The Mathematics of Infinity - Softcover

Inhaltsangabe

Historically, ideas of infinitesimals and continuity arose from spatial and kinematic considerations. Even today, Platonists frequently rely on infinitistic physical thought experiments to bolster their support of actual infinity. To many, it seems simply obvious that there could exist actual infinities in the physical world (for example, an actual infinity of stars), and they infer that actual infinity is also a coherent idea in pure mathematics (Russell, 1935–6; Benardete, 1964, p.31). I shall examine the idea of physical infinity in §4; it turns out that it is so paradox-ridden that it counts more against actual infinity than in favour of it. However, it must be said that constructivists have so far failed to provide an alternative account of physics based on potential infinity.

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