Deleuze’s theory of dialectical ideas: The influence of lautman and heidegger



In Diffйrence et rйpйtition, Deleuze’s overall ontology is structured by his theory of dialectical Ideas or problems. This theory draws features from Plato, Kant, and classical calculus. However, Deleuze bring those features together by fitting them into a theory of Ideas/problems developed by the mathematician and philosopher Albert Lautman. Lautman sought to explain the nature of the problems or dialectical Ideas with which mathematics engages and the solutions or mathematical theories which attempt to comprehend them. Lautman drew heavily upon Martin Heidegger’s early ontology to develop his theory of Ideas/problems. Although Deleuze seldom cited Heidegger, understanding how Lautman serves as a mediator between the two shows that certain elements in Heidegger’s ontology indirectly shaped Deleuze’s. This line of Heidegger’s influence has been largely unrecognized and unexplored in Deleuze scholarship. In this article the author seeks (1) to clarify Deleuze’s theory of dialectical Ideas or problems through an analysis of its debts to Lautman and Heidegger and (2) to demonstrate Heidegger’s crucial influence via Lautman on Deleuze’s ontology. In order to do this he focuses on five core claims that Deleuze’s theory of dialectical Ideas adopts from Lautman’s. The article provides an extensive reconstruction of what those claims mean in Lautman’s theory and discusses Lautman’s use of Heidegger to explain key parts of his position. The five core claims of Deleuze/Lautman that the author outlines are: (1) Ideas/problems are different in kind from solutions and do not disappear with solutions; (2) Ideas/problems are dialectical; (3) Ideas/problems are transcendent in relation to solutions; (4) Ideas/problems are simultaneously immanent in those solutions; (5) the relation between Ideas/problems and solutions is genetic, that is, solutions are generated on the basis of the determining conditions of Ideas/problems.

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