Cast of characters

The adverbs I wish to consider fall into six groups of near-synonyms, as follows.

1. Always, invariably, universally, without exception

2. Sometimes, occasionally, [once]

3. Never

4. Usually, mostly, generally, almost always, with few exceptions, [ordinarily], [normally]

5. Often, frequently, commonly

6. Seldom, infrequently, rarely, almost never

Bracketed items differ semantically from their list-mates in ways I shall not consider here; omit them if you prefer.

First guess: quantifiers over times?

It may seem plausible, especially if we stop with the first word 011 each list, that these adverbs function as quantifiers over times. That is to say that always, for instance, is a modifier that combines with a sentence Φ to make a sentence Always Φ that is true iff the modified sentence Φ, is true at all times. Likewise, we might guess that Sometimes Φ, Never Φ, Usually Φ, Often Φ, and Seldom Φ are true, respectively, iff Φ is true at some times, none, most, many, or few. But it is easy to find various reasons why this first guess is too simple.

First, we may note that the times quantified over need not be moments of time. They can be suitable stretches of time instead. For instance,

(7) The fog usually lifts before noon here

means that the sentence modified by usually is true on most days, not at most moments. Indeed, what is it for that sentence to be true at a moment?