In logic, the connotation of a word is what’s shared among all of the referents of the word. For example, the connotation of the word “food” is anything edible. What’s essential to being food is being edible. The denotation of a word, then, is all of the referents of the word. For example, the denotation of the word “food” includes the broccoli in my refrigerator.

The connotation and the denotation are often in synchrony. Knowing that the word “food” connotes being edible lets you figure out what that word denotes—the broccoli in my refrigerator is one of countless examples—and knowing what that word denotes lets you figure out what it connotes. But the connotation and the denotation are also often not in synchrony. That comes about when the referents change. Imagine, for instance, a small but well-known Christian denomination that changes from monotheism (which is the standard Christian doctrine) to polytheism. The individuals in the denomination, long well-known as “Christians,” all change from professing monotheism to professing polytheism. The connotation and the denotation fall out of step with each other. The word “Christian,” which traditionally includes belief in monotheism in its connotation (along with belief in Jesus of Nazareth as the Messiah, belief in the New Testament as scripture, etc., as the distinguishing criteria of being Christian), also traditionally includes the individuals in that denomination in its denotation.

We must decide whether to:

1. Either change the familiar connotation of the word “Christian,” the connotation that we’re used to, such that it newly accepts polytheism in its connotational range, which preserves the familiar denotational range. [the inclusive move]
2. Or change the familiar denotation of that word such that it newly rejects the individuals in the aforementioned denomination in its denotational range, which preserves the familiar connotational range. [the exclusive move]

That is, we must decide whether to:

1. Either pin down what the word refers to and then change what it means when what it refers to changes.
2. Or pin down what the word means and then change what it refers to when the world changes.

Interestingly, pinning down or fixing the denotation of the subject of a proposition makes for a synthetic proposition (because the proposition “Christians believe in monotheism” is thereby made to be non-tautologically true) and pinning down or fixing the connotation instead makes for an analytic proposition (because the same proposition is thereby made to be tautologically true).

Also interestingly, the question of whether to either denotation-fix or connotation-fix is social. A social negotiation must happen between the inclusive and the exclusive: between the people who prefer the denotation-fix-inclusive move and the people who prefer the connotation-fix-exclusive move.