7.2. Generalizations and quantifiers

7.2.0. Overview

Our symbolic analysis of generalizations is somewhat analogous to our analysis of conditionals: we use a single symbol and distinguish different kinds of generalization by the use of negation.

7.2.1. The universal quantifier
The basic logical constant we use to analyze generalizations comes in two varieties; both are operators that apply to a one-place predicate, one to assert that it is true of all reference values in the extension of another predicate and the other to assert that it is true of all reference values whatsoever.

7.2.2. Analyzing generalizations
The restatement of a generalization using expansion and its classification as either affirmative or negative and either direct or complementary translate directly into a symbolic analysis of it.

7.2.3. Compound restrictions
The formula specifying the domain of a symbolic generalization is often logically complex; bounds and exceptions are one source of this complexity.