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(2002) Synthese 133 (3).
In 1887 Georg Cantor gave an influential but cryptic proof of theimpossibility of infinitesimals. I first give a reconstruction ofCantor's argument which relies mainly on traditional assumptions fromEuclidean geometry, together with elementary results of Cantor's ownset theory. I then apply the reconstructed argument to theinfinitesimals of Abraham Robinson's nonstandard analysis. Thisbrings out the importance for the argument of an assumption I call theChain Thesis. Doubts about the Chain Thesis are seen to render thereconstructed argument inconclusive as an attack on the infinitelysmall.
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Full citation:
Moore, M. E. (2002). A Cantorian argument against infinitesimals. Synthese 133 (3), pp. 305-330.
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