Philosophical realism – usually not treated as a position of its own but as a stance towards other subject matters – is the view that a certain kind of thing has mind-independent existence, i.e. that it exists even in the absence of any mind perceiving it or that its existence is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality entirely.
Plato (left) and Aristotle (right), a detail of The School of Athens, a fresco by Raphael. In Plato's metaphysics, ever-unchanging Forms, or Ideas, exist apart from particular physical things, and are related to them as their prototype or exemplar. Aristotle's philosophy of reality also aims at the universal. Aristotle finds the universal, which he calls essence, in the commonalities of particular things.
Philosophy of mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities.
Kurt Gödel
Bertrand Russell
David Hilbert
Leopold Kronecker