied to an undergraduate of Oxford or Cambridge who is not a member of any one of the Colleges.
  When De Morgan was ten years old, his father died. Mrs. De Morgan resided at various places in the southwest of England, and her son received his elementary education at various schools of no great account. His mathematical talents went unnoticed until he was fourteen, when a family-friend discovered him making an elaborate drawing of a figure in Euclid with ruler and compasses. She explained the aim of Euclid to Augustus, and gave him an initiation into demonstration.
  
  wn.com/Augustus_De_Morgan
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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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  Avicenna
  Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā (Persian پورسينا Pur Sina [ˈpuːr ˈsiːnɑː] "son of Sina"; c. 980, Afshana near Bukhara– 1037, Hamadan, Iran), commonly known as Ibn Sīnā or by his Latinized name Avicenna, was a Persianpolymath, who wrote almost 450 treatises on a wide range of subjects, of which around 240 have survived. In particular, 150 of his surviving treatises concentrate on philosophy and 40 of them concentrate on medicine.
  His most famous works are The Book of Healing, a vast philosophical and scientific encyclopaedia, and The Canon of Medicine, which was a standard medical text at many medieval universities. The Canon of Medicine was used as a text-book in the universities of Montpellier and Leuven as late as 1650. Ibn Sīnā's Canon of Medicine provides a complete system of medicine according to the principles of Galen (and Hippocrates).
  His corpus also includes writing on philosophy, astronomy, alchemy, geology, psychology, Islamic theology, logic, mathematics, physics, as well as poetry. He is regarded as the most famous and influential polymath of the Islamic Golden Age.
  
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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.
  
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  Chrysippus
  Chrysippus of Soli (Ancient Greek: Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus; c. 279 BC – c. 206 BC) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. A prolific writer, Chrysippus expanded the fundamental doctrines of Zeno of Citium, the founder of the school, which earned him the title of Second Founder of Stoicism.
  Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. Ethics, he taught, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unruly passions which depress and crush the soul. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world.
  
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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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  David Hilbert
  David Hilbert, FRS (German pronunciation: [ˈdaːvɪt ˈhɪlbɐt]; January 23, 1862 – February 14, 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
  Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
  Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
  
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  Duns Scotus
  John (Johannes, Ioannes) Duns Scotus, O.F.M. (c. 1256 – November 18, 1308) was one of the more important theologians and philosophers of the High Middle Ages. He was given the medieval accolade Doctor Subtilis (Subtle Doctor) for his penetrating and subtle manner of thought.
  Scotus has had considerable influence on Roman Catholic thought. The doctrines for which he is best known are the "univocity of being," that existence is the most abstract concept we have, applicable to everything that exists; the formal distinction, a way of distinguishing between different aspects of the same thing; and the idea of haecceity, the property supposed to be in each individual thing that makes it an individual. Scotus also developed a complex argument for the existence of God, and argued for the Immaculate conception of Mary.
  Little is known of Scotus' life. He was probably born in 1265, probably at Duns, in Berwickshire, Scotland. In 1291 he was ordained as a priest in Northampton, England. A note in Codex 66 of Merton College, Oxford, records that Scotus "flourished at Cambridge, Oxford and Paris. He began lecturing on Peter Lombard's Sentences at the prestigious University of Paris in the Autumn of 1302. Later in that academic year, however, he was expelled from the University of Paris for siding with then Pope Boniface VIII in his feud with Philip the Fair of France, over the taxation of church property.
  
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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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  Ernst Schröder
  Ernst Schröder (25 November 1841, Mannheim, Baden, Germany – 16 June 1902, Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic (a term he may have invented), by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental Vorlesungen über die Algebra der Logik (Lectures on the algebra of logic), in 3 volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day.
  Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Hesse, Kirchhoff, and Franz Neumann. After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. Two years later, he took up a chair in mathematics at the Polytechnische Schule in Karlsruhe, where he spent the remainder of his life. He never married.
  
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  Ernst Zermelo
  Ernst Friedrich Ferdinand Zermelo (German: [ʦɛrˈmeːlo]; 1871–1953) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy.^{[citation needed]} He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.
  He graduated from Berlin's Luisenstädtisches Gymnasium in 1889. He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (Untersuchungen zur Variationsrechnung). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose guidance he began to study hydrodynamics. In 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899.
  In 1910, Zermelo left Göttingen upon being appointed to the chair of mathematics at Zurich University, which he resigned in 1916. He was appointed to an honorary chair at Freiburg im Breisgau in 1926, which he resigned in 1935 because he disapproved of Hitler's regime. At the end of World War II and at his request, Zermelo was reinstated to his honorary position in Freiburg.
  
