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Hegel, the Other and the nature of his Logic

Hegel's endeavor in the Wissenschaft der Logik witnesses some different senses of what is meant with 'logic'. I was into the chapter on Dasein (chapter 2 of Lehre vom Sein) where he discusses something and its other in the context of presenting something as a double negation that increases determination and produces concreteness. Hegel offers a theory about negation as concrescence that draws from the Spinozist association between negation and determination. He also offers a route of thinking that expresses determinate negation as it follows thought from indeterminate being towards something - and towards the other through a determination. Further, he explores how the border (the limit, the distinction) between something and (its) other appears both when we focus on what is near to its negation. It is hence simultaneously a study on determinate negation, a study on how it is thought and how it moves around the focus of thought. It is, of course, a grand project that eludes formalization and contrasts with the usual way of doing formal logic. But logic has gone a large way since Hegel's time, and the formal study of explosion through contradiction is perhaps a crucial step. Hegel intends to study the negative and negation in different ways simultaneously. Formal logic can perhaps approach it by employing several systems at once - a universal or abstract logic approach will pull them together even if what binds them cannot be properly formal. Of course, the contemporary friction between Hegel's project and formal logic would have to deal with the issue of the limits of formalization; Hegel argued that thinking is somehow tied to the ingredients of natural languages - but this is so perhaps precisely because ordinary language enjoys a plasticity no formal system has yet achieved. But Reza Negarestani association of language, logic and computation could be a path in which the landscape could be changing.

In any case, Hegel assumes what I call substantivism. That is, the Other (or Grenze) is not really indexical, rather it can be described as symmetrical with a something it contrasts with. Asymmetry is thought thoroughly as provisional, and ultimate symmetry is the goal if the whole picture is somehow to be envisaged. This is like the fourth axiom in Euclid's system: once the ultimate system is thought through a assymmetrical, a different picture emerges from the beginning. I was wondering if there is a way to explore these alternatives in a manageable way - not necessarily through an axiomatic system. I believe there is a way to show that Hegel's Logik is also what inaugurates a genre that doesn't collapse in that of formal logic. If this is so, the structure of the genre could also provide a basis for a(n artificial) language that is neither ordinary nor formal.


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