Document (#28661)

Author

Borwein, J.
Stanway, T.

Title

Knowledge and community in mathematics

Source

Mathematical intelligencer. 27(2005) no.2, S.7-16

Year

2005

Abstract

"Each society has its regime of truth, its "general politics" of truth: that is, the types of discourse which it accepts and makes function as true; the mechanisms and instances which enable one to distinguish true and false statements, the means by which each is sanctioned; the techniques and procedures accorded value in the acquisition of truth; the status of Chose who are charged with saying what counts as truth." (Michel Foucault) Henri Lebesgue once remarked that "a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy." He went an to add that this was "an opinion, moreover, which has been expressed by many philosophers." The idea that mathematicians can do mathematics without a precise philosophical understanding of what they are doing is, by observation, mercifully true. However, while a neglect of philosophical issues does not impede mathematical discussion, discussion about mathematics quickly becomes embroiled in philosophy, and perforce encompasses the question of the nature of mathematical knowledge. Within this discussion, some attention has been paid to the resonance between the failure of twentieth-century efforts to enunciate a comprehensive, absolute foundation for mathematics and the postmodern deconstruction of meaning and its corresponding banishment of encornpassing philosophical perspectives from the centre fixe. Of note in this commentary is the contribution of Vladimir Tasic In his book, Mathematics and the Roots of Postmodern Thought, he comments an the broad range of ideas about the interrelationship between language, meaning, and society that are commonly considered to fall under the umbrella of postmodernism. Stating that "attempts to make sense of this elusive concept threaten to outnumber attempts to square the circle," he focuses his attention an two relatively welldeveloped aspects of postmodern theory: "poststructuralism" and "deconstruction.' He argues that the development of these theories, in the works of Derrida and others, resonates with the debates surrounding foundationism which preoccupied the philosophy of mathematics in the early stages of the last century and may even have been partly informed by those debates. Our present purpose is not to revisit the connections between the foundationist debates and the advent of postmodern thought, but rather to describe and discuss some of the ways in which epistemological relativism and other postmodern perspectives are manifest in the changing ways in which mathematicians do mathematics and express mathematical knowledge. The analysis is not intended to be a lament; but it does contain an element of warning. lt is central to our purpose that the erosion of universally fixed perspectives of acceptable practice in both mathematical activity and its publication be acknowledged as presenting significant challenges to the mathematical community.

Field

Mathematik

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5. Lange, C.: Ontologies and languages for representing mathematical knowledge on the Semantic Web (2011) 0.18

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