Q: What is the difference in meaning between “John didn’t come yesterday—he must have been ill” and “John didn’t come yesterday—he will have been ill”? I realize that “must” is more popular than “will” in such constructions, but does one express more certainty than the other?
A: The words “will” and “must” in your examples are epistemic modal verbs, auxiliary verbs that express probability.
As Rodney Huddleston and Geoffrey K. Pullum explain in the Cambridge Grammar of the English Language, “epistemic modality qualifies the speaker’s commitment to the truth.”
“While It was a mistake represents an unqualified assertion,” Huddleston and Pullum write, “It must have been a mistake suggests that I am drawing a conclusion from evidence rather than asserting something of whose truth I have direct knowledge.”
In your first example (“John didn’t come yesterday—he must have been ill”), the auxiliary “must” indicates that the writer (or speaker) believes John was probably ill.
In our opinion, the expression “he will have been ill” indicates somewhat more probability than “he must have been ill” (though some might argue the point). And both of them indicate a much greater probability than “he may have been ill”—another example of epistemic modality.
Huddleston and Pullum note that epistemic modality is “commonly expressed by other means than modal auxiliaries.” For example, by adverbs (“he was probably ill”), verbs (“I believe he was ill”), adjectives (“he was likely to be ill”), and nouns (“in all likelihood, he was ill”).
There are two other principal kinds of modality: deontic, which expresses permission or obligation (“He may have one more chance, but he must come tomorrow”), and dynamic, which expresses willingness or ability (“I won’t come today, but I can come tomorrow”).
In A Comprehensive Grammar of the English Language, the authors, Randolph Quirk et al., say, “At its most general, modality may be defined as the manner in which the meaning of a clause is qualified so as to reflect the speaker’s judgment of the likelihood of the preposition it expresses being true.”
Quirk divides the modal verbs into two types:
“(a) Those such as ‘permission,’ ‘obligation,’ and ‘volition’ which involve some kind of intrinsic human control over events, and
“(b) Those such as ‘possibility,’ ‘necessity,’ and ‘prediction,’ which do not primarily involve human control of events, but do typically involve human judgment of what is or is not likely to happen.”
Quirk adds that the two categories “may be termed intrinsic and extrinsic modality respectively,” since “each one of them has both intrinsic and extrinsic uses: for example, may has the meaning of permission (intrinsic) and the meaning of possibility (extrinsic); will has the meaning of volition (intrinsic) and the meaning of prediction (extrinsic).”
“However, there are areas of overlap and neutrality between the intrinsic and extrinsic senses of a modal: the will in a sentence such as I’ll see you tomorrow then can be said to combine the meanings of volition and prediction.”
Another point to consider, Quirk writes, “is that the modals themselves tend to have overlapping meanings, such that in some circumstances (but not in others), they can be more or less interchangeable.”
In other words, there’s a lot of ambiguity here. Or, as Quirk puts it, “the use of modal verbs is one of the more problematic areas of English grammar.”