We give the meaning of ∀ by specifying what it takes for a sentence containing ∀ to be true:
\begin{enumerate}
\item Give every object a name.
\item For each name in turn, create a new sentence like this: delete the quantifier and replace all instances of the variable it binds with that name.
\item If ALL of the new sentences are true, so is the original sentence.
\end{enumerate}
