请输入您要查询的百科知识：

　

词条 Existential generalization
释义

  1. Quine

  2. See also

  3. References

{{Transformation rules}}

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

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

  • Inference rules

References

1. ^{{cite book |last=Copi |first=Irving M. |last2=Cohen |first2=Carl |title=Introduction to Logic |publisher=Prentice Hall |year=2005}}
2. ^{{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |coauthors= |year=1991 |publisher=Wadsworth Publishing }}
3. ^pg. 347. Jon Barwise and John Etchemendy, Language proof and logic Second Ed., CSLI Publications, 2008.
4. ^{{cite book |author1=Willard Van Orman Quine |author1-link=Willard Van Orman Quine|author2=Roger F. Gibson |title=Quintessence |contribution= V.24. Reference and Modality |location=Cambridge, Massachusetts |publisher=Belknap Press of Harvard University Press |year=2008 |url=http://www.worldcat.org/title/quintessence-basic-readings-from-the-philosophy-of-wv-quine/oclc/728954096 }} Here: p.366.
{{DEFAULTSORT:Existential Generalization}}{{Logic-stub}}

2 : Rules of inference|Predicate logic
随便看

　

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

　

Copyright © 2023 OENC.NET All Rights Reserved
京ICP备2021023879号 更新时间：2024/11/13 12:25:09