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
