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Language, Proof And Logic
Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four software programs, where three of them are logic related (Boole, Fitch and Tarski's World) and the other (Submit) is an internet-based grading service. The name is a pun derived from ''Language, Truth, and Logic'', the philosophy book by A. J. Ayer. On September 2, 2014, there was launched a massive open online course (MOOC) with the same name, which utilizes this educational software package. Description A short description of the programs: * Boole (named after George Boole) - a program that facilitates the construction and checking of truth tables and related notions ( tautology, tautological consequence, etc.); * Fitch (named after Frederic Brenton Fitch) - a natural deduction proof environment in Fitch-style calculus for giving and chec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Education and career Born in Independence, Missouri to Kenneth T. and Evelyn Barwise, Jon 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 Yale University and the University of 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. In his last year, Barwise was invited to give the 2000 Gödel Lecture; he died prior to the lecture. Philosophical and logical work Barwise contended that, by being explicit about the context in whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Etchemendy
John W. Etchemendy (born 1952 in Reno, Nevada) is an American logician and philosopher who served as Stanford University's twelfth Provost. He succeeded John L. Hennessy to the post on September 1, 2000 and stepped down on January 31, 2017. Education and career John Etchemendy received his bachelor's and master's degrees at the University of Nevada, Reno before earning his PhD in philosophy at Stanford in 1982. He has been a faculty member in Stanford's Department of Philosophy since 1983, prior to which he was a faculty member in the Philosophy Department at Princeton University. He is also a faculty member of Stanford's Symbolic Systems Program and a senior researcher at the Center for the Study of Language and Information at Stanford. At Stanford, Etchemendy served as director of the Center for the Study of Language and Information from 1990 to 1993, senior associate dean in the School of Humanities and Sciences from 1993 to 1997, and chair of the Department of Philosophy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Language, Truth, And Logic
''Language, Truth and Logic'' is a 1936 book about meaning by the philosopher Alfred Jules Ayer, in which the author defines, explains, and argues for the verification principle of logical positivism, sometimes referred to as the ''criterion of significance'' or ''criterion of meaning''. Ayer explains how the principle of verifiability may be applied to the problems of philosophy. ''Language, Truth and Logic'' brought some of the ideas of the Vienna Circle and the logical empiricists to the attention of the English-speaking world. Historical background According to Ayer's autobiographical book, ''Part of My Life'', it was work he started in the summer and autumn of 1933 that eventually led to ''Language, Truth and Logic'', specifically ''Demonstration of the Impossibility of Metaphysics''—later published in ''Mind'' under the editorship of G.E. Moore. The title of the book was taken ("To some extent plagiarized" according to Ayer) from Friedrich Waismann's ''Logik, Sprache, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massive Open Online Course
A massive open online course (MOOC ) or an open online course is an online course aimed at unlimited participation and open access via the Web. In addition to traditional course materials, such as filmed lectures, readings, and problem sets, many MOOCs provide interactive courses with user forums or social media discussions to support community interactions among students, professors, and teaching assistants (TAs), as well as immediate feedback to quick quizzes and assignments. MOOCs are a widely researched development in distance education, first introduced in 2008, that emerged as a popular mode of learning in 2012, a year called the "Year of the MOOC". Early MOOCs (cMOOCs: Connectivist MOOCs) often emphasized open-access features, such as open licensing of content, structure and learning goals, to promote the reuse and remixing of resources. Some later MOOCs (xMOOCs: extended MOOCs) use closed licenses for their course materials while maintaining free access for students. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Boole
George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of ''The Laws of Thought'' (1854) which contains Boolean algebra. Boolean logic is credited with laying the foundations for the Information Age. Early life Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole senior (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had 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.H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tautology (logic)
In mathematical logic, a tautology (from el, ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be Contingency (philosophy), logically contingent. Such a formula can be made either true or false based on the values assigned to its propositi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frederic Brenton Fitch
Frederic Brenton Fitch (September 9, 1908, Greenwich, Connecticut – September 18, 1987, New Haven, Connecticut) was an American logician, a Sterling Professor at Yale University. Education and career At Yale, Fitch earned his B.A in 1931 and his Ph.D. from Yale in 1934 under the supervision of F. S. C. Northrop. From 1934 to 1937 Fitch was a postdoc at the University of Virginia. In 1937 he returned to Yale, where he taught until his retirement in 1977. His doctoral students include Alan Ross Anderson, Ruth Barcan Marcus, and William W. Tait. Work Fitch was the inventor of the Fitch-style calculus for arranging formal logical proofs as diagrams. In his 1963 published paper "A Logical Analysis of Some Value Concepts" he proves "Theorem 5" (originally by Alonzo Church), which later became famous in context of the knowability paradox. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fitch-style Calculus
Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a notational system for constructing formal proofs used in sentential logics and predicate logics. Fitch-style proofs arrange the sequence of sentences that make up the proof into rows. A unique feature of Fitch notation is that the degree of indentation of each row conveys which assumptions are active for that step. Example Each row in a Fitch-style proof is either: * an assumption or subproof assumption. * a sentence justified by the citation of (1) a rule of inference and (2) the prior line or lines of the proof that license that rule. Introducing a new assumption increases the level of indentation, and begins a new vertical "scope" bar that continues to indent subsequent lines until the assumption is discharged. This mechanism immediately conveys which assumptions are active for any given line in the proof, without the assumptions needing to be rewritten on every line (as with sequent-style proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tarski's World
Tarski's World is a computer-based introduction to first-order logic written by Jon Barwise and John Etchemendy. It is named after the mathematical logician Alfred Tarski. The package includes a book, which serves as a textbook and manual, and a computer program which together serve as an introduction to the semantics of logic through games in which simple, three-dimensional worlds are populated with various geometric figures and these are used to test the truth or falsehood of first-order logic sentences. The program is also included in Language, Proof and Logic Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four sof ... package. The programme was later extended into Hyperproof. The programme * Barwise, J., & Etchemendy, J. (1993). ''Tarski's world''. Stanford, Calif: CSLI Publ. * Barker ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Tarski
Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician and mathematician. 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. Educated in Poland at the University of Warsaw, and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics, he immigrated to the United States in 1939 where he became a naturalized citizen in 1945. Tarski taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death in 1983. Feferman A. His biographers Anita Burdman Feferman and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
