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61 relations: A Mathematician's Apology, A Mathematician's Miscellany, Alfred North Whitehead, Allegory (category theory), Alonzo Church, Axiom, Axiom of choice, Axiom of infinity, Axiom of reducibility, Axiom schema of replacement, Begriffsschrift, Bertrand Russell, Boolean algebra, Cardinal number, Catch-22 (logic), Completeness (logic), Concatenation, Consistency, Ernst Zermelo, First-order logic, Formal system, Formalism (philosophy of mathematics), Foundations of mathematics, Frank P. Ramsey, Gödel's completeness theorem, Gödel's incompleteness theorems, Geometry, Gottlob Frege, Hilbert's second problem, Information Processing Language, Ivor Grattan-Guinness, Jean van Heijenoort, Kurt Gödel, Logical truth, Ludwig Wittgenstein, Mathematical logic, Metamath, Michel Weber, Model theory, Modern Library, Modus ponens, Ordered pair, Ordinal number, Proposition, Propositional calculus, Propositional function, Real analysis, Real number, Rudolf Carnap, Rule of inference, ..., Russell's paradox, Set theory, Sheffer stroke, Stanford Encyclopedia of Philosophy, Stephen Cole Kleene, Syntax, The Principles of Mathematics, Tractatus Logico-Philosophicus, Truth table, Type theory, Zermelo–Fraenkel set theory. Expand index (11 more) »
A Mathematician's Apology
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy.
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A Mathematician's Miscellany
A Mathematician's Miscellany is an autobiography and collection of anecdotes by John Edensor Littlewood.
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Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.
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Allegory (category theory)
In the mathematical field of category theory, an allegory is a category that has some of the structure of the category of sets and binary relations between them.
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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.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Axiom of infinity
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom of reducibility
The axiom of reducibility was introduced by Bertrand Russell in the early 20th century as part of his ramified theory of types.
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Axiom schema of replacement
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.
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Begriffsschrift
Begriffsschrift (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.
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Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
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Catch-22 (logic)
A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules.
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Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
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Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.
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Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo (27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
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Formalism (philosophy of mathematics)
In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be considered to be statements about the consequences of certain string manipulation rules.
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Foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
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Frank P. Ramsey
Frank Plumpton Ramsey (22 February 1903 – 19 January 1930) was a British philosopher, mathematician and economist who made fundamental contributions to abstract algebra before his death at the age of 26.
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Gödel's completeness theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
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Hilbert's second problem
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems.
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Information Processing Language
Information Processing Language (IPL) is a programming language created by Allen Newell, Cliff Shaw, and Herbert A. Simon at RAND Corporation and the Carnegie Institute of Technology at about 1956.
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Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.
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Jean van Heijenoort
Jean Louis Maxime van Heijenoort (July 23, 1912 – March 29, 1986) was a pioneer historian of mathematical logic.
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Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
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Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.
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Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Metamath
Metamath is a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems covering conventional results in logic, set theory, number theory, group theory, algebra, analysis, and topology, as well as topics in Hilbert spaces and quantum logic.
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Michel Weber
Michel Weber is a Belgian philosopher, born in Brussels in 1963.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Modern Library
The Modern Library is an American publishing company.
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Modus ponens
In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
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Proposition
The term proposition has a broad use in contemporary analytic philosophy.
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Propositional calculus
Propositional calculus is a branch of logic.
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Propositional function
A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined.
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Real analysis
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rudolf Carnap
Rudolf Carnap (May 18, 1891 – September 14, 1970) was a German-born philosopher who was active in Europe before 1935 and in the United States thereafter.
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Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
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Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Sheffer stroke
In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written ↑, also written | (not to be confused with "||", which is often used to represent disjunction), or Dpq (in Bocheński notation), denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".
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Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users.
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Stephen Cole Kleene
Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.
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Syntax
In linguistics, syntax is the set of rules, principles, and processes that govern the structure of sentences in a given language, usually including word order.
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The Principles of Mathematics
The Principles of Mathematics (PoM) is a book written by Bertrand Russell in 1903.
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Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus (TLP) (Latin for "Logico-Philosophical Treatise") is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime.
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Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).
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Type theory
In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Mathematica Principia, Principia mathematica, Ramified Theory of Types, Ramified Type Theory, Ramified theory of types, Ramified type theory, Russell-Whitehead, Whitehead-Russell axioms.
References
[1] https://en.wikipedia.org/wiki/Principia_Mathematica
