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At page 170 of Being and Event Badiou ends his reading of Hegel’s philosophy by locating a ‘fragile verbal footbridge’ at its heart.  The unity of his system is said to depend upon a fragile construction which aims to span a gap that for Badiou must be treated very differently.  I am interested in the history of philosophy which runs throughout Being and Event.  The assessment of Hegel here (in Meditation 15) echoes his treatment of Spinoza (in Meditation 10) which I puzzled over in a previous post.  There the ‘fragile verbal footbridge’ thrown across the gap in Spinoza’s system is the infinite mode.  In Meditation 15 Hegel’s understanding of infinity is interrogated by Badiou.  He is seen to be seeking to rejoin qualitative infinity and quantitative infinity at a key point in his system, a point which shows what is really at stake in his philosophy.  For Badiou this is a moment where we encounter an abyss or void and not the fullness of the dialectic.  The crucial question is whether we wager upon a solution that cannot be grounded upon an existing and established procedure of knowledge like Hegel’s dialectic.  Hegel is said to be attempting to assimilate quantitative infinity to qualitative infinity in order to fill in this gap.  Badiou argues that this fails because in Hegel’s system quantitative infinity proliferates while qualitative infinity contracts:  ‘There is no symmetry between the same and the other, between proliferation and identification.  However heroic the effort, it is interrupted de facto by the exteriority itself of the pure multiple.  Mathematics occurs here as discontinuity within the dialectic.  It is this lesson that Hegel wishes to mask by suturing under the same term – infinity – two disjoint discursive orders’ (p. 169).  ?

This critique and Badiou’s overriding concern with quantitative infinity or extensive multiplicity has the strange effect of making Hegel resemble Gilles Deleuze.  The ‘contracted self’ explored in Deleuze’s Difference and Repetition forms part of an account of individuation, of the contraction of individuating differences.  This aspect of Deleuze’s philosophy has been neglected by those who accuse him of prioritising the virtual and undermining the actual.  I would argue that the mediating role of individuation ensures that the roles of both the actual and the virtual are realised in Deleuze’s account.  James Brusseau takes a different approach in his Isolated Experiences when he critiques what he sees as an over-emphasis upon individuation in Deleuze, something that is to the detriment of the external world.  Individuation can either be neglected, seen to dominate or, as I would advocate, shown to be necessary to a full account of experience involving both the actual and the virtual.  Despite the similarity between Deleuze and Hegel which is suggested by Badiou’s reading of Hegel we can also locate a key difference.  Difference is positive for Deleuze while it is negative Hegel.  The emphasis upon quality over quantity in both systems does unify them in relation to Badiou’s championing of quantity and extensive multiplicity but when it comes to the nature of difference a key distinction needs to be established.   

It can be argued that Hegel lacks a theory that recognises the type of problems that matter for thinkers like Deleuze and Badiou.  This follows, I would argue, because for Hegel difference is negative.  He lacks a ‘positive’ theory of problems of the kind that Deleuze and Badiou seek, one that animates thought and differentiates experience.  Instead he has a theory of the subsumption of problems in the movement of his dialectic so that this movement of contraction does not have the same effect as Deleuze’s contraction of individuating differences.  Badiou argues that Hegel’s dialectic voids the other in an ‘introjection of alterity’ (p. 168).  While the quantitative externalises identity, the qualitative internalises differences that are otherwise external without this giving rise to any outpouring in the world as is the case in Deleuze’s account of individuation.  Deleuze and Badiou want to break with the one and to affirm the multiple, but they choose different multiplicities: the former intensive multiplicities and the latter extensive multplicities.  For Badiou the extensive proliferates while the intensive contracts and this sets him against both the positive difference of Deleuze and the negative difference of Hegel insofar as these are qualitative conceptions of difference that operate through contraction.  We can only maintain the role of the void as evental site and of the wager of being faithful to what might be an event if we think through the nature of the extensive and quantitative in our ontology.  Thus Deleuze and Hegel start to sound alike but in the end it is the theory of positive problems that structures the accounts of Deleuze and Badiou, that accounts for theory and practice, and that applies to different disciplines.  Deleuze’s notion of contraction involves differences that cannot be contained, that pour out in the external world just like the individuating differences of hunter and prey mark out and develop hunting fields of animals.  Differences do then proliferate in an external realm for Deleuze, providing an account of the quantitative.  This is of course a huge debate but it seems to me that it is insofar as Hegel seeks to subsume problems in the movement of his dialectic that he differs from Deleuze and Badiou.  The differences between Deleuze and Badiou come down to how problems make a positive difference or how genuine transformations or events can occur.  Does this require extensive or intensive multiplicities?  Does it require the void as the evental site or fullness as the concrete source of transformation?      

