Lebedev, Oleg
[UCL]
In his First book of Euclid’s Elements the neo-platonic thinker Proclus acknowledges that geometry proceeds in a theoretical and immaterial manner, but also pays a particular attention to its relation to matter, so that sciences like geodesy, optics, catoptrics, mechanics, and even what he calls ‘scenography’ emanate out of it, doing some good to ‘mortal humanity’. While maintaining the primacy of theorems over problems, Proclus defines the conditions of the problem in terms of an order of events and affections, so that the main working method of a geometrician is differentiated into procedures of organizing movement (removal, addition, substitution, expansion and delimitation). This distinction between (1) a theorematic demonstration developing what was already inscribed in an axiom and (2) the construction/drawing of figures implied by the very nature of a geometrical problem is summed up in Difference and Repetition, but runs throughout Deleuze’s thought (for instance in his reevaluation of kantian schematism or in the distinction found in A Thousand Plateaus between royal science and minor science). Instead of analytic geometry going back to the initial, simpler figure at rest, Deleuze always promoted the real movement of non-metric multiplicities, where the synthesis is forced to compose consecutive principles. The aim of this paper is to demonstrate how this defense of descriptive and projective geometry, which science would like to turn into a mere practical dependency of analytic geometry, unveils an important issue in pedagogy and learning. Ultimately, it is argued that the axiomatic element should always be made dependent upon a problematic, ‘intuitionist’, or ‘constructivist’ current emphasizing a calculus of problems very different from axiomatics. Only on this condition will thought cease presupposing the answer as the simplicity of an essence, and will it reconnect the abstract movement of representative understanding with the real movement which traverses the conditions of the problem. Be it in science or philosophy, it is working on the limits that allows us to distinguish the singular from the ordinary, making us happy in our search for something new. These considerations on the role of experimentation in a science as abstract as geometry thus serve as the basis for unveiling the sensible, rhythmic origin of any learning. In that regard affects, concepts, and percepts are indeed the three inseparable forces in every scholarship.


Bibliographic reference |
Lebedev, Oleg. ‘Quod Erat Faciendum’: The Theorematic and the Problematic in Deleuze.Annual National Deleuze Conference (Enschede, du 17/05/2017 au 18/05/2017). |
Permanent URL |
http://hdl.handle.net/2078.1/184615 |