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For dialecticism, we have paraconsistent logic. Is it possible to formalize the logic of Hegel, other European philosophers' systems, or 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
    Commented Nov 23, 2019 at 15:04
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    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
    Commented Nov 24, 2019 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. .
    – user20253
    Commented Nov 24, 2019 at 13:02
  • Hegel's logic is the continuation of Heraclitus whose maxim is we exist and exist-not, as clearly expressed in section 817 of his "Doctrine of Essence": The being of illusory being consists solely in the sublatedness of being, in its nothingness; this nothingness it has in essence and apart from its nothingness, apart from essence, illusory being is not. He added a concept of shine and developed to Notion as discussed in a recent post. Thus one formalization of his logic is simply Falsism... Commented Oct 13, 2022 at 23:31

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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

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  • 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
    Commented Dec 25, 2019 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. Commented Dec 25, 2019 at 20:34
  • My bad, I was only thinking about the math component. Commented Dec 25, 2019 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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No, Hegel's notion of logic is directly against formal logic (even contemporary paraconsistent logic).

For example, in §119 of his Shorter Logic, Hegel said that "6 miles to the west" and "6 miles to the east" are a pair of instances of "The Maxim of Excluded Middle", which is the maxim of the definite undestanding.

Hegel used the word "contradiction" in a variety of senses: difference, contrariety, and formal contradiction (P & ~P). In his account, the journey of concept, namely, is from difference to contrariety. And therefore it leads to "ground" (grund).

But surely the example above does not count as a formal contradiction, thus not an instance of The Maxim of Excluded Middle (in the sense of the law of excluded middle). And this cannot be said as a mistake of his time. Because Lebniz would definitely never make this kind of mistake, which reminds me of the remark in a letter from Gauss to H.C. Schumacher (1 November 1844):

That you believe a philosopher exprofesso to be free of confusion in concepts and definitions is something I find almost astonishing. Nowhere else are they more common than in philosophers who are not mathematicians, and Wolff was no mathematician, though he put together many compendiums. Just look around at the modern philosophers, at Schelling, Hegel, Nees von Esenbeck and consorts—don't their definitions make your hair stand on end? Read in the history of ancient philosophy what the men of the day, Plato and others (I except Aristotle), gave as explanations. And even in Kant matters are often not much better; his distinction between analytic and synthetic propositions seems to me to be either a triviality or false (Gauss 1863-1929, Vol. xii, pp. 62-3). (From Kant to Hilbert, p. 293.)

As for the treatment of Hegel to what he called "The Maxim of Excluded Middle", we can offer three interpretations to Hegel:

  1. He simply made a mistake.
  2. He targeted a strawman.
  3. He was making a speech act, or say "destruction", or "知其白 守其黑" in Chinese.
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  • As Devil's Advocate one could say that it is part of the method (harhar). Basically, truth realises itself through intuitive exploration in thinking and enaction in Hegel. Thus, any cementation of truth (like in logical laws) and lack of plasticity would go against the idea of his philosophy. It is why his logic is a methodology of becoming, not a system of propositions about how things are.
    – Philip Klöcking
    Commented Oct 13, 2022 at 8:17

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