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Plural quantification, the Glossary

Index Plural quantification

In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values.[1]

Table of Contents

  1. 38 relations: Abstract and concrete, Adam Morton, Arity, Barry Smith (ontologist), Bertrand Russell, David Lewis (philosopher), Ernst Schröder (mathematician), First-order logic, Foundations of mathematics, Fred Landman, Friederike Moltmann, Generalized quantifier, George Boolos, Godehard Link, Gottfried Wilhelm Leibniz, Gottlob Frege, Homogeneity (semantics), John Stuart Mill, Mathematical logic, Mathematics, Monadic predicate calculus, Monadic second-order logic, Nominalism, Nonfirstorderizability, Ontological commitment, Paradox, Peter Lasersohn, Peter Simons (academic), Plural, Problem of universals, Remko Scha, Second-order logic, Sentence (mathematical logic), Set theory, The Principles of Mathematics, Variable (mathematics), Variadic function, Willard Van Orman Quine.

  2. Quantifier (logic)

Abstract and concrete

In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities.

See Plural quantification and Abstract and concrete

Adam Morton

Adam Morton (1945 – 2020) was a Canadian philosopher.

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Arity

In logic, mathematics, and computer science, arity is the number of arguments or operands taken by a function, operation or relation.

See Plural quantification and Arity

Barry Smith (ontologist)

Barry Smith (born 4 June 1952) is an academic working in the field of Applied Ontology.

See Plural quantification and Barry Smith (ontologist)

Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, logician, philosopher, and public intellectual.

See Plural quantification and Bertrand Russell

David Lewis (philosopher)

David Kellogg Lewis (September 28, 1941 – October 14, 2001) was an American philosopher.

See Plural quantification and David Lewis (philosopher)

Ernst Schröder (mathematician)

Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Grand Duchy of Baden – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic.

See Plural quantification and Ernst Schröder (mathematician)

First-order logic

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

See Plural quantification and First-order logic

Foundations of mathematics

Foundations of mathematics is the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc.

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Fred Landman

Fred (Alfred) Landman (פרד לנדמן; born October 28, 1956) is a Dutch-born Israeli professor of semantics.

See Plural quantification and Fred Landman

Friederike Moltmann

Friederike Moltmann is a German linguist and philosopher.

See Plural quantification and Friederike Moltmann

Generalized quantifier

In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. Plural quantification and generalized quantifier are quantifier (logic).

See Plural quantification and Generalized quantifier

George Boolos

George Stephen Boolos (September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.

See Plural quantification and George Boolos

Godehard Link (born 7 July 1944 in Lippstadt) is a professor of logic and philosophy of science at the University of Munich.

See Plural quantification and Godehard Link

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (– 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics, such as binary arithmetic, and statistics.

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Gottlob Frege

Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.

See Plural quantification and Gottlob Frege

Homogeneity (semantics)

In formal semantics, homogeneity is the phenomenon where plural expressions that seem to mean "all" negate to "none" rather than "not all".

See Plural quantification and Homogeneity (semantics)

John Stuart Mill

John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, politician and civil servant.

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Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Plural quantification and Mathematics

Monadic predicate calculus

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols.

See Plural quantification and Monadic predicate calculus

Monadic second-order logic

In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets.

See Plural quantification and Monadic second-order logic

Nominalism

In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels.

See Plural quantification and Nominalism

Nonfirstorderizability

In formal logic, nonfirstorderizability is the inability of a natural-language statement to be adequately captured by a formula of first-order logic.

See Plural quantification and Nonfirstorderizability

Ontological commitment

In formal semantics, an ontological commitment of a language is one or more objects postulated to exist by that language.

See Plural quantification and Ontological commitment

Paradox

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation.

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Peter Lasersohn

Peter Lasersohn is a professor of linguistics at the University of Illinois at Urbana-Champaign.

See Plural quantification and Peter Lasersohn

Peter Simons (academic)

Peter Murray Simons, (born 23 March 1950) is a British retired philosopher and academic.

See Plural quantification and Peter Simons (academic)

Plural

The plural (sometimes abbreviated as pl., pl, or), in many languages, is one of the values of the grammatical category of number.

See Plural quantification and Plural

Problem of universals

The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?" The problem of universals relates to various inquiries closely related to metaphysics, logic, and epistemology, as far back as Plato and Aristotle, in efforts to define the mental connections a human makes when they understand a property such as shape or color to be the same in nonidentical objects.

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Remko Scha

Remko Jan Hendrik Scha (15 September 1945 – 9 November 2015) was a professor of computational linguistics at the faculty of humanities and Institute for Logic, Language and Computation at the University of Amsterdam.

See Plural quantification and Remko Scha

Second-order logic

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.

See Plural quantification and Second-order logic

Sentence (mathematical logic)

In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables.

See Plural quantification and Sentence (mathematical logic)

Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.

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The Principles of Mathematics

The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.

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Variable (mathematics)

In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object.

See Plural quantification and Variable (mathematics)

Variadic function

In mathematics and in computer programming, a variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments.

See Plural quantification and Variadic function

Willard Van Orman Quine

Willard Van Orman Quine (known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century".

See Plural quantification and Willard Van Orman Quine

See also

Quantifier (logic)

References

[1] https://en.wikipedia.org/wiki/Plural_quantification

Also known as Anadic predicate, Anadic relation, Multigrade predicate, Multigrade relation, Plural logic, Plural quantifier, Plural reference, Variably polyadic predicate, Variably polyadic relation.