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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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  Georg Cantor
  Georg Ferdinand Ludwig Philipp Cantor ( /ˈkæntɔr/ KAN-tor; German: [ɡeˈɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.
  
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  George Boole
  George Boole ( /ˈbuːl/; 2 November 1815 – 8 December 1864) was an English-born mathematician and logician. His work was in the fields of differential equations and algebraic logic, and he is now best known as the author of The Laws of Thought. As the inventor of the prototype of what is now called Boolean logic, which became the basis of the modern digital computer, Boole is regarded in hindsight as a founder of the field of computer science. Boole said,
  ... no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise ... those universal laws of thought which are the basis of all reasoning ...
  George Boole's father, John Boole (1779–1848), was a tradesman in Lincoln and gave him lessons. He had an elementary school education, but little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin; which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. At age 16 Boole took up a junior teaching position in Doncaster, at Heigham's School, being at this point the breadwinner for his parents and three younger siblings. He taught also in Liverpool, briefly.
  
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• George Boolos
  George Stephen Boolos (September 4, 1940, New York City – May 27, 1996) was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
  Boolos graduated from Princeton University in 1961 with an A.B. in mathematics. Oxford University awarded him the B.Phil in 1963. In 1966, he obtained the first Ph.D. in philosophy ever awarded by the Massachusetts Institute of Technology, under the direction of Hilary Putnam. After teaching three years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career until his death from cancer.
  A charismatic speaker well known for his clarity and wit, he once delivered a lecture (1994b) giving an account of Gödel's second incompleteness theorem, employing only words of one syllable. At the end of his viva, Hilary Putnam asked him, "And tell us, Mr. Boolos, what does the analytical hierarchy have to do with the real world?" Without hesitating Boolos replied, "It's part of it".
  An expert on puzzles of all kinds, in 1993 Boolos reached the London Regional Final of The Times crossword competition. His score was one of the highest ever recorded by an American. He wrote a paper on "the hardest logic puzzle ever"—one of many puzzles created by Raymond Smullyan.
  
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  Gerhard Gentzen
  Gerhard Karl Erich Gentzen (November 24, 1909, Greifswald, Germany – August 4, 1945, Prague, Czechoslovakia) was a German mathematician and logician. He had his major contributions in the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died in 1945 after the Second World War, because he was deprived of food after being arrested in Prague.
  Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. At great risk to his career Gentzen kept in contact with Bernays until the beginning of the Second World War. In November 1933, he joined the Sturmabteilung to pass the state exam for teachers.^{[citation needed]} In 1935, he corresponded with Abraham Fraenkel from Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in 1933 until his resignation under Nazi pressure, made strong efforts to bring him to the Institute for Advanced Study in Princeton.
  
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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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  Giuseppe Peano
  Giuseppe Peano (Italian pronunciation: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician, whose work was of philosophical value. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin.
  Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the University of Turin in 1876, graduating in 1880 with high honours, after which the University employed him to assist first Enrico D'Ovidio, and then Angelo Genocchi, the Chair of Infinitesimal calculus. Due to Genocchi's poor health, Peano took over the teaching of the infinitesimal calculus course within 2 years. His first major work, a textbook on calculus, was published in 1884 and was credited to Genocchi. A few years later, Peano published his first book dealing with mathematical logic. Here the modern symbols for the union and intersection of sets appeared for the first time.
  
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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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• Haskell Curry
  Haskell Brooks Curry (September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel, much of the development was done by Curry. Curry is also known for Curry's paradox and the Curry–Howard correspondence. There are three programming languages named after him, Haskell, Brooks and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.
  Curry was born on September 12, 1900, in Millis, Massachusetts, to Samuel Silas Curry and Anna Baright Curry, who ran a school for elocution. He entered Harvard University in 1916 to study medicine but switched to mathematics before graduating in 1920. After two years of graduate work in electrical engineering at MIT, he returned to Harvard to study physics, earning a MA in 1924. Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica, the attempt by Alfred North Whitehead and Bertrand Russell to ground mathematics in symbolic logic. Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to Göttingen where he could work with Heinrich Behmann and Paul Bernays, who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic.
  
