"Structuralism and positivism are two different kinds of philosophy."
Translation:Ο δομισμός και ο θετικισμός είναι δύο διαφορετικά είδη φιλοσοφίας.
if you are talking about something abstract, the article is omitted
I believe this is a good rule of thumb in general
I suppose you meant "don't omit" in the second half of your question?
I actually learned a useful example while learning Portuguese.
Faculdade de Medicina do Universidade de... (insert city name)
"de" just means "of"
"do" is the contraction of "de+o", "o" being the masculine definite article
"Medicine" doesn't really belong to the faculty, but the faculty does belong to the university. So it's more about whether something actuallybelongs to something else.
About this exercise and similar ones: It sounds better without the article, but if you included the article, nobody would correct you because the meaning would be clear in any case, with or without the article.