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Peirce's Law
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law of excluded middle written in a form that involves only one sort of connective, namely implication. In propositional calculus, Peirce's law says that ((''P''→''Q'')→''P'')→''P''. Written out, this means that ''P'' must be true if there is a proposition ''Q'' such that the truth of ''P'' follows from the truth of "if ''P'' then ''Q''". In particular, when ''Q'' is taken to be a false formula, the law says that if ''P'' must be true whenever it implies falsity, then ''P'' is true. In this way Peirce's law implies the law of excluded middle. Peirce's law does not hold in intuitionistic logic or intermediate logics and cannot be deduced from the deduction theorem alone. Under the Curry–Howard isomorphism, Peirce's law is the type of continuation operators, e.g. call/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 usua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuation
In computer science, a continuation is an abstract representation of the control state of a computer program. A continuation implements ( reifies) the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process's execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment. Continuations are useful for encoding other control mechanisms in programming languages such as exceptions, generators, coroutines, and so on. The "current continuation" or "continuation of the computation step" is the continuation that, from the perspective of running code, would be derived from the current point in a program's execution. The term ''continuations'' can also be used to refer to first-class continuations, which are constructs that give a programming language the ability to save the execution state at any point and return to that point at a lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur W
Arthur is a common male given name of Brythonic origin. Its popularity derives from it being the name of the legendary hero King Arthur. The etymology is disputed. It may derive from the Celtic ''Artos'' meaning “Bear”. Another theory, more widely believed, is that the name is derived from the Roman clan '' Artorius'' who lived in Roman Britain for centuries. A common spelling variant used in many Slavic, Romance, and Germanic languages is Artur. In Spanish and Italian it is Arturo. Etymology The earliest datable attestation of the name Arthur is in the early 9th century Welsh-Latin text '' Historia Brittonum'', where it refers to a circa 5th to 6th-century Briton general who fought against the invading Saxons, and who later gave rise to the famous King Arthur of medieval legend and literature. A possible earlier mention of the same man is to be found in the epic Welsh poem ''Y Gododdin'' by Aneirin, which some scholars assign to the late 6th century, though this is still ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Weiss (philosopher)
Paul Weiss (; May 19, 1901 – July 5, 2002) was an American philosopher. He was the founder of '' The Review of Metaphysics'' and the Metaphysical Society of America. Early life and education Paul Weiss grew up on the Lower East Side of New York City. His father, Samuel Weiss (d. 1917), was a Jewish emigrant who moved from Europe in the 1890s. He worked as a tinsmith, a coppersmith, and a boilermaker. Paul Weiss's mother, Emma Rothschild (Weiss) (d. 1915), was a Jewish emigrant who worked as a servant until she married Samuel. Born into a Jewish family, Paul lived among other Jewish families in a working-class neighborhood in the Yorkville section of Manhattan. Originally given the Hebrew name "Peretz," Weiss says in his autobiography that the name "Paul" was his "registered name" and "part of his mother's attempt to move upward in the American world."Weiss, Paul. The Philosophy of Paul Weiss. Ed. Lewis Hahn. Chicago : Open Court, 1995. He had three brothers, two older and on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Hartshorne
Charles Hartshorne (; June 5, 1897 – October 9, 2000) was an American philosopher who concentrated primarily on the philosophy of religion and metaphysics, but also contributed to ornithology. He developed the neoclassical idea of God and produced a modal proof of the existence of God that was a development of Anselm of Canterbury's ontological argument. Hartshorne is also noted for developing Alfred North Whitehead's process philosophy into process theology. Early life and education Hartshorne (pronounced harts-horn) was born in Kittanning, Pennsylvania, and was a son of Reverend Francis Cope Hartshorne (1868-1950) and Marguerite Haughton (1868-1959), who were married on April 25, 1895, in Bryn Mawr, Montgomery County, Pennsylvania. Rev. F. C. Hartshorne, who was a minister in the Protestant Episcopal Church, was rector of St. Paul's Episcopal Church in Kittanning from 1897 to 1909, then rector of St. Peter's Episcopal Church in Phoenixville, Pennsylvania for 19 years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce Bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), see the (Chronological Overview) on the (Writings) page for Charles Sanders Peirce. Abbreviations Click on abbreviation in order to jump down this page to the relevant edition information. Click on the abbreviation appearing with that edition information in order to return here. Main editions (posthumous) Other Primary literature Bibliographies and microfilms Other bibliographies of primary literature * Burks, Arthur W. (1958). "Bibliography of the Works of Charles Sanders Peirce." CP 8:260–321. * Cohen, Morris R. (1916). "Charles S. Peirce and a Tentative Bibliography of His Published Writings." '' The Journal of Philosophy, Psychology, and Scientific Methods'' 13(26):726–37. *Fisch, Max H. (1964). "A First Supplemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term ''fuzzy logic'' was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univ ... [...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 logically contingent. Such a formula can be made either true or false based on the values assigned to its propositional variables. The dou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excluded Middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradiction, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law (or principle) of the excluded third, in Latin ''principium tertii exclusi''. Another Latin designation for this law is ''tertium non datur'': "no third ossibilityis given". It is a tautology. The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the futu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scheme (programming Language)
Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT AI Lab and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.Common LISP: The Language, 2nd Ed., Guy L. Steele Jr. Digital Press; 1981. . "Common Lisp is a new dialect of Lisp, a successor to MacLisp, influenced strongly by ZetaLisp and to some extent by Scheme and InterLisp." The Scheme language is standardized in the official IEEE standard1178-1990 (Reaff 2008) IEEE Standard for t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
