Plato believed and argued that "forms" or "ideas" or "universals" (or perhaps "qualities" or "properties") existed independently of the physical world. In his book, The Last Superstition, Ed Feser pretty much agrees with him. In fact he summarizes nine arguments in favor of this view on pp. 42- 47, which I won't try to further summarize, but merely list:
1. The "one over many" argument.
2. The argument from geometry.
3. The argument from mathematics in general.
4. The argument from the nature of propositions.
5. The argument from science.
6. The vicious regress problem.
7. The "words are universals too" problem.
8. The argument from the objectivity of concepts and knowledge.
9. The argument from the possibility of communication.
I find all of the arguments listed to be cogent and the conclusion that Forms exist independently of material reality to be true. Which is why Feser's (apparent) rejection of Plato's view in favor of Aristotle's view of the Forms puzzles me. Aristotle believed that the Forms were real, but that they did not exist independently of the material world. But most if not all of the arguments that Feser presented for the reality of the Forms would seem to refute Aristotle's position as well.
I remained puzzled by this until I read further, and found out that Feser doesn't really accept Aristotle's view of the Forms. He accepts something known as "Scholastic Realism," where the Forms exist in the mind of God, independently of the material world. So good, Feser remains consistent.
Only now I'm puzzled why he took away the Platonic Forms with the left-hand of Aristotle, only to give them back with the right-hand of Scholasticism. Oh well, after putting up with Feser fighting against ID, until he really admitted that there was nothing wrong with it, only with Dembski's (apparent) interpretation of it, I guess I shouldn't be surprised.