At page 170 of Being and Event Badiou ends his reading of Hegel’s philosophy by locating a ‘fragile verbal footbridge’ at its heart.  The unity of his system is said to depend upon a fragile construction which aims to span a gap that for Badiou must be treated very differently.  I am interested in the history of philosophy which runs throughout Being and Event.  The assessment of Hegel here (in Meditation 15) echoes his treatment of Spinoza (in Meditation 10) which I puzzled over in a previous post.  There the ‘fragile verbal footbridge’ thrown across the gap in Spinoza’s system is the infinite mode.  In Meditation 15 Hegel’s understanding of infinity is interrogated by Badiou.  He is seen to be seeking to rejoin qualitative infinity and quantitative infinity at a key point in his system, a point which shows what is really at stake in his philosophy.  For Badiou this is a moment where we encounter an abyss or void and not the fullness of the dialectic.  The crucial question is whether we wager upon a solution that cannot be grounded upon an existing and established procedure of knowledge like Hegel’s dialectic.  Hegel is said to be attempting to assimilate quantitative infinity to qualitative infinity in order to fill in this gap.  Badiou argues that this fails because in Hegel’s system quantitative infinity proliferates while qualitative infinity contracts:  ‘There is no symmetry between the same and the other, between proliferation and identification.  However heroic the effort, it is interrupted de facto by the exteriority itself of the pure multiple.  Mathematics occurs here as discontinuity within the dialectic.  It is this lesson that Hegel wishes to mask by suturing under the same term – infinity – two disjoint discursive orders’ (p. 169).  ?

This critique and Badiou’s overriding concern with quantitative infinity or extensive multiplicity has the strange effect of making Hegel resemble Gilles Deleuze.  The ‘contracted self’ explored in Deleuze’s Difference and Repetition forms part of an account of individuation, of the contraction of individuating differences.  This aspect of Deleuze’s philosophy has been neglected by those who accuse him of prioritising the virtual and undermining the actual.  I would argue that the mediating role of individuation ensures that the roles of both the actual and the virtual are realised in Deleuze’s account.  James Brusseau takes a different approach in his Isolated Experiences when he critiques what he sees as an over-emphasis upon individuation in Deleuze, something that is to the detriment of the external world.  Individuation can either be neglected, seen to dominate or, as I would advocate, shown to be necessary to a full account of experience involving both the actual and the virtual.  Despite the similarity between Deleuze and Hegel which is suggested by Badiou’s reading of Hegel we can also locate a key difference.  Difference is positive for Deleuze while it is negative Hegel.  The emphasis upon quality over quantity in both systems does unify them in relation to Badiou’s championing of quantity and extensive multiplicity but when it comes to the nature of difference a key distinction needs to be established.   

It can be argued that Hegel lacks a theory that recognises the type of problems that matter for thinkers like Deleuze and Badiou.  This follows, I would argue, because for Hegel difference is negative.  He lacks a ‘positive’ theory of problems of the kind that Deleuze and Badiou seek, one that animates thought and differentiates experience.  Instead he has a theory of the subsumption of problems in the movement of his dialectic so that this movement of contraction does not have the same effect as Deleuze’s contraction of individuating differences.  Badiou argues that Hegel’s dialectic voids the other in an ‘introjection of alterity’ (p. 168).  While the quantitative externalises identity, the qualitative internalises differences that are otherwise external without this giving rise to any outpouring in the world as is the case in Deleuze’s account of individuation.  Deleuze and Badiou want to break with the one and to affirm the multiple, but they choose different multiplicities: the former intensive multiplicities and the latter extensive multplicities.  For Badiou the extensive proliferates while the intensive contracts and this sets him against both the positive difference of Deleuze and the negative difference of Hegel insofar as these are qualitative conceptions of difference that operate through contraction.  We can only maintain the role of the void as evental site and of the wager of being faithful to what might be an event if we think through the nature of the extensive and quantitative in our ontology.  Thus Deleuze and Hegel start to sound alike but in the end it is the theory of positive problems that structures the accounts of Deleuze and Badiou, that accounts for theory and practice, and that applies to different disciplines.  Deleuze’s notion of contraction involves differences that cannot be contained, that pour out in the external world just like the individuating differences of hunter and prey mark out and develop hunting fields of animals.  Differences do then proliferate in an external realm for Deleuze, providing an account of the quantitative.  This is of course a huge debate but it seems to me that it is insofar as Hegel seeks to subsume problems in the movement of his dialectic that he differs from Deleuze and Badiou.  The differences between Deleuze and Badiou come down to how problems make a positive difference or how genuine transformations or events can occur.  Does this require extensive or intensive multiplicities?  Does it require the void as the evental site or fullness as the concrete source of transformation?