3.1.1. Connectives

The connective we will study in this chapter is negation, which is associated with the English word not. As has been the case with conjunction, we will use the term negation also for the sentences produced by the operator negation. We will represent the form of such sentences symbolically using ¬ (the not sign) as our sign for negation so that ¬ φ is the negation of φ. To indicate negations using English, we will use not as an alternative to ¬, writing it, too, in front of the negated sentence so that, in this notation, not φ is the negation of φ.

The use of the term connective for negation is standard but in some ways not very apt. The word not in English is not a combining operator; it is not a conjunction (in the grammatical sense) that serves to connect clauses but instead an adverb, a modifier of a single clause. Thus it would be a mistake to associate the term connective too closely with the ideas of connection or combination. A application of a connective is better thought of as an operation that forms or generates a sentence from one or more sentences. This operation may combine or modify, and it may do both.

We will extend the terminology used for conjunction and refer, however inaptly, to any sentence generated by a connective as compound and refer to the one or more sentences it is generated from as components. When analyzing English sentences, the ultimate components we encounter may not be parts, in any grammatical sense, of the sentences we analyze. They will rather be the sentences whose logical forms we do not describe; that is, they are the unanalyzed residue of our analysis.