His entire teaching career was spent on the philosophy faculty at the University of Wisconsin, where he was promoted to full professor in 1905.
He served as President of the Western Division of the American Philosophical Society during the 1907-1908 term.
Sharp was among the first philosophers to focus on business ethics, in which he discussed the fair treatment of employees, consumers, and competitors.
Sharp was also among the first philosophers to perform empirical studies of moral intuitions, conducting surveys at the University of Wisconsin, both of highly educated liberal arts students and of agricultural students who had had limited formal education.
He is credited with being the first moral philosopher to use a variant of the now famous trolley problem in which a switchman must choose between saving many strangers or his own daughter from a runaway train.