In S9 he does have 3 PhDs. If I am remembering correctly, it's Philology, Anthropology, and Archaeology. All fields are interrelated so it's possible. In fact, many American universities have anthropologists and archaeologists teaching in the same department. While archaeology is a distinct field, many universities categorize it as a subfield in anthropology.

Philogy also interlaps, but I know less about that as a specific field.

The show focuses on Daniel as an archaeologist and linguists the most. In area of speciality seems to be Egypt. I know an archaeologist, one of my old mentors, that focuses on writing systems and langauge in an acrchaeological context and he teaches in the anthropology department. So he's basically an anthropologist (he teches a variety of courses), he considers himself an archaeologist. I figure that Daniel considers himself as archaeologists as well, even though he could get by as an anthropologist if he really wanted to.