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Number and Numbers

Book by Alain Badiou · 1 quotes · Mathematics, Number, Recursion

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Number and Numbers Quotes

“4.19. Dedekind's approach is a singular combination of Descartes' Cogito and the idea of the idea in Spinoza. The starting point is the very space of the Cogito, as 'closed' configuration of all possible thoughts, existential point of pure thought. It is claimed (but only the Cogito assures us of this) that something like the set of all my possible thoughts exists. From Spinoza's causal 'serialism' (regardless of whether or not he figured in Dedekind's historical sources) are taken both the existence of a parallelism' which allows us to identify simple ideas by way of their object (Spinoza says: through the body of which the idea is an idea), and the existence of a reflexive redoubling, which secures the existence of 'complex' ideas, whose object is no longer a body, but another idea. For Spinoza, as for Dedekind, this process of reflexive redoubling must go to infinity. An idea of an idea (or the thought of a thought of an object) is an idea. So there exists an idea of the idea of a body, and so on.”

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