Apropos my previous post on the *Cahiers pour L’Analyse* and the website dedicated to it:

Fabio Cunctator at Hypertiling has posted a partial translation of Meillassoux’ article “Contigence et Absolutisation de l’Un”. What is fascinating about the translated part is that in it, Meillassoux sketches the outline of his argument for the absolute possibility of mathematical statements, the argument that *After Finitude* only hints at. I don’t yet have anything to say about the strength of Meillassoux’ argument (Pete at deontologistics suspects that it might involve a conflation of aletheic modality and deontic modality), but merely want to note that it seems to indicate the contemporary relevance of the *Cahiers*:

Meillassoux claims that there is an essential difference between the “ontic one” and the “semiotic one”, between the object or mark and the sign. The sign devoid of meaning, as utilized in mathematical formalization, is radically self-identical, *as type*. So for instance, in the series 11111111, if the 1s are considered as *marks *they are all different from one another. However, considered as *signs* they are completely identical instances of the type 1. This identity is, according to Meillassoux, due to the *contingency* of the signs as signs – the particular shapes of the signs used as variables, constants, etc., in mathematics has no bearing on the argument and can be chosen at random. And presumably, this contingency of the signs of mathematical formalization is the same *absolute* contingency that Meillassoux’ principle of factiality establishes.

Now, is this argument an attempt to *ground* the view of mathematics put forward by the early Badiou in articles like “Marque et Manque: à propos de Zéro”? This quote, from the synopsis of that article, might suggest as much:

The whole of ‘Mark and Lack’ presumes, then, an ‘inaugural confidence in the permanence’ and self-identity or self-substitutability of logico-mathematical marks or graphemes (156). Given any mark

x, logic must always treatxas strictly and unequivocally identical with itself. Badiou thus takes for granted a position that Miller associates, in ‘Suture’, with Leibniz and Frege (CpA 1.3:43): scientific knowledge depends on the exclusion of the non-identical, with the proviso that ‘the concept of identity holds only for marks’, i.e. mathematical inscriptions. ‘Science as a whole takes self-identity to be a predicate of marks rather than of the object’, a rule which applies to the ‘facts of writingproper to Mathematics as it does for the ‘inscriptions of energyproper to Physics’, along with the instruments used to measure them. (The entire synposis can be found here)

The “fact of science” which Badiou claims to be a groundless, contingent breach in the fabric of ideology, would then turn out to be “grounded”, if that is the right word, in the principle of factiality.

Just a remark; the reference to Frege as supporting the idea that identity concerns signs is certainly wrong, given that one of the most relevant contributions of Frege is that identity concerns objects and the fact that the same object is presented with two different modes of presentation. Since the paper “Sense and Reference” Frege rejects explicitly the claim that identity concerns only marks (a theory he criticizes with the label of “formalism”). Therefore if Badiou takes for granted what Miller says, and what Miller says is false, therefore Badiou says something false (at least concerning Frege).

Hi Carlo,

thanks for the comment. You are indeed right that Frege does not hold identity to concern only signs.

I’d have to go back and check to be sure, but I would be surprised, though, if Badiou really adduces Frege as support for such a claim, since Badiou at this point clearly wants to give something like a Hilbertian and thus indeed formalist correction to Miller, in order to acheive a theory of number that aligns with an Althusserian conception of science rather than a psychoanalytical one. So I believe that the “provisio” mentioned above, i.e., that “the concept of identity holds only for marks”, is Badiou’s own provisio, not something he ascribes neither to Frege nor Miller.