In a the context of a paper, there's a paragraph-title: "Philanthropism in American culture", I'm in general only familiar with the word philanthropy, hence I'm not sure what an appropriate title would be.
The OED defines "philanthropism" as
This follows from meaning 2.A of "-ism":
Sometimes there are not two different words (eg "catholicism" which can refer to an individual's belief or practice, or to the movement), but in this case there are two. Similarly we can distinguish "anarchy" from "anarchism".
So in your particular case, either is possible, but they will have slightly different meanings: "philanthropy" would focus on the individual people (or acts) that are philanthropic; "philanthropism" would focus on the system or theory or philosophy of philanthropy (if there is one).
Philanthropy is the act of philanthropy itself.
Philanthropism is characteristic of philanthropy, the system.
It's made a little more clear if we consider other words, such as alcohol or communist:
The -ism suffix comes from the Latin ismus to indicate a state or condition.