Definition:Predicate/Is of Identity

Definition

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.

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 2$: The Axiom of Specification