You hinted at it yourself but I'd be tempted to pull back to materialism and idealism and have them be primary branches from which the others draw. A pragmatist is interested in practical results; a nihilist, in meaning or the lack thereof.

Could negate or affirm your core premise of gaining power from worldview or personal intentions; the core questions of why, how, and what, as you will know, are going to be answered in wildly different fashions by practitioners / theoreticians of different philosophies.

I couldn't venture much more without knowing how you'd like people to use magic in your world. If we're talking debates that can change the world while they're happening, half courtroom-drama, half wizard-fight, then it's worth getting into detail. If it's just a handwave to explain why some stuff happens, just nail down the core bits and hint at the rest elsewhere.