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Number and Numbers QUOTES

Number and Numbers QUOTES

1 " 4.23..If 'thought' means: instance of the subject in a truth-procedure, then there is no thought of this thought, because it contains no knowledge. "

― Alain Badiou , Number and Numbers

2 " 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

3 " The audacity of thought is not to repeat 'to the limit' that which is already entirely retained within the situation which the limit limits; the audacity of thought consists in crossing a space where nothing is given. We must learn once more how to succeed. "

― Alain Badiou , Number and Numbers

4 " In the ordinal view, number is thought as a link in a chain, it is an element of a total order. In the cardinal view, it is rather the mark of a 'pure quantity' obtained through the abstraction of domains of objects having 'the same quantity'. The ordinal number is thought according to the schema of a sequence, the cardinal number, according to that of a measurement. "

― Alain Badiou , Number and Numbers

5 " 4.13. The most striking aspect of Dedekind's definition is that it determines infinity positively, and subordinates the finite negatively. This is its especially modern accent, such as is almost always found in Dedekind. An infinite system has a property of an existential nature: there exists a biunivocal correspondence between it and one of its proper parts. The finite is that for which such a property does not obtain. The finite is simply that which is not infinite, and all the positive simplicity of thought hinges on the infinite. "

― Alain Badiou , Number and Numbers

6 " The 'economy of number' proposed by Peano is an economy of signs whose paradigm is algebraic, whose transparency is consensual, and whose operational effectiveness is therefore not in doubt. He thus participates forcefully in that movement of thought, victorious today, that wrests mathematics from its antique philosophical pedestal and represents it to us as a grammar of signs where all that matters is the making explicit of the code. "

― Alain Badiou , Number and Numbers