existential quantifier


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existential quantifier

n
(Logic) logic a formal device, for which the conventional symbol is ∃, which indicates that the open sentence that follows is true of at least one member of the relevant universe of interpretation, as (∃x) Fx meaning "something is (an) F," "something Fs," or "there are (some) Fs."
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

ex′isten′tial quan′tifier


n.
Logic.
a quantifier indicating that the sentential function within its scope is true for at least one value of the variable included in the quantifier.
[1935–40]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.existential quantifier - a logical quantifier of a proposition that asserts the existence of at least one thing for which the proposition is true
logical quantifier, quantifier - (logic) a word (such as `some' or `all' or `no') that binds the variables in a logical proposition
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
quantificateur existentiel
References in periodicals archive ?
The ontological commitments we require to show the necessity of ultimately founded propositions are, on the one hand, the possibilist interpretation of the existential quantifier or the assumption of a constant domain of the possible worlds W*; and, on the other hand, the modal logic S5.
It is pertinent to observe that the relative order of the existential quantifier and negation in (3) is the opposite of the order of the indefinite some and negation in (1): adult English only licenses the "nonisomorphic" interpretation of sentences like (1).
In addition, [for all], the universal quantifier, and [there exists], the existential quantifier, can occur in formulas.
Now consider a quantifier that behaves exactly like the universal quantifier (over individuals) in models with domains of cardinality [greater than or equal to] n, but like the existential quantifier in models with domains of cardinality < n.
60) Following this, Kolmogorov does not give the interpretation of the existential quantifier, as we would expect, since intuitionistically the existential quantifier cannot be defined using the universal and negation; but elsewhere in the paper he gives ample explanations of the meaning of existential claims in intuitionistic mathematics, and in particular, of the central point concerning them: that the person who makes the claim must be able to indicate a particular instance of it.
To eliminate an existential quantifier [exists]z [element of] U, we use the lemma above, by translating its statement into first-order logic.
Although it is a statement that there are at least two objects, (Two) is composed only of standard logical terminology: negation, identity, and first-order existential quantifiers. Since (Two) is a logical consequence of 0 [not equal to] 0, then according to our logicist (Two) is itself analytic and logically true, provided that analyticity and logical truth are closed under logical consequence, or at least the introduction rule for the first-order existential quantifier.
The rules for the independent existential quantifier elimination require the introduction of function letters (to express the independence).
"Being, existence, and ontological commitment" presents five theses of Quinian metaontology: (1-3) being is not an activity, is the same as existence, and is univocal; (4) the existential quantifier adequately captures the sense of being; (5) ontological disputes can be settled by determining the ontological commitments implied by established beliefs (this last is restated and illustrated in chapters four, eight, and ten).
Fitch's Paradox is presented as a problem for realism, and is 'solved', I think, by denying that existential quantifier elimination is legitimate.
However, the relation between these two representations, as well as the relation between the universal and the existential quantifier representation, is not made clear (it seems to me that the two exercises devoted to these issues are not very helpful).
For (ii), we slightly modify the previous formula [Phi] by turning the existential quantifier [exists]z into a universal quantifier [inverted] Az, and by replacing the last two conjuncts with