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" I think… that love encompasses the experience of the possible transition from the pure randomness of chance to a state that has universal value. Starting out from something that is simply an
encounter, a trifle, you learn that you can experience the world on the basis of difference and not only in terms of identity. And you can even be tested and suffer in the process. In today’s world, it is generally thought that individuals only pursue their own self-interest. Love is an antidote to that. Provided it isn’t conceived only as an exchange of mutual favours, or isn’t calculated way in advance as a profitable investment, love really is a unique trust placed in chance. It takes us into key areas of the experience of what is difference and, essentially, leads to the idea that you can experience the world from the perspective of difference. In this respect it has universal implications: it is an individual experience of potential universality, and is thus central to philosophy, as Plato was the first to intuit. "
― Alain Badiou , In Praise of Love
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" 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. "
― Alain Badiou , Number and Numbers