Categories: Articles to be expanded since March 2007 | All articles to be expanded | 1903 births | 1995 deaths | 20th century mathematicians | American mathematicians | American logicians | Formal methods people | Princeton University alumni | Princeton University faculty | University of California, Los Angeles faculty The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The Mathematics Genealogy Project is a web-based database that gives an academic genealogy based on dissertation supervision relations. ... Image File history File links Portal. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other uses, see Reason (disambiguation). ... The history of logic documents the development of logic as it occurs in various rival cultures and traditions in history. ... Philosophical logic is the application of formal logical techniques to problems that concern philosophers. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... The metalogic of a system of logic is the formal proof supporting its soundness. ... Reasoning is the act of using reason to derive a conclusion from certain premises. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis which would, if true, best explain the relevant evidence. ... Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ... This article is about the word proposition as it is used in logic, philosophy, and linguistics. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... In logic, an argument is a set of statements, consisting of a number of premises, a number of inferences, and a conclusion, which is said to have the following property: if the premises are true, then the conclusion must be true, or highly likely to be true. ... In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... An argument is cogent if and only if the truth of the arguments premises would render the truth of the conclusion probable (i. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ... are you kiddin ? i was lookin for it for hours ... Look up fallacy in Wiktionary, the free dictionary. ... A syllogism (Greek: — conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Syntax in logic is a systematic statement of the rules governing the properly formed formulas (WFFs) of a logical system. ... The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so conscientious logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. ... In logic, WFF is an abbreviation for well-formed formula. ... An axiom is a sentence or proposition that is not proved or demonstrated and is considered as obvious or as an initial necessary consensus for a theory building or acceptation. ... Look up theorem in Wiktionary, the free dictionary. ... In mathematical logic, a formal system is consistent if it does not contain a contradiction, or, more precisely, for no proposition φ are both φ and ¬φ provable. ... (This article discusses the soundess notion of informal logic. ... In mathematical logic, a theory is complete, if it contains either or as a theorem for every sentence in its language. ... A logical system or theory is decidable if the set of all well-formed formulas valid in the system is decidable. ... In logic and mathematics, a formal system consists of two components, a formal language plus a set of inference rules or transformation rules. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ... Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate logic, propositional calculus, or sentential calculus. ... In mathematics, a finitary boolean function is a function of the form f : Bk → B, where B = {0, 1} is a boolean domain and where k is a nonnegative integer. ... In logic, the monadic predicate calculus is the fragment of predicate calculus in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters. ... In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are theorems of the formal system. ... In logic, a logical connective is a syntactic operation on sentences, or the symbol for such an operation, that corresponds to a logical operation on the logical values of those sentences. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ... ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ... In philosophical logic, a modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. ... Michaels the greatest boyfriend in the whole wide world, and Id love to call him in a phonebooth sometime. ... In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. ... doxastic logic is a modal logic that is concerned with reasoning about beliefs. ... Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. ... Introduced by Giorgi Japaridze in 2003, Computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. ... Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ... In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ... Relevance logic, also called relevant logic, is any of a family of non-classical substructural logics that impose certain restrictions on implication. ... A non-monotonic logic is a formal logic whose consequence relation is not monotonic. ... A paraconsistent logic is a logical system that attempts to deal nontrivially with contradictions. ... Dialetheism is a paraconsistent logic typified by its tolerance of at least some contradictions. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... Look up paradox in Wiktionary, the free dictionary. ... Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. ... Is logic empirical? is the title of two articles that discuss the radical concept, that the empirical facts about quantum phenomena may provide grounds for revising classical logic. ... Aristotle (Greek: AristotélÄ“s) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... George Boole [], (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. ... Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... Rudolf Carnap (May 18, 1891, Ronsdorf, Germany – September 14, 1970, Santa Monica, California) was an influential philosopher who was active in central Europe before 1935 and in the United States thereafter. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ... Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. ... [...]I dont believe in natural science. ... David Hilbert (January 23, 1862, Königsberg, East Prussia – February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ... Saul Aaron Kripke (born in November, 1940, Long Beach, New York) is an American philosopher and logician now emeritus from Princeton and professor of philosophy at CUNY Graduate Center. ... Giuseppe Peano Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher who has been a central figure in Western philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science. ... For people named Quine, see Quine (surname). ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician. ... // Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ... Alan Mathison Turing, OBE (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ... Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England – December 30, 1947 Cambridge, Massachusetts, USA) was an English-born mathematician who became a philosopher. ... For a more comprehensive list, see the List of logic topics. ... This is a list of topics in logic. ... A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. ... This is a list of rules of inference. ... This is a list of mathematical logic topics, by Wikipedia page. ... This is a list of basic discrete mathematics topics, by Wikipedia page. ... Set theory Axiomatic set theory Naive set theory Zermelo set theory Zermelo-Fraenkel set theory Kripke-Platek set theory with urelements Simple theorems in the algebra of sets Axiom of choice Zorns lemma Empty set Cardinality Cardinal number Aleph number Aleph null Aleph one Beth number Ordinal number Well... This is a list of paradoxes, grouped thematically. ... This is a list of fallacies. ... In logic, a set of symbols is frequently used to express logical constructs. ...