# Existential generalization

Transformation rules |
---|

Propositional calculus |

Rules of inference |

Rules of replacement |

Predicate logic |

In predicate logic, **existential generalization**^{[1]}^{[2]} (also known as **existential introduction**, **∃I**) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. 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:

Where *a* replaces all free instances of *x* within *Q*(*x*).^{[3]}

## Quine[edit]

According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that "∀*x* *x*=*x*" implies "Socrates=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 quantifications 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 referentially.^{[4]}

## See also[edit]

## References[edit]

**^**Copi, Irving M.; Cohen, Carl (2005).*Introduction to Logic*. Prentice Hall.**^**Hurley, Patrick (1991).*A Concise Introduction to Logic 4th edition*. Wadsworth Publishing.**^**pg. 347. Jon Barwise and John Etchemendy,*Language proof and logic*Second Ed., CSLI Publications, 2008.**^**Willard Van Orman Quine; Roger F. Gibson (2008). "V.24. Reference and Modality".*Quintessence*. Cambridge, Massachusetts: Belknap Press of Harvard University Press. Here: p.366.

This logic-related article is a stub. You can help Wikipedia by expanding it. |