Concept

Existential quantification

Overview

In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"), read as "there exists", "there is at least one", or "for some". Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.

Quantification in general is covered in the article on quantification (logic). The existential quantifier is encoded as U+2203 ∃ THERE EXISTS in Unicode, and as \exists in LaTeX and related formula editors.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. The logical basis of the theory alone belongs to philosophy, and alone will occupy us to-night. The way the problem of continuity enters into philosophy is, broadly speaking, the following: Space and time are treated by mathematicians as consisting of points and instants, but they also have a property, easier to feel than to define, which is called continuity, and is thought by many philosophers to be destroyed when…

   Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy

   States what Existential quantification is; the author is tied to Existential quantification in the knowledge graph.

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2. All types of series are capable of formal definition, and their properties can be deduced from the principles of symbolic logic by means of the Algebra of Relatives. The notion of a limit, which is fundamental in the greater part of higher mathematics, used to be defined by means of quantity, as a term to which the terms of some series approximate as nearly as we please. But nowadays the limit is defined quite…

   Bertrand Russell, Mysticism and Logic and Other Essays

   States what Existential quantification is; the author is tied to Existential quantification in the knowledge graph.

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3. The copula is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition, The earth is round, the Predicate is the word _round_, which denotes the quality affirmed, or (as the phrase is) predicated: _the earth_, words denoting the object which that quality is affirmed of, compose the…

   John Stuart Mill, A System of Logic

   States what Existential quantification is.

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Philosophers who discussed Existential quantification

• Willard Van Orman Quine

Related ideas

• First-order logic
• Giuseppe Peano
• Parity (mathematics)
• Logical conjunction
• Logical connective
• Mathematical logic
• Real number
• Natural number
• Domain of discourse
• Power set
• Symbol (formal)
• Rule of inference
• Saunders Mac Lane
• Logical truth
• Bertrand Russell
• Quantifier (logic)
• Logic
• Property (philosophy)
• Category theory
• De Morgan's laws
• Universal quantification
• Mathematical proof
• E
• Existence

Opposing perspectives

• Proposition

Place in the tradition

Part of Analytic philosophy.

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