Re-solving the Learning Paradox: Epistemological and Ontological Questions for Radical Constructivists

Over 30 years ago, a debate between Jean Piaget and Noam Chomsky revived an ancient learning paradox filst intioduced by Plato (Piattelli-Palmarini, 1980) Chomsky challenged Piaget to explain how one could constrnct more advanced knowledge horn one's existing (less advanced) knowledge Chomsky argued that, without such an explanation fo1 learning, we must assume the innativist position that all potential cognitive operating is somehow encoded in the hmnan genome A different paradox motivated Piaget's development of constluctivist epistemology. Since Plato, western philosophy had assumed that we could measure the liuth of human knowledge by means of its match with an ontological reality; on the other hand, human experience does not permit the test of such a match (Piaget, 1971/1970; von Glasersfeld, 1991) How could we test whether the world we know, epistemologically, matches an ontological reality beyond om experience? "Radical constructivism is a theory whose roots lie in the rejection of illegitimate claims for epistemological certainty" (Confrey, 1994, p. 3) This article examines the learning paradox from a radical constructivist perspective and in a mathematical context, introducing underlying assumptions and various solutions along the way. I begin by explaining constructivist positions on epistemology and ontology This discussion will distinguish the two branches of philosophy that often get entangled in discussions of the learning paradox. Indeed, we will see that the conflation of epistemology and ontology presents one of two thorny issues arising in previous literature on the topic I then introduce several attempts to resolve the paradox in mathematical contexts. Many ftuitful approaches rely on Peirce's idea of abduction, which war1ants its own section Finally, we will consider the ontological paradox that remains once the epistemological one withers away