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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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  Hilary Putnam
  Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. He is known for his willingness to apply an equal degree of scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposes its flaws. As a result, he has acquired a reputation for frequently changing his own position. Putnam is currently Cogan University Professor Emeritus at Harvard University.
  In philosophy of mind, Putnam is known for his argument against the type-identity of mental and physical states based on his hypothesis of the multiple realizability of the mental, and for the concept of functionalism, an influential theory regarding the mind-body problem. In philosophy of language, along with Saul Kripke and others, he developed the causal theory of reference, and formulated an original theory of meaning, inventing the notion of semantic externalism based on a famous thought experiment called Twin Earth.
  
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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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• 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.
  
  wn.com/Jacques_Derrida
• Jon Barwise
  Kenneth Jon Barwise (June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.
  Born in Independence, Missouri to Kenneth T. and Evelyn, he was a precocious child.
  A pupil of Solomon Feferman at Stanford University, Barwise started his research in infinitary logic. After positions as assistant professor at the Universities of Yale and Wisconsin, during which time his interests turned to natural language, he returned to Stanford in 1983 to direct the Center for the Study of Language and Information. He began teaching at Indiana University in 1990. He was elected a Fellow of the American Academy of Arts and Sciences in 1999.
  Barwise contended that, by being explicit about the context in which a proposition is made, the situation, many problems in the application of logic can be eliminated. He sought ... to understand meaning and inference within a general theory of information, one that takes us outside the realm of sentences and relations between sentences of any language, natural or formal. In particular, he claimed that such an approach resolved the liar paradox. He made use of Peter Aczel's non-well-founded set theory in understanding "vicious circles" of reasoning.
  
  wn.com/Jon_Barwise
• 
  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.
  
  wn.com/Kurt_Gödel
• 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.
  
  wn.com/Leonard_Bloomfield
• Leopold Löwenheim
  Leopold Löwenheim (26 June 1878 in Krefeld, Germany (also the birthplace of Max Zorn) – 5 May 1957 in Berlin) was a German mathematician, known for his work in mathematical logic. The Nazi regime forced him to retire because under the Nuremberg Laws he was considered only three quarters Aryan. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics.
  Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory.
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  wn.com/Leopold_Löwenheim
• 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".
  
  wn.com/Lev_Vygotsky
• 
  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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• 
  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.
  
  wn.com/Noam_Chomsky
• Paul Bernays
  Paul Isaac Bernays (17 October 1888, London – 18 September 1977, Zurich) was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator with, David Hilbert.
  Bernays spent his childhood in Berlin. Bernays attended the Köllner Gymnasium, 1895-1907. At the University of Berlin, he studied mathematics under Issai Schur, Edmund Landau, Ferdinand Georg Frobenius, and Friedrich Schottky; philosophy under Alois Riehl, Carl Stumpf and Ernst Cassirer; and physics under Max Planck. At the University of Göttingen, he studied mathematics under David Hilbert, Edmund Landau, Hermann Weyl, and Felix Klein; physics under Voigt and Max Born; and philosophy under Leonard Nelson.
  In 1912, the University of Berlin awarded him a Ph.D. in mathematics, for a thesis, supervised by Landau, on the analytic number theory of binary quadratic forms. That same year, the University of Zurich awarded him the Habilitation for a thesis on function theory and Picard's theorem. The examiner was Ernst Zermelo. Bernays was Privatdozent at the University of Zurich, 1912-17, where he came to know George Pólya.
  
  wn.com/Paul_Bernays
• 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.
  
  wn.com/Paul_Ricœur
• 
  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.
  
  wn.com/Paul_Tillich
• Peter Geach
  Peter Thomas Geach, MA, FBA ( /ˈɡiːtʃ/; born 29 March 1916) is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.
  Geach was educated at Balliol College, Oxford. He taught at Birmingham University (1951–1966) and from 1966 at the University of Leeds where he was Professor of Logic in the Department of Philosophy. Geach was given the title of Emeritus Professor of Logic on his retirement in 1981.
  Geach was elected a Fellow of the British Academy (FBA) in 1965.
  He has been awarded the papal cross "Pro Ecclesia et Pontifice" by the Holy See for his philosophical work.
  His early work includes the classic texts Mental Acts and Reference and Generality, the latter defending an essentially modern conception of reference against medieval theories of supposition.
  His Catholic perspective is integral to his philosophy. He is perhaps the founder of Analytical Thomism (though the current of thought running through his and Elizabeth Anscombe's work to the present day was only ostensibly so named forty years later by John Haldane), the aim of which is to synthesise Thomistic and Analytic approaches. He defends the Thomistic position that human beings are essentially rational animals, each one miraculously created. He dismisses Darwinistic attempts to regard reason as inessential to humanity, as "mere sophistry, laughable, or pitiable." He repudiates any capacity for language in animals as mere "association of manual signs with things or performances."
  
