6. Predications

6.1. Naming and describing

6.1.0. Overview

We will now begin to study a wider variety of logical forms in which we identify components of sentences that are not also sentences.

6.1.1. A richer grammar
A variety of grammatical categories can be defined using the idea of an individual term, an expression whose function is to name an individual object.

6.1.2. Logical predicates
When the subject is removed from a sentence, a grammatical predicate is left behind; a logical predicate is what is left when any number of individual terms are removed.

6.1.3. Extensionality
The truth value of a sentence in which a predicate is applied depends only on the reference values of the terms the predicate is applied to, so the meaning of predicate is a function from reference values to truth values.

6.1.4. Identity
We will study the special logical properties of only one predicate, the one expressed by the equals sign and by certain uses of the English word is.

6.1.5. Analyzing predications
When the analysis of truth-functional structure is complete, we may go on to analyze atomic sentences as the applications of predicates to individual terms.

6.1.6. Individual terms
While individual terms are not limited to proper names, they do not include all noun phrases, only ones whose function is like that of proper names.

6.1.7. Functors
Individual terms can be formed from other individual terms by operators analogous to predicates.

6.1.8. Examples and problems
These operators enable us to continue the analysis of sentences beyond the analysis of predications by analyzing individual terms themselves.