From: Jurriaan Bendien <adsl675281@tiscali.nl>

Date: Sun Feb 22 2009 - 18:15:55 EST

Date: Sun Feb 22 2009 - 18:15:55 EST

The assumption of the paper seems to be that the development of mathematical

ideas can be fully explained in terms of a logic internal to the discipline.

But this assumes that mathematics does not have an effect on the rest of the

social world, and that the social world has no effect on mathematical

activity. This seems hardly credible, and so, to explain mathematical

development (why, for example, some problems are pursued while others are

ignored) one would have to refer both to endogenous influences (internal to

the discipline) and exogenous ones (external to it). In that case, the

dialectic is not simply a dialectic of ideas, but also an interaction

between ideas and practical life circumstances, and a dialectic of societal

development. If the development of mathematical ideas can be explained fully

in terms of a logic internal to the discipline, we should be able to make

useful predictions about the actual future trajectory of mathematical

development based on its current structure, but in reality the predictions

have often failed rather spectacularly, in the sense that they did not

anticipate new developments that were also logical possibilities implied by

existing knowledge.

Jurriaan

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Received on Sun Feb 22 18:17:46 2009

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