3.2 Everyone

Let's think about the following sentence:

``Everyone in the room fainted.''

This means that if x is an entity in the room, x fainted. However, ``everyone'' is a name that is not bound to anything, so we cannot use it in a proposition. We need a way to bind a name, say x, to each entity in everyone:

``For all (x is an entity in the room), x fainted.''

The above sentence explicity bound x to be an entity in the room. Furthermore, the ``for all'' part says ``it doesn't matter whom in the room x is bound to, the predicate is still true.'' The mathematical representation is as follows, assuming $\mathrm{E}_r$ means the set of all entities in the room, and $\mathrm{P}(x)$ means ``x fainted'':

$\forall x \in \mathrm{E}_r: \mathrm{P}(x)$