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In paraconsistent logic, we have dialecticism. So is it possible to formalize the logic of Hegel, like Anton Friedrich Koch in "Hegel's on the logical big bang and the evolution of logical space", and formalize all the European philosophers' system, at least their arguments?

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    Can you clarify what you mean by "formalize all the European philosophers' system, at least their arguments?" – J D Nov 23 '19 at 15:04
  • Such as predicate logic,make use of philosophical logic,make a variation of classical logic like Relevance logic. – AnduinWilde Nov 23 '19 at 16:09
  • It is called dialetheism, but despite the superficial similarities it has little to do with Hegel's logic. Hegel conceived of Logic in a different old sense, as the conceptual movement in acquisition of knowledge, see What are the differences between philosophies presupposing one Logic versus many logics? It is closer to what is now called epistemology and is not formalizable as such. – Conifold Nov 24 '19 at 1:01
  • I suspect Hegel's logic may be formalised and thus considerably simplified, but I don't know of anyone who has attempted it. I would guess that it follows the structure required for non-dualism. This is not dialethism but is Aristotelian. It cannot be used to formalise the arguments of European philosophers. These are already either formal or not. . – PeterJ Nov 24 '19 at 13:02
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Hegel's logic has already been formalized by physicist and mathematician Urs Schreiber. However, there are likely only a few dozen people on earth who can understand it due to the formalization being done with cutting edge mathematical logic (such as homotopy type theory) and with a deep familiarity with the Science of Logic: https://ncatlab.org/nlab/show/Science+of+Logic

  • Welcome to SE Philosophy! Thanks for your contribution. Please take a quick moment to take the tour or find help. You can perform searches here or seek additional clarification at the meta site. – J D Dec 25 '19 at 17:39
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    I'm under the presumption that not many people people understand the Science of Logic. For example, there is only one book which comprehensively analyzes the last third of the logic, and not many people have read that book (Hegel's Theory of Judgement by Ioannis Trisokkas). Compare this to scholarship of other Hegel works. In general, scholarship on the Science of Logic is very limited. Out of those people with a thorough understanding, even fewer are familiar with mathematical logic, let alone homotopy type theory. – helloimhamid Dec 25 '19 at 20:34
  • My bad, I was only thinking about the math component. – Noah Schweber Dec 25 '19 at 23:58
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There is an attempt at formalization ( using algebraic concepts such as group, ring, etc) in Dubarle and Doz, Logique et dialectique.

A review here :

https://philpapers.org/rec/DUBLED-2

https://www.cambridge.org/core/journals/dialogue-canadian-philosophical-review-revue-canadienne-de-philosophie/article/logique-et-dialectique-par-d-dubarle-et-a-doz-collection-sciences-humaines-et-sociales-paris-larousse-1972-246-pages/8589D02F247FB6FEC4A84E1975CEC29B


In a humorous way, one could say that Hegel's Logic can be formalized as follows :

A = non-A = A & non-A

( Being is Nothingness/ Nothingness is being / Being and Nothingness are both Becoming, which, reciprocally, is both Being and Nothingness)

See : beginning of the Science of Logic.

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