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5.1 Scope

You were introduced to scope in the last chapter. Scope is the extent of a connective, how much of the sentence it governs.

Scope: how much of the sentence a connective governs.

If a connective just governs atomic sentences, it has narrow scope.

If it governs the whole sentence, it has wide scope.

Scope is also a relative concept: one connective might be wider or narrower than another, even though neither has wide or narrow scope.

As you can see in the example problem, each occurrence of a connective has its own scope. If two negations appear in one sentence they each have their own scope.

So when we say "A connective that just governs atomic sentences has narrow scope", it is implied that we are talking about a connective occurrence.

Every complex sentence has exactly one connective with wide scope, which we call the main connective.

Main connective: the connective with wide scope; the connective the governs the whole sentence.

The ability to recognize a sentence's main connective is a critical skill, because the main connective tells us what kind of sentence it is: a conjunction, disjunction, or negation.

Once we start doing proofs, the main connective is the part of a sentence that tells us what proof-strategies to use.

5.1 Scope