Introduction to Philosophy: Overhead

Introduction to Philosophy	Notes	*This is not a substitute for coming to class - or for reading* the material.**	Richard Lee
Philosophy 2003	Notes	Copyright © 2007, Richard Lee	Spring 2007

The Quantifier Shift Fallacy

Each thing at some point does not exist
does not entail
At some point each thing does not exist.

In less ambiguous language and more generally:

For each x, there is a y, such that . . .
does not entail
There is a y, such that for each x . . .

For example,

For each class at the University, there is a teacher, such that that teacher teaches that class.
does not entail
There is a teacher, such that for each class at the University that teacher teaches that class.

Aquinas argues from

For each thing there is a time such that it did not exist at that time. (I.e., each being at some time fails to exist.)
to
There is a time such that for each thing it did not exist at that time. (I.e., there is a time at which no thing existed.)

This inference is invalid. His argument, therefore, is unsound.

Richard Lee, rlee@uark.edu, last modified: 31 January 2003