# Quantifier shift

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A [[quantifier shift]] is a formal logical fallacy in which the quantifiers of a statement are improperly transposed. While this cannot always be easily recognized in common language, it can be expressed in both formal and informal terms. | A [[quantifier shift]] is a formal logical fallacy in which the quantifiers of a statement are improperly transposed. While this cannot always be easily recognized in common language, it can be expressed in both formal and informal terms. | ||

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:For every '''x''' there is a '''y''' such that '''R'''. Therefore, for every '''y''' there is an '''x''' such that '''R'''. | :For every '''x''' there is a '''y''' such that '''R'''. Therefore, for every '''y''' there is an '''x''' such that '''R'''. |

## Revision as of 23:25, 9 August 2011

A **quantifier shift** is a formal logical fallacy in which the quantifiers of a statement are improperly transposed. While this cannot always be easily recognized in common language, it can be expressed in both formal and informal terms.

- For every
**x**there is a**y**such that**R**. Therefore, for every**y**there is an**x**such that**R**.

The classical illustration of this fallacy is as follows:

- Everybody has something to believe in. Therefore, there is something that everybody believes in.

## Use in Apologetics

This is most commonly illustrated in First Cause arguments for the existence of God.

- Every event has a cause. Therefore, there is an event that caused all subsequent events.