The Problem of Universals is a complex philosophical problem that encompasses all of the above questions. It is a fundamental question in metaphysics, and there is no easy answer.

Nominalism and Realism are the two main positions on the Problem of Universals. Nominalism holds that universals are nothing more than names, while Realism holds that universals are real entities that exist independently of the mind.

The argument from particulars states that universals cannot exist because they are not particulars. The argument from change states that universals cannot exist because they cannot change. The argument from error states that universals cannot exist because they can be mistaken for particulars.

The argument from predication states that universals must exist because we can predicate them of particulars. The argument from science states that universals must exist because they are necessary for scientific explanation. The argument from mathematics states that universals must exist because they are necessary for mathematical reasoning.

Conceptualism is a position on the Problem of Universals that holds that universals are both mental concepts and real entities. This position is a compromise between Nominalism and Realism.

The argument from language states that universals must exist because they are necessary for language. The argument from thought states that universals must exist because they are necessary for thought. The argument from science states that universals must exist because they are necessary for scientific explanation.

Idealism is a position on the Problem of Universals that holds that universals are mental concepts. This position is similar to Conceptualism, but it goes further in denying the existence of real entities.

The argument from experience states that universals must be mental concepts because they are only experienced as mental concepts. The argument from coherence states that universals must be mental concepts because they are necessary for the coherence of experience. The argument from parsimony states that universals must be mental concepts because it is the simplest explanation for their existence.

Materialism is a position on the Problem of Universals that holds that universals are real entities that exist independently of the mind. This position is similar to Realism, but it goes further in denying the existence of mental concepts.

The argument from science states that universals must be real entities because they are necessary for scientific explanation. The argument from common sense states that universals must be real entities because they are part of our everyday experience. The argument from parsimony states that universals must be real entities because it is the simplest explanation for their existence.

Dualism is a position on the Problem of Universals that holds that universals are both mental concepts and real entities. This position is similar to Conceptualism, but it goes further in affirming the existence of both mental concepts and real entities.

The argument from experience states that universals must be both mental concepts and real entities because they are experienced as both mental concepts and real entities. The argument from coherence states that universals must be both mental concepts and real entities because they are necessary for the coherence of experience. The argument from parsimony states that universals must be both mental concepts and real entities because it is the simplest explanation for their existence.

William of Ockham was a nominalist, while Plato, Aristotle, and Thomas Aquinas were all realists.

Plato, Aristotle, and Thomas Aquinas were all realists, while William of Ockham was a nominalist.

Peter Abelard was a conceptualist, while Plato, Aristotle, and William of Ockham were all realists.