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I was told, a while ago now, that if I wanted to study Hegel, even Hegelian Marxism, I'd be best off studying his logic first.

Having recently asked this question I was wondering how do contemporary logicians formalize Hegelian logic using the terminology and symbolism of modern formal logic?

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    Do you mean, how do contemporary logicians feel, personally or otherwise, about Hegelian logic? Or do you mean, how do contemporary logicians formalize Hegelian logic using the terminology and symbolism of modern formal logic? Because, the phrase "How do logicians think about Hegel's logic" sounds like you're asking for people's general opinions on Hegel and his logic, but "Does it e.g. replace LNC (law of non-contradiction) with new assumptions?" sounds like you're asking a more technical question of how Hegelian logic is formalized, and both of those are different questions. – Not_Here Aug 25 '18 at 22:23
  • @Not_Here why not both? – user34654 Aug 25 '18 at 22:31
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    What logic can do this? Perhaps something can be done, there are so many flavors, I have no idea. But logic is often a snapshot, and the world moves, only the foolish cling to the given. The given is the bourgeois understanding. By the way, of the modern Marxists, Marcuse was far and away the best Hegel scholar. His attempted Dissertation under Heidegger was on Hegel. – Gordon Aug 26 '18 at 0:32
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    Aufheben en.m.wikipedia.org/wiki/Aufheben – Gordon Aug 26 '18 at 0:46
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    @user3293056. Okay, thanks, point taken. I have left my upvote because I still think you have put a good question. I have added to my answer. Perhaps the new material will help. Welcome to PSE btw - Best : Geoffrey – