Ockham's Razor and Plato's Beard (Or, "The Possible Relevance of the Philosophy of Mathematics, and the Problem of Universals in Particular, to the Philosophy of Mathematics Education, and the Problem of Constructivism in Particular")

William of Ockham responds from the dead to an article appearing in the January 1992 issue of the Journal for Research in Mathematics Education, in which Paul Cobb, Erna Yackel, and Terry Wood propose a "constructivist alternative to the representational view of mind." Ockham, now a convert to Platonism, argues three points. First, that by opposing construction to representation, Cobb et al. misinterpret the postepistemological perspective of Richard Rorty's 1979 influential book, Philosophy and the Mirror of Nature. Second, that by opposing mathematics in the students' mind to mathematics in the environment, and, in particular, by attempting to argue that the representational theory of mind opens the "learning paradox," Cobb et al. misinterpret Carl Bereiter (1985), confuse ontological and epistemological issues, stumble into the perennial philosophical problem of universals, and indicate that they might be interested in discussing the philosophy of mathematics. Third, that in arguing for a relatively pure, "radical" constructivism, Cobb et al. mistake the pragmatic force of the constructivist argument, confuse matters of value with matters of taste, and attempt to fashion too dogmatic a connection between theory and practice in mathematics education.