Elementary Foundations: An introduction to topics in discrete mathematics

Let $x$ be a variable in the domain of all living humans. Define predicates

and consider the statement

which says “every three-hundred-year-old Augustana student is tall”. This statement is true, since a conditional $p\to q$ is true when $p$ is false, and $A(x)\wedge B(x)$ is false for each and every $x\text{:}$ there is no living human who is both three hundred years old and is an Augustana student (issues concerning the existence of vampires notwithstanding). But by the same reasoning, the statement “every three-hundred-year-old Augustana student is not tall” is true. This seems to be a contradiction: how can every three-hundred-year-old Augustana student be both tall and not tall? The answer is that you can say anything you like about things that do not exist and your statement will be true. So you should avoid altogether making claims about things that do not exist.