id: 02324924
dt: j
an: 1998f.04076
au: Otte, M.
ti: Limits of constructivism: Kant, Piaget and Peirce.
so: Sci. Educ. (Dordrecht) 7, No. 5, 425-450 (1998).
py: 1998
pu: Springer Netherlands, Dordrecht
la: EN
cc: E20
ut: mathematical epistemology; empiristic epistemology; kant; piaget; peirce
ci:
li: doi:10.1023/A:1008635517122
ab: The paradox of mathematical knowledge that mathematics cannot be conceived
of as completely separated from empirical experience and yet cannot be
explained by empiricist epistemology, can only be resolved if one
accepts that the causal interactions between knower and environment
have themselves a generalizing tendency, a sort of continuity, rather
than consisting just of singular events. Kant resolves the schism
between the continuous and the distinct in a constructivist manner. He
assumes that all our knowledge-extending cognitions are synthetic. This
synthesis does not lie in the matter of experience but springs from the
function of cognizant consciousness. Piaget adhered to a Kantianism
where ’the categories are not there at the outset’. He conceives of
the subject as constructing itself as well as of the emerging
subject’s structure as the source of the apprehension of the world
and believes in a Kantianism which emphasizes man’s active being and
potential for unlimited self-development. But he has no use for the
Kantian idea of space and time as forms of mathematical intuition.
Kantian thought is also central to Peirce’s philosophy and conception
of mathematics. But Peirce emphasizes the role of perception and
analysis as its prerequisites. Peirce’s and Piaget’s origins in
Kantianism are exhibited when both try to replace the Aristotelian
notion of abstraction and generalization by something more suitable for
mathematical epistemology. Peirce proposes that ’hypostatic
abstraction’ is the chief explanation for the power of mathematical
reasoning and explains: ’This operation is performed when something,
that one has thought about any subject, is itself made a subject of
thought’. Piaget speaks of ’reflective abstraction’ in this
context, making it the basis of mathematical knowledge; but separating
it completely from empirical abstraction. (orig.)
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