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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.
Against Pointillisme about geometry’, forthcoming
 in Proceedings of the 28th Ludwig Wittgenstein Symposium
, 2006
"... This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory’s fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or pointsized objects located there; so that properties of spatial ..."
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This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory’s fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or pointsized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the pointbypoint facts. More specifically, this paper argues against pointillisme about the structure of space andor spacetime itself, especially a paper by Bricker (1993). A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of “Newtonian ” ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics. 1
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.