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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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• Raymond Smullyan
  Raymond Merrill Smullyan (born May 25, 1919) is an American mathematician, concert pianist, logician, Taoist philosopher, and magician.
  Born in Far Rockaway, New York, his first career (like Persi Diaconis a generation later) was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church.
  Born in Far Rockaway, New York, he showed musical talent, winning a gold medal in a piano competition when he was aged 12. The following year, his family moved to Manhattan and he attended Theodore Roosevelt High School in The Bronx as this school offered courses suited to his musical talents, but he left to study on his own as the school did not offer similar courses in mathematics.
  He attended several colleges, studying mathematics and music.
  While a Ph.D. student, Smullyan published a paper in the 1957 Journal of Symbolic Logic showing that Gödelian incompleteness held for formal systems considerably more elementary than that of Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed at Tarski's theorem, which is much easier to prove and equally disturbing philosophically. The culmination of Smullyan's lifelong reflection on the classic limitative theorems of mathematical logic is quite readable:
  
  wn.com/Raymond_Smullyan
• 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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  Stephen Cole Kleene
  Stephen Cole Kleene (January 5, 1909, Hartford, Connecticut, United States – January 25, 1994, Madison, Wisconsin) was an American mathematician who helped lay the foundations for theoretical computer science. One of many distinguished students of Alonzo Church, Kleene, along with Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory. Kleene's work grounds the study of which functions are computable. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixpoint theorem. He also invented regular expressions, and was a leading American advocate of mathematical intuitionism.
  Kleene pronounced his last name /ˈkleɪniː/ KLAY-nee. Commonplace mispronunciations include /ˈkliːniː/ and /ˈkliːn/. (His son, Ken Kleene, wrote: "As far as I am aware this pronunciation is incorrect in all known languages. I believe that this novel pronunciation was invented by my father.")^{[citation needed]}
  
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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.
  
  wn.com/Thomas_Hobbes
• Thoralf Skolem
  Thoralf Albert Skolem (23 May 1887 – 23 March 1963) (Norwegian pronunciation: [ˈtuːɾɑlf ˈskuːləm]) was a Norwegian mathematician known mainly for his work on mathematical logic and set theory.
  Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the university entrance examinations in 1905. He then entered Det Kongelige Frederiks Universitet to study mathematics, also taking courses in physics, chemistry, zoology and botany.
  In 1909, he began working as an assistant to the physicist Kristian Birkeland, known for bombarding magnetized spheres with electrons and obtaining aurora-like effects; thus Skolem's first publications were physics papers written jointly with Birkeland. In 1913, Skolem passed the state examinations with distinction, and completed a dissertation titled Investigations on the Algebra of Logic. He also traveled with Birkeland to the Sudan to observe the zodiacal light. He spent the winter semester of 1915 at the University of Göttingen, at the time the leading research center in mathematical logic, metamathematics, and abstract algebra, fields in which Skolem eventually excelled. In 1916 he was appointed a research fellow at Det Kongelige Frederiks Universitet. In 1918, he became a Docent in Mathematics and was elected to the Norwegian Academy of Science and Letters.
  
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  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".
  
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  William of Ockham
  William of Ockham ( /ˈɒkəm/; also Occam, Hockham, or several other spellings; c. 1288 – c. 1348) was an English Franciscan friar and scholastic philosopher, who is believed to have been born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the fourteenth century. Although he is commonly known for Ockham's razor, the methodological principle that bears his name, William of Ockham also produced significant works on logic, physics, and theology. In the Church of England, his day of commemoration is 10 April.
  William of Ockham joined the Franciscan order at an early age. It is believed that he studied theology at the University of Oxford from 1309 to 1321, but never completed his master's degree (the usual undergraduate degree in those times). Because of this, he acquired the byname Venerabilis Inceptor, or "Worthy Beginner" (an inceptor was a student formally admitted to the ranks of teachers by the university authorities). He was also known as the Doctor Invincibilis or "Unconquerable Teacher."
  
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  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

8: the Mormon Proposition (2010)

Actors

• R (for Some Language/sexual References)

Director

• Reed Cowan

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