By Badiou, Alain
Articles from Alain Badiou, that have been released in Cahiers pour l'analyse. Scans from the English translations, that have been released in proposal and shape (ed. Hallward & Peden).
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Extra resources for Mark and Lack, Infinitesimal Subversion
Sample text
The variable, as inscription which disjoins the constructible from the occupiable - governing which constants belong to the former but not to the latter - testifies to the intra-systemic trace of the system's reality. The operator of the real for a domain, it in fact authorizes within that domain the writing of the impossible proper to it. The existent has as its category a being-able-not-to-be the value of a variable at the place it marks. In this regard, the variable is the exact inverse of the infinity-point, whose inscription it prepares.
The relation of order is obviously transgressive. Take a, the infinity-point relative to this relation: a is 'larger' than every element of R: it is infinitely large. , all of which will be infinitely large (larger than every constant of R). We should note, by the way, that the infinity-point a, the scriptural instru ment of the recasting, retains no particular privilege within the recast domain - a good illustration of the effacement of the cause in the apparatus of a struc ture. In particular, even if a is formally inscribed as a unique constant of trans gression, it is no more the smallest infinite number than it is the largest - as we have just seen.
It will be found that the rules of the finite succeed in the infinite [ . ] and that [ 1 27) vice versa the rules of the infinite succeed in the finite [ . . ]: this is because all . . 21 Abraham H. Fraenkel, Einleitung in die Mengenlehre, in Grundlehren der mathematischen Wissenschaften, vol. 9 (Berlin: Springer, 1928). 22 In his Philosophie de lalgebre (Paris: PUF, 1962), Jules Vuillemin also denounces any recourse to indivisibles as an intellectual regression: '[ . . ] if one understands by differentials magnitudes at once smaller than our assignable magnitude and nevertheless different from zero, one returns to the precritical epoch of calculus' ( 5 23).
