The Dialogical Nature of Mathematics

This chapter sketches an account of mathematics based on the underlying explanatory metaphor of conversation and dialogue. ¹ It suggests that mathematics is dialogical in a number of central defining ways, through the underlying •

textual basis of mathematics, mathematical knowledge and proof;

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nature of a number of central mathematical concepts;

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origins and nature of proof; and

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social processes whereby mathematical knowledge is created, warranted and learnt.

This account is offered as part of a social constructivist philosophy of mathematics (Ernest, in press), which sits at the crossroads of two major currents of modern thought, the recent fallibilist tradition in the philosophy of mathematics, and the multidisciplinary use of conversation as a basic underlying metaphor for human knowing and interaction.