Thursday, December 2, 2010

Horizon - Peter Hallward (Badiou: Subject to Truth, p.319)


A horizon is not an objective structure of the world or the universe, but a limit specific to a particular prescription or conceptualization, however indecisive or abstract. Even the mathematical demonstration of an unending sequence of ever larger infinite numbers, while it certainly establishes the banal and numerically limitless dimension of all numbers, is nevertheless obliged to acknowledged a kind of specifically numerical "horizon," that is, an unreachable limit that no numbering operation takes place: this is the limit indicated, as we know, by the impossibility of a single set of all sets. Such an impossible set would precisely be a set without horizon in this sense, that is, a set that excludes anything accessible.

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