# Quantifier shift

From Iron Chariots Wiki

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.

- <math>\forall x \exists y Rxy \vdash \exists y \forall x Rxy</math>

- 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.