Citations of:
A path to the epistemology of mathematics: homotopy theory
In Jeremy Gray & Jose Ferreiros (eds.), The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press. pp. 239260 (2006)
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We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against nonstandard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dartthrowing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) 