Chapter 2
Identity in logic and the classical law
of thought
Indiscernibles
In his book Word and Object (§24), Willard Van Orman Quine, an influential
philosopher of the 20th century, remarked that although the notion of identity is
so simple, confusion over it is quite common. The confusion begins with the
equals sign ‘=’, which is the most common symbol used in basic arithmetic and
logic to express identity:
(1) , which means
x 1 is the same thing as x 2.Elementary school pupils are from first grade familiarized with this symbol,
which thus becomes such a basic tool of mental operations that most people do
not give much thought to it. Until their first class in Logic 101. Logicians do not
use terms and symbols lightly, for they are after universal principles and rules of
thought. Accordingly, they have produced a huge literature about identity and
identification contemplating the questions of how ‘=’ should properly be used
and what it means when it is used properly.
The simplest case is:
(2) Aristotle = Aristotle,