This is an oversimplification or bottom line to what each Philosophy discipline does.
This is the organization of bodies of knowledge in ancient times.
Natural: the predecessor of science particularly the study of the universe and physics. Characters would be familiar concepts of pressure, gravity, buoyancy, velocity, etc while unable to define it.
Geometry: Math involving shapes, size, relative positions, and physical dimensions. Requires: Literacy, Arithmetics.
MetaPhysics: The study of the realm beyond the physical universe.
Theology: The study of divine knowledge from religious sources, ritual and practice.
Socratic: The skill of asking the right problem solving questions. The GM secretly rolls to see if the information the PCs want are what results in their line of questioning.
Platonic: The skill clear definition of ideas, concepts and essences. The GM rolls secretly to see if the right concepts comes across.
Aristotelian: The skill of objectively measuring and distilling observation and perception. The GM secretly rolls to see if the PC catches gap's in the chain of logic or assumptions that have no place in the problem.
Confucian: The reciprocative relationship among individuals in order to establish order. This is a very rudimentary and early kind of Political theory. The GM rolls secretly if the PC notices any imbalance in relationships among organization.
Buddhism: The mental discipline to frame situations and experiences to the advantage of the observer. This lets the Philosopher suppressing emotional distraction. The GM may roll again with Buddhism to negate disadvantageous morale affects.
Moizm: Another empirical based philosophy that focuses on value moderation or denial of objects while maximization with people. The GM may roll secretly for the PCs against Moizm in formulating defensive strategy.
Taoism: The skill of developing laws, punishing and rewarding. This is an effective skill in managing military discipline in high stress situations. Similar to Leadership skill for a long running organization and not just a small group.
I wish my Philosophy teachers would have framed it this way. It would have been more fun.