Final answer:
The correct answer is option (2) Professor. Professor Emerson Sillerton's profession is a Professor.
Step-by-step explanation:
Professor Emerson Sillerton's profession can be clearly determined from the context given in the passage. It mentions that "nothing on earth obliged Emerson Sillerton to be an archaeologist, or indeed a professor of any sort." This implies that Sillerton has chosen his profession of his own volition.
While both terms are used, the use of "indeed" suggests that being a professor is the more encompassing term for his role. Therefore, the correct answer is 2) Professor.