Fallacy of Every and All
Jump to navigation Jump to search
To not recognize such a shift in meaning is to commit the Fallacy of Every and All.
Let $x$ and $y$ be natural numbers.
- $\forall x \, \exists y : x = y$: for every $x$ there is some $y$ such that $x$ equals $y$.
Since $x = x$, this is true.
- $\exists y \, \forall x: x = y$: there is some $y$ such that for every $x$, $x$ equals $y$.