Mathematics in Motion: Cartesian Mechanism and the Prospect of Intelligent Machines
Darko Draskovic · IRIS · 2019
Descartes' dualism deflnes the scope of the present work. Descartes' doctrine of God and man, res cogitans, is understood as a metaphysical and epistemologi- cal grounding for his physics, res extensa. The lattcr is examined as a horizon for the concepts of mechanism and machine. In addition, the thesis proposes a correlative reading of Cartesian dualism via the général distinction between philosophy and mathematics. Both of these readings are grounded in two basic conceptual distinction: 1) between reflexivity (referring back to itself) and in- nerness (containing itself) of auto, and linearity and outwardness of hetero, 2) between being productive and being product. Subject is understood as reflex- ive and productive: God is ontologically productive by means of auto-causality and man is epistemologically productive by means of self-consciousness. On the other hand, nature présents us with a linear dispersion and outwardness of space (or matter). While philosophy is concerned with the paradoxes of true reflexivity (= auto), modem mathematics articulâtes its basic stance in an ef¬fort to eliminate, by means of axiomatization and formalization, paradoxes of self-containment (set tlieory) and auto-reference (mathematical logic). Descartes' universal mathematics plays the rôle of a new logos and his physics can be understood as a locus of the new idea of physis as actualized geometrical translation (= the source of individuation of natura.1 entities). Furthermore, Descartes' philosophy of nature can be seen not only as a transformation of physis into mathematical kinesis (— mechanism) but also as a recasting of physis as techne (= machine): nature is artificial and natural phenomena are artifacts. Nature as matter (= géométrie space) in motion (= géométrie translation) is, as a technology of machine production, a self-creative power. While every machine is mechanism, not every mechanism is machine. Automation, understood as 1) internai principle of motion (engine) and 2) feedback (cybernetics), t-urns a simple mechanism into a complex (emergent) machine. One of the central tenets of the present work is that auto-mation introduces some sort of auto, i.e. reflexivity in the material reality as such. Acknowledging that human mind is one of the principal bedrocks of reflex¬ivity, the thesis also asks a converse question whether Descartes' philosophy supplies us with means of thinking the possibility of machine mind. To answer the question, the thesis deploys the différence between (self)presentation ( cog- ito) and (self)représentation (cogitare) - understood as a distinction between pre-logical and logical as well as between pre-linguistic and linguistic, and fur- ther specifîed as the différence between consciousness (intuition) and intelli¬gence (déduction). Although Descartes does not admit of intelligence without consciousness, the thesis goes on to show that intellect understood as repré¬sentation (linguistic) and intelligence (logic) can be implemented as symbolic mechanistic system. Consequently, man's political capacity is not deposited, as in pre-modern philosophy (animal rationale), in his logic or linguistic faculties (= res cogitans), and should be, rather, looked for in cogito - a reflexive "part" that cannot be implemented b.y and in mechanism.