A friend recently told me that "can" is a rare verb without an infinitive. I have since looked it up and discovered it is an auxiliary verb. In my mind it modifies a "proper" verb in much the same way an adverb does.
"I can jump puddles"
"I could do it"
"to jump" and "to do" are OK, "to can" is wrong (meaning "to be able to").
"I am able to jump puddles"
"I was able to do it"
So, are words like "can/could", "must", "will/would", etc. actually verbs or are they only auxiliary or modal verbs and not "proper" verbs? I was also chatting to a Frenchman and he said in French auxiliary verbs are just called auxiliaries and are not considered to be verbs, so is it the same in English? It seems to me that if you can't "to" or "-ing" a word it is not proper verb.
"to jump", "jumping" - OK
"to must", "musting" - wrong
However, if auxiliary and modal verbs are actually verbs is there a word to describe a non-modal, non-auxiliary verb?
Please, no comments about canning factories or making wills. I already know that the words "can" and "will" can be infinitives but with a different meaning.
Black bears, brown bears and polar bears are actually bears. Koalas and pandas are not bears yet some people call them koala bears and panda bears because they look a bit like bears. Likewise jellyfish and starfish are not fish but are aquatic animals as fish are. Alternative names for them are sea jellies and sea stars. Ironically, the seahorse is actually a fish. Things are not always what they're called. So are auxiliary verbs actually verbs or just called verbs?