Bickhard M. H. (1991) The import of Fodor’s anti-constructivist argument. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience\>Epistemological foundations of mathematical experience. Springer, New York: 14–25. Fulltext at https://cepa.info/2970

Excerpt: Fodor argues that the construction of genuinely novel concepts is impossible and, therefore, that all basic concepts available to human beings are already present as an innate endowment (1975, 1981). This radical innatism – along with related conclusions such as an innate modularity of available representations and a corresponding innate limitation in the potential knowledge that human beings might be capable of (1983) – has been seen by many as a reductio ad absurdum of Fodor’s position, and his arguments have consequently been dismissed. I will argue that Fodor’s arguments deserve much more careful attention than that: in particular, his arguments are a reductio of one of his essential presuppositions, but it happens to be a presupposition that he shares with virtually all of psychology and philosophy. Fodor’s conclusions, then, are reductios of the major portion of contemporary studies of cognition and epistemology (Campbell and Bickhard, 1987). Furthermore, even when the critical presupposition is isolated, it is difficult to construct a genuine alternative. Most attempts at correcting any part of the logical difficulties involved have inadvertently presupposed the pernicious premise elsewhere in the system (Bickhard, 1980a, 1982, 1987).

Glasersfeld E. von (1991) Abstraction, re-presentation, and reflection. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience\>Epistemological foundations of mathematical experience. Springer, New York: 45–67. Fulltext at https://cepa.info/1418

Konold C. & Johnson D. K. (1991) Philosophical and psychological aspects of constructivism. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience\>Epistemological foundations of mathematical experience. Springer, New York: 1–13. Fulltext at https://cepa.info/2969

Excerpt: Clifford Geertz (1983) speaks of “genre blurring” to refer to, among other things, the cross-fertilization of the social sciences and the humanities. In the process, the social sciences are giving up their long-held objective of patterning themselves after the physical sciences. This volume might be looked at as a case study of such genre blurring. Some of the contributors come from academic backgrounds other than mathematics and mathematics education. They include academics trained in psychology, philosophy, and classical studies. This diversity is reflected to some extent in the lack of overlap in the works each chapter references. But there is a stronger rationale for characterizing these chapters as cross-disciplinary: one finds within single chapters, references culled from a variety of disciplines. Although the authors come from and draw on diverse disciplines, they share a core perspective. This shared perspective is a species of constructivism. There are many possible tacks to take in an introductory chapter such as this. What seems the most appropriate in this case is to orient the reader who is interested in mathematics education, for example, but who may be unaware of constructivist epistemology. Accordingly, we describe general philosophical and psychological issues that underlie the constructivism advocated by these authors. Having done this, we provide a brief overview of the volume in which we highlight the primary focus of each chapter.

Steffe L. P. (1991) The learning paradox: A plausible counterexample. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience\>Epistemological foundations of mathematical experience. Springer, New York: 26–44.

In the summer of 1985, Carl Bereiter published an article in the Review of Educational Research titled Toward a Solution of the Learning Paradox. Ever since, it has been my intention to provide a counterexample to the paradox. Fodor (1980b), who is credited by Bereiter as clearly stating the learning paradox, views learning as being necessarily inductive. “Let’s assume, once again, that learning is a matter of inductive inference, that is, a process of hypothesis formation1 and confirmation” (p. 148). Given his view of learning, Fodor states the learning paradox in the following way.

Thompson P. W. (1991) To experience is to conceptualize: A discussion of epistemology and mathematical experience. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience\>Epistemological foundations of mathematical experience. Springer, New York: 260–281. Fulltext at https://cepa.info/3904