I was thinking about the etymology of words like “executor” and “bettor” that use the suffix “-or” to denote the person who performs a verb, instead of the more usual “-er”.
For some reason, it’s never occured to me that “liar” has an even more peculiar construction. Does anyone know the etymology of “liar”? And are there other examples of words with an “-ar” ending? I can’t think of any, but you may do better since I’ve had too many beers and you haven’t.
I don’t think scholar, pillar, or *vicar *count, though, because they are not derived directly from verbs. A scholar doesn’t schol, a pillar doesn’t pill, and a vicar doesn’t vic. Most agent nouns end in -er or -or, rather than -ar.
Somewhat off-topic, but regarding agent nouns ending in -or, I was taught that if you can take the root word and make it end in -ion, the agent noun will end in -or. For example, direction->director, edition->editor. There are, of course, exceptions, but it works a lot of the time.
But I think that “schooler” would be the agent noun derived from the verb “school”, and it would have to mean someone who schools somebody else, rather than somebody who is schooled, otherwise they would be the patient, not the agent. “Scholar” is closely related to “school”, true, but in my book that does make it an agent noun.