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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. ..."
Abstract

Cited by 2 (1 self)
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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.
On the calculating power of Laplace’s demon (Part I)
, 2006
"... We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a s ..."
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We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a start on our programme by proposing a general logical framework for describing physical theories, and analysing several possible formulations of a simple Newtonian theory from the point of view of determinism. Our emphasis throughout is on clarifying the precise physical and metaphysical assumptions that typically underlie a claim that some physical theory is ‘deterministic’. A sequel paper is planned, in which we shall apply similar methods to the analysis of other physical theories. Along the way, we discuss some possible repercussions of this kind of investigation for both physics and logic. 1
When is.999... less than 1?
"... We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is “an infinite number of 9s ” merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone’s “semicolon ” notation? Is it p ..."
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We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is “an infinite number of 9s ” merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone’s “semicolon ” notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol.999... be inculcated in a prelimit teaching environment? The problem of the unital evaluation is hereby examined from the preR, prelim viewpoint of the student. 1.