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PLURALISM IN MATHEMATICS
, 2004
"... We defend pluralism in mathematics, and in particular Errett Bishop’s constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic. ..."
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We defend pluralism in mathematics, and in particular Errett Bishop’s constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic.
A DEFENCE OF MATHEMATICAL PLURALISM
, 2004
"... We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context. ..."
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We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.
A Constructivist Perspective on Physics
, 2002
"... This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question o ..."
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This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible spacetime continuum. I argue (contrary to Hellman) that these do not pose any insuperable problem for constructivism, and that constructivism may have a useful new perspective to offer on physics. References ...