en>Zfeinst: /* Copula correlations */

2014-01-09T22:18:26Z

Copula correlations

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In [[predicate logic]], '''existential generalization'''<ref>Hurley</ref><ref>Copi and Cohen</ref> (also known as '''existential introduction''', '''∃I''') is a [[validity|valid]] [[rule of inference]] that allows one to move from a specific statement to a quantified generalized statement. In [[first-order logic]], it is often used as a rule for the [[existential quantifier]] (∃) in formal proofs.

Example: "Rover loves to wag his tail. Therefore, something loves to wag its tail."

In the [[Fitch-style calculus]]:

:<math> Q(a) \to\ \exists{x}\, Q(x)</math>

Where ''a'' replaces all free instances of ''x'' within ''Q''(''x'').<ref>pg. 347. Jon Barwise and John Etchemendy, ''Language proof and logic'' Second Ed., CSLI Publications, 2008.</ref>

== Quine ==

[[Universal instantiation]] and '''Existential Generalization''' are two aspects of a single principle, for instead of saying that '(x)(x=x)' implies 'Socrates is Socrates', we could as well say that the denial 'Socrates≠Socrates' implies '(∃x)(x≠x)'. The principle embodied in these two operations is the link between [[quantification]]s and the singular statements that are related to them as instances. Yet it is a principle only by courtesy. It holds only in the case where a term names and, furthermore, occurs [[Reference|referentially]].<ref>Quine,W.V.O., Quintessence, Extensionalism, Reference and Modality, P366</ref>

==See also==
*[[Existential quantification]]
*[[Inference rules]]

==References==
{{Reflist}}

{{DEFAULTSORT:Existential Generalization}}
[[Category:Rules of inference]]
[[Category:Predicate logic]]

{{Logic-stub}}

Financial correlation - Revision history

en>Zfeinst: /* Copula correlations */