6.1.4. Identity

We used special notation for all the connectives that figured in our analyses of logical form, and they all had logical properties that we studied. However, 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, and they will be assigned meanings only when we specify an interpretation of this vocabulary.

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

Sentences like these are equations. Equations are thus a special 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:

Once in symbolic form, these equations are very simple. The greater complexity found in most interesting mathematical equations is due to the complexity of the individual terms they contain. To exhibit that complexity in our analyses, we will need to analyze individual terms, something we will begin to do in 6.1.7.