Synthese 84 (1):43 - 58 (1990)
|Abstract||In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The axiom set does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view truth not as something to be defined within the closed world of a formal system but rather in terms of the schema network within which the formal system is embedded. We differ from Piaget in that we see mathematical knowledge as based on social processes of mutual verification which provide an external drive to any necessary dynamic of reflective abstraction within the individual. From this perspective, we argue that axiom schemas tied to a preferred interpretation may provide a necessary intermediate stage of reflective abstraction en route to acquisition of the ability to use formal systems in abstracto.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Uwe Riss (2011). Objects and Processes in Mathematical Practice. Foundations of Science 16 (4):337-351.
Carlo Cellucci (1993). From Closed to Open Systems. In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
Michael A. Arbib (1986). The Construction of Reality. Cambridge University Press.
Nancy J. Nersessian (2005). Abstraction Via Generic Modeling in Concept Formation in Science. Poznan Studies in the Philosophy of the Sciences and the Humanities 86 (1):117-144.
Jack A. Rowell (1989). Piagetian Epistemology: Equilibration and the Teaching of Science. Synthese 80 (1):141 - 162.
Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
Paul Cortois (1996). The Structure of Mathematical Experience According to Jean Cavaillèst. Philosophia Mathematica 4 (1):18-41.
Kit Fine (2002). The Limits of Abstraction. Oxford University Press.
Julian C. Cole (2009). Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics. Australasian Journal of Philosophy 87 (4):589-608.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. Foundations of Science 15 (1).
Added to index2009-01-28
Total downloads28 ( #44,013 of 548,984 )
Recent downloads (6 months)1 ( #63,327 of 548,984 )
How can I increase my downloads?