Negative Infinity

Here is a section from a piece I wrote on Badiou last year that touches on ‘negative infinity’, a problem that Marx, I think, identifies as a problem inherent in the value-form. Does the elevation to money into the role of universal equivalent solve the problem of identity given in the expanded form of value, in Section 3 of Chapter 1?

For further reading: Hegel talks about this directly in paragraphs 89 to 98 of the Encyclopedia Logic.

III

What is missing here is that the unhappy consciousness is an expression of what Hegel calls ‘negative infinity’.[i] Hegel’s criticism of traditional Christianity is exactly that its God is transcendental. For this Christianity, ‘[t]he death of Christ means that God has withdrawn from the world, and that there are no longer any mediators between individual and God’.[ii] The vogue for Epicurus and Spinoza during Hegel’s youth subsequently led him to pursue the redemption of the Christian God under the notion that an absolute God must by definition be immanent in the world: if God is not in the world there is a place where God is not — God is not absolute.[iii] Accounting for the infinite within the finite (God in the world) then becomes a dominant motif in Hegel. This culminates in the ‘Absolute Idea’ that closes his logic.

In the early paragraphs of the Philosophy of Right, Hegel sets out the basic movement of his dialectic of will. First, the will denies all limits; negating determination and naming itself infinite. Second, the will cancels this denial, and determines itself within the (finite) world. But this denial is a determination without the universality given (negatively) in the first moment. And so we finally have, third, ‘the unity of both these moments’.[iv] He describes this final moment as the ‘self-determination of the ego’ and it is at this point that negative infinity, or the unhappy consciousness, gives way to the substantial being that he calls true or good infinity.

With the simple denial of limits all that is achieved is an infinite repetition of negation. Everything appears as a limit from the one-sided standpoint of the abstractly infinite will. This is a bad negation, a repetition compulsion. The location of the infinite within the finite, ‘the unity of both these moments’, breaks this logic. What previously appeared as a limit is now a determination of the will itself. ‘It is the will whose potentialities have become fully explicit which is truly infinite’, Hegel says, ‘because its object is itself and so is not in its eyes an “other” or a barrier; on the contrary, in its object this will has simply turned backward into itself’.[v]


[i] G. W. F. Hegel, Logic: Being Part One of the Encyclopaedia of the Philosophical Sciences (1830), trans. W. Wallace, Oxford, Oxford University Press, 1975, p. 137. See also: Hegel, Philosophy of Right (1821), trans. T. M. Knox, Oxford, Oxford University Press, 1967, p. 21-2.

[ii] F. Beiser, Hegel, New York, Routledge, 2005, p. 137.

[iii] See Beiser, Hegel, chapters 1 and 2.

[iv] Hegel, Philosophy of Right, pp. 21–3.

[v] Hegel, Philosophy of Right, p. 30.

Excerpt From: J. Collerson. ‘Negation and Politics: A reply to Matthew Sharpe on Alain Badiou’ in Arena Journal, New Series, No. 32. 2009, pp. 201-14.

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