David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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In ¸ Itekellersetal:Sp. 65--79 (2006)
A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The ﬁrst case illustrates the hypothesis that a suﬃciently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises issues of ontological multiplicity and relativity encountered in the natural sciences as well.
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