BADIOU ON SPINOZA (1): the enigmatic status of « infinity »

Badiou’s « immanence of truths » project attempts to draw on the recent mathematical elaborations of transfinite numbers to project light on the problems of philosophy and also on its history. An important outcome of his investigations is the conceptual analysis of the problems arising from the insufficiently or inadequately theorised occurrences of the concept of the infinite. In this talk Badiou examines the diverse senses of « infinite » in Spinoza’s system.

Badiou starts (8m10s) with the conceptual assembly composed of the terms in Spinoza’s ETHICS that convoke the notion of the « infinite »:

Substance (the infinite and eternal essence, substantial infinite, absolute but internally differentiated), attributes (which express infinitely the infinite and eternal essence of Substance, intrinsic infinity of the attributes), infinite number of attributes (numerical, extrinsic infinity), and infinity of modes. Thus we can distinguish different « figures » of the infinite in Spinoza’s ETHICS.

Badiou observes that Spinoza needs the modes for logical, and not causal, reasons, as

« the infinite cannot directly produce the finite… the infinite and the finite are distinct from the point of view of the operational mode, i.e. of causality, which is THE operational procedure for Spinoza ».

One must distinguish the immanent productivity of Substance from the causal chains that go from infinite mode to infinite mode or from finite mode to finite mode, without interaction between the two.

« Infinite is not at all a univocal word in Spinoza. It goes, it « sweeps », through the whole territory of experience, from its very being, its absolute being, which is Substance, to the singular thing which is the mode, in all these cases one can speak of the infinite, and the mediation of all that is the absolute ».

So there are four « systemic occurrences of infinity » in Spinoza’s thought, not just one

1. infinity of Substance
2. intrinsic infinity of the attributes
3. extrinsic infinity of the attributes, due to their infinite number
4. obligatory existence of infinite modes

So « infinite » is in a relatively enigmatic position for Spinoza, precisely because one may legitimately ask is there a univocal signification for all these infinites, or if there are different significations, and to what extent one can think this difference ».

One response has been to examine the nature of the attributes in Spinoza’s system. This has led to diverse rival interpretations: Deleuze’s interpretation in terms of expression and in opposition an interpretation in terms of immanent productivity. The attribute can be seen as perspective or interpretation expressing the absolute (Deleuze) or immanent composition of the absolute (Badiou, as we shall see later).

Another issue open to discussion is the idea that what manifests the homogeneity of the infinite is its « structural transversality », that the order and the connexion between things in each attribute are isomorphic. In response to this one can object that despite this unity one cannot eliminate a certain difference of being immanent to Substance. One can not think the difference between the infinity of the attributes and and that of the modes if one reduces everything to the same because the causal order is the same.

Another problem concerns the difficulty of giving examples of the infinite modes, which Spinoza only does in his correspondance. The question arises of whether a singular thing is intrinsically finite. Why can’t there exist singular things which are infinite?

The distinction between attribute and mode (and between Substance and mode) does not necessarily coincide with the distinction between infinite and finite. This is what Spinoza tries to illustrate when he speaks of the figure of the whole universe, which he gives as an example of infinite mode associated with the attribute of extension.

Badiou wishes to join the discussion

by proposing an integrally rational construction of the concept of attribute, i.e. permitting to think, not just in the context of Spinoza but in general, to think the integral rationality of the concept of the absolute as interiority of the absolute itself.

Badiou wishes to align himself with the interpretation of the attributes in Spinoza as « ontological correlations immanent to Substance », and not perspectives or points of view on Substance as in Deleuze.