Affirming the Infinite, §10, Logic of Expression. Simon Duffy

by Corry Shores
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[The following summarizes part of Simon Duffy's extraordinary book, The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. My commentary is in brackets. Duffy's work is remarkable, so I highly recommend this book. If it costs too much, perhaps encourage your library to obtain a copy.]

Affirming the Infinite

Simon Duffy

The Logic of Expression:

Quality, Quantity and Intensity in Spinoza, Hegel andDeleuze

Chapter 1

"Spinoza from the point of view of an idealist or a materialist dialectic"

§10 The problem of the ‘bad infinite’

Previously we discussed Hegel’s misinterpretation of Spinoza’s infinite. It is not merely the infinite divisibility of finite extensions. Conceiving it so is often the doing of our imaginations rather than our more able rational faculties.

Macherey builds from Gueroult’s commentary to argue that Hegel misses Spinoza’s point: finite things are not infinite by force of their cause. Finitely-extended modes are nonetheless infinite insofar as they express the infinite of substance, which is their immanent cause. (25c)

Macherey evokes the distinction between

1) what is infinite by its nature. Substance is absolutely infinite; and

2) what is infinite by force of its cause. The attributes or modes of substance are infinite in this way.

He further distinguishes

1) what is infinite because it has no limits; and

2) what is infinite because it cannot be determined by numbers. It is unlimited or indefinite despite the fact that it is bound within a maximum and minimum.

When we use reason, we may adequately understand things. But our imagination is inadequate for this purpose. Substance is absolutely infinite. We can only conceive it through reason, and not through imagination. We can, however, imagine substance’s affections. But when we do so, we understand them inadequately as unlimited and indefinite. Only reason can adequately understand affections as infinite by force of their cause. (26a)

Unless we maintain these distinctions, we will run into contradictions when conceiving the infinite.

According to Macherey, the bad infinite is the unlimited or indefinite. It is the same thing as the actual infinite. When using reason, we understand it adequately as the actual infinite, but when using our imagination, we inadequately conceive it as the bad infinite.

For Macherey, we adequately understand something when we grasp it affirmatively in terms of its cause. Hegelian dialectic views the infinite in terms of negations, and hence does not understand it adequately.

According to Macherey, the actual infinite, as apprehended adequately in the mode, ‘is not different to that infinity constitutive of substance, but is formally the same’. The actual infinite is therefore the immanent expression in the affections, or the finite modes, of infinite substance, which is their cause. (26-27)

Duffy, Simon. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate Publishing, 2006.