The Infinitesimal as Theological Principle: Representing the Paradoxes of God and Nothing in Cohen, Rosenzweig, Scholem, and Barth

In a letter to Schelling dated August 30, 1795, Hegel mentions that he wants to write an essay exploring "what it could mean to approach God?" (was es heißen könne, sich Gott zu nähern?).¹ Hegel, throughout his entire career, and Schelling, at least throughout the first thirty years of his even longer one, pursued the answer to this question in terms of a dialectics of mediation, reconciliation, and identity. According to this view, to approach God means to come to the awareness, either in the representational mode (Vorstellungsdenken) of religion or in the conceptual form of philosophy, of the fundamental identity between God and man, both of whom are mediated as one in Spirit. It was against this view that the figures explored in this essay rebelled, even if their projects could also be formulated in terms of a series of similar questions, like what does it mean for man to approach God and the world and, in the reverse, what does it mean for God to approach man and the world. In all four cases mathematics will play a role in formulating what they might mean by the crucial term "to approach," because for all of them mathematics, and specifically the notions of the infinitesimal and the limit, provide a mode of representing the fundamental aspect of religious experience, namely the paradox that the "nothing" at the heart of non-identity can generate a movement toward an Other such that the distance can become infinitely small without collapsing into sameness. The reason why basic high school calculus can serve as the source (Ursprung) of this way of thinking through and representing religion is that it itself contains precisely this paradoxical structure: not the famous "identity of identity and non-identity" that the early Hegel formulated (together with the young Schelling) but a non-identity that is at once irreducible and productive. It was Hermann Cohen's contribution to foreground this powerful philosophical and theologically promising role for the infinitesimal and differential limit. Man, God, and World do approach each other (to use the main cornerstones or apexes from Rosenzweig), but there is always the infinitesimal gap, infinitely small perhaps yet absolute, at the limit or, as Barth says, at the "Todeslinie" between them.² Moreover, if according to Peter Gordon calculus was for Rosenzweig a "metaphor" rather than a logical principle, it can uniquely serve this function in the strong, Aristotelian sense—"from metaphor we can best get hold of something fresh" and "set the scene before our eyes"—because its formulation of the relation between the infinite and the finite is paradoxically non-visualizable and concretely graphic.³ Perhaps we can use this peculiar aspect of the representability of the infinitesimal as a way of understanding Rosenzweig's perplexing statement that his abstract work was actually an example of "absolute empiricism," or Scholem's early call for a "mathematical mystic" and "mystical mathematician."⁴ This does not mean that we ought to give absolute priority to the mathematical; this is just one of the rhetorics crossing and connecting these thinkers and allowing them to find a way to express the inexpressible realities of God and nothingness.

The motivation for Hermann Cohen to turn to the method of the infinitesimal was not originally theological. But he did want to explore what the deeper significance of the infinitesimal is and to provide a philosophical justification for that significance (and in this it will come to have theological relevance). What is it about this tool and about reality that the tool so effectively explains? Specifically, according to Cohen, mathematics deals with equalities (Gleichheit) and equations (Gleichungen), while logic deals with identity (Identität). The difference is important since already Leibniz said that equality is really just infinitely small inequality: "Auf diese Weise kann auch die Gleichheit [aequalitas] als unendlich kleine Ungleichheit [inaequalitas] betrachtet werden, wo der Unterschied kleiner ist als eine beliebig kleine gegebene Größe."⁵ Cohen wonders what it says about reality that such (in)equalities and...