\begin{definition}[Definition:Predicate/Is of Identity]
Consider the sentence:
:'''Socrates is the philosopher who taught Plato.'''
This could be reworded as:
:'''The object named Socrates has the property of being the philosopher who taught Plato.'''
However, the meaning that is ''really'' being conveyed here is that of:
:'''The object named Socrates ''is the same object as'' the object which is the philosopher who taught Plato.'''
In this context, '''is''' is not being used in the same way as the ''is'' of predication.
When being used to indicate that one object is the same object as another object, '''is''' is called '''the ''is'' of identity'''.
In this context, ''is'' means the same as equals.
\end{definition}