My paper at the conference THE ULTIMATE CAPITAL IS THE SUN // METABOLISM IN CONTEMPORARY ART, POLITICS, PHILOSOPHY AND SCIENCE (http://theultimatecapital.org) organized by Matteo Pasquellini, Elena Agudio, Dorothee Albrecht, Bonaventure Ndikung and Eylem Sengezer at Akademie der Künste in Berlin, October 25/26 2014.

ABSTRACT

My paper will consider some of the circumstances in which the understanding of mathematics came to change from its classical sense in, roughly, the artes liberales tradition as „the art of learning,“ intransitively so (‚mathematics‘ literally means: all that pertains to Gk. mathema, „that which can be learnt“), to an understanding almost entirely dominated by the criteria of usefulness and applicability in the early 20th century. Today, we hardly remember that this is a rather recent tendency, and to speak of mathematics as a subject in its own right (something that Husserl, Whitehead, Wittgenstein and Heidegger still did) sounds awkwardly stiff and wakes perhaps associations that unfold along the lines of that for which a mechanically calculate-able solution can be found within a finite number of steps. The interest with raising these backgrounds is not simply to keep them from oblivion. My point is that they can support the distinction of two different legacies of thinking about computability: 1) the well-known Turing/Church way, for which the assumption of a transparency of arithmetics for objective reasoning is central, and 2) a manner for which the role of arithmetics is no less constitutive for objective reasoning, but not in a transparent way. Instead algebraic law-like formality is constitutive for the contractual, symbolic constitutions of objectivity. I will suggest to call this the Babbage/Boole/Dedekind way. I will conclude my paper with positioning Michel Serres philosophy of media and communication in relation to this distinction.

BACKGROUND READINGS

Michel Serres, The Parasite (University of Minnesota Press 2007 [1980])

–– , The Natural Contract (University of Michigan Press 1995 [1990]).

–– , „Motoren. Vorüberlegungen zu einer allgemeinen Theorie der Systeme“, in Hermes IV, Verteilung (Merve, Berlin 1992, pp. 43-91).

–– , „Thinking and Information,“ keynote address delivered at the Philosophy after Nature Conference in Utrecht, September 2014, organized by the Society for European Philosophy and Forum for European Philosophy.

James Potter, Reason’s Nearest Kin, Philosophies of Arithmetics from Kant to Carnap (Oxford University Press, 2002).

Howard Stein, “Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth Century Transformations in Mathematics”, in W. Aspray and P. Kitcher (eds.) History and Philosophy of Mathematics (University of Minnesota Press, 1988).

Reck, E.H. (2003) „Frege, Natural Numbers, and Arithmeticʻ s Umbilical Cord“ in: Manuscrito  26:2, 2003, Special Issue: Logic, Truth and Arithmetic: Essays on Gottlob Frege, M. Ruffino, guest editor, pp. 427-470.