Are modal verbs finite or non finite?
I agree with you; I think the modals are non finite. They do not change to signal tense, number, and person, and they lack several other characteristics of true verbs. There is not widespread agreement about the “past tense” of can-could and will-would. Those supposed past tense forms never express the past without an adverb that expresses past. If we say, “I could,” it doesn’t mean that now I cannot. With true verbs, the past tense expresses an action that’s finished. “I could eat.” No one would mistake that for the past tense. There are many other examples of modals in their “past” form functioning in the present tense. The best evidence against their being finite verbs though is the fact that they are not used without adverbs to express past time. EDIT: I just found another source, Marianne Celce-Murcia and Diane Larsen-Freeman, The Grammar Book, 1983. These authors point out that usage of the “past tense” of modals is not reliable at all in, for example, reported (indirect) speech,