The verbs in this list all have the following characteristics:
They are auxiliary verbs, which means they allow subject-auxiliary inversion and can take the negation not,
They convey functional meaning,
They are defective insofar as they cannot be inflected, nor do they appear in non-finite form (i.e. not as infinitives, gerunds, or participles),
They are nevertheless always finite and thus appear as the root verb in their clause, and
They subcategorize for an infinitive, i.e. they take an infinitive as their complement
The verbs/expressions dare, ought to, had better, and need not behave like modal auxiliaries to a large extent, although they are not productive (in linguistics, the extent commonly or frequently used) in the role to the same extent as those listed here. Furthermore, there are numerous other verbs that can be viewed as modal verbs insofar as they clearly express modality in the same way that the verbs in this list do, e.g. appear, have to, seem etc. In the strict sense, though, these other verbs do not qualify as modal verbs in English because they do not allow subject-auxiliary inversion, nor do they allow negation with not. Verbs such as be able to and be about to allow subject-auxiliary inversion and do not require do support in negatives but these are rarely classified as modal verbs because they inflect and are a modal construction involving the verb to be which itself is not a modal verb. If, however, one defines modal verb entirely in terms of meaning contribution, then these other verbs would also be modals and so the list here would have to be greatly expanded.
Defectiveness
In English, modals form a very distinctive class of verbs. They are auxiliary verbs like be, do, and have, but unlike other such verbs, they are grammatically defective. For example, have → has vs. should → *shoulds and do → did vs. may → *mayed, etc. In clauses that contain two or more verbs, any modal that is present always appears leftmost in the verb catena (chain). Thus, modal verbs are always finite and, in terms of syntactic structure, the root of their containing clause. The following dependency grammar trees illustrate this point:
The verb catenae are in blue. The modal auxiliary in both trees is the root of the entire sentence. The verb that is immediately subordinate to the modal is always an infinitive. The fact that modal auxiliaries in English are necessarily finite means that within the minimal finite clause that contains them, they can never be subordinate to another verb, e.g.,
a. Sam may have done his homework. The modal auxiliary may is the root of the clause. b. *Sam has may done his homework. Fails because the modal auxiliary may is not the root of the clause. a. Jim will be helped. The modal auxiliary will is the root of the clause. b. *Jim is will be helped. Fails because the modal auxiliary will is not the root of the clause. Such limits in form (tense, etc.) and syntactic distribution of this class of verbs are motivation of the designation defective. Other constructions are frequently used for such a "missing" form in place of a modal, including "be able to" for can, "have to" for must, and "be going to" for shall and will (designating the future). It is of note that in this way, English modal auxiliaries are unlike modal verbs in other closely related languages; see below.
In English, main verbs but not modal verbs always require the auxiliary verb do to form negations and questions, and do can be used with main verbs to form emphatic affirmative statements. Neither negations nor questions in early modern English used to require do.
