6.1.4. Identity

Although all the connectives that figured in our analyses of logical form received special notation and had logical properties we studied, only one predicate will count as logical vocabulary in this sense. Other predicates and all unanalyzed individual terms will be, like unanalyzed component sentences, part of the non-logical vocabulary which is assigned a meaning only by an interpretation.

The predicate that is part of our logical vocabulary will be referred to as identity. It is illustrated in the following sentences:

George Bush is the U.S. president
The winner was Funny Cide
n = 3
The morning star and the evening star are the same thing.

We will refer to such sentences as equations; they constitute a particular kind of predication.

In our symbolic notation, we will follow the third example and use the sign = to mark identity. As English notation, we will use the word is. We will represent unanalyzed individual terms by lower case letters, so we can analyze the sentences above as follows:

George Bush is the U.S. president
George Bush = the U.S. president
g = p
g is p
g: George Bush; p: the U.S. president
The winner was Funny Cide
the winner = Funny Cide
w = f
w is f
f: Funny Cide; w: the winner
n = 3
n = t
n is t
n: n; t: 3
The morning star and the evening star are the same thing
the morning star = the evening star
m = e
m is e
m: the morning star; e: the evening star
Glen Helman 28 Aug 2008