The Collaborative International Dictionary of English v.0.48:

Platonism \Pla"to*nism\, n. [Cf. F. Platonisme.]
   1. The doctrines or philosophy by Plato or of his followers.
      [1913 Webster]

   Note: Plato believed God to be an infinitely wise, just, and
         powerful Spirit; and also that he formed the visible
         universe out of pre["e]xistent amorphous matter,
         according to perfect patterns of ideas eternally
         existent in his own mind. Philosophy he considered as
         being a knowledge of the true nature of things, as
         discoverable in those eternal ideas after which all
         things were fashioned. In other words, it is the
         knowledge of what is eternal, exists necessarily, and
         is unchangeable; not of the temporary, the dependent,
         and changeable; and of course it is not obtained
         through the senses; neither is it the product of the
         understanding, which concerns itself only with the
         variable and transitory; nor is it the result of
         experience and observation; but it is the product of
         our reason, which, as partaking of the divine nature,
         has innate ideas resembling the eternal ideas of God.
         By contemplating these innate ideas, reasoning about
         them, and comparing them with their copies in the
         visible universe, reason can attain that true knowledge
         of things which is called philosophy. Plato's professed
         followers, the Academics, and the New Platonists,
         differed considerably from him, yet are called
         Platonists. --Murdock.
         [1913 Webster]

   2. An elevated rational and ethical conception of the laws
      and forces of the universe; sometimes, imaginative or
      fantastic philosophical notions.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Platonism
    n 1: (philosophy) the philosophical doctrine that abstract
         concepts exist independent of their names [syn:
         Platonism, realism]