Finite Infinity: Reading Gasché Reading Derrida Reading Hegel… "and so on without an end"

Jacques Derrida never credited the notion of "finitude" as such. "Finitude" as such, that is, as an anthropological limit, must go through the sieve of deconstruction, in the very interest of deconstruction, of its statute and range. Indeed, deconstruction could be reread as an appeal to "finitude" against the pretensions of onto-theological metaphysics. In Of Grammatology, Derrida is fully aware of this risk:

That the logos is first imprinted and that that imprint is the writing-resource of language, signifies, to be sure, that the logos is not a creative activity, the continuous full element of the divine word, etc. But it would not mean a single step outside of metaphysics if nothing more than a new motif of "return to finitude," of "God's death," etc., were the result of this move. It is that conceptuality and that problematic that must be deconstructed. They belong to the onto-theology they fight against. Differance is also something other than finitude.

(Derrida 1997, 68)

The appeal to "finitude" as such, contra the traditional, metaphysical conception of the logos as absolute, unconditioned, infinite, remains within metaphysics by confirming its fundamental structure: being a system of hierarchically organized oppositions, metaphysics encompasses "finitude" as its moment, as the complementary opposite required by the determination of the infinite. Therefore, an appeal to finitude would end up turning the hierarchy upside down, yet leaving the oppositional structure, which grounds both terms (finite and infinite), unaltered.¹

Therefore, we must first deconstruct this oppositional structure and in particular the classical opposition between the finite and the infinite that overdetermines the notion of "finitude," to see differance emerge as something that differentiates itself from "finitude" by differing the meaning of it.

This deconstruction must necessarily go through the Hegelian speculation, which represents the deepest and most accurate determination of the finite/infinite opposition within the horizon of the metaphysical tradition. Here, the finite appears explicitly as a moment that is dialectically subordinated to the affirmation of the positive infinite that accomplishes itself in the form of the concept and thus of the Absolute Knowledge. In the Science of Logic, Hegel breaks down the moments of finite/infinite dialectics as follows:

The infinite

(a) in simple determination, is the affirmative as negation of the finite;

(b) but is thereby in alternating determination with the infinite, and is abstract, one-sided infinite;

(c) is the self-sublation of this infinite and of the finite in one process. This is the true infinite.

The infinite is the negation of negation, the affirmative, being that has reinstated itself out of restrictedness. The infinite is, in a more intense sense than the first immediate being; it is the true being; the elevation above restriction. At the mention of the infinite, soul and spirit light up, for in the infinite the spirit is at home, and not only abstractly; rather, it rises to itself, to the light of its thinking, its universality, its freedom. What is first given with the concept of the infinite is this, that in its being-in-itself existence is determined as finite and transcends restriction. It is the very nature of the finite that it transcend itself, that it negate its negation and become infinite. … Itisnotinthe sublation of the finite in general that infinity in general comes to be, but the finite is rather just this, that through its nature it comes to be itself the infinite. Infinity is its affirmative determination, its vocation, what it truly is in itself. The finite has thus vanished into the infinite and what is, is only the infinite.

(Hegel 2010, 109–10)

Toward a Deconstruction of Finitude

Derrida never engaged explicitly in the deconstruction of the opposition between the finite and the infinite and of its speculative solution, but we may register the traces of it disseminated in several texts, apparently dedicated to other authors and problems. For instance, in "The Ends of Man": while examining the dialectical movement that, within the Philosophy of the Subjective Spirit, secures the transition from Anthropology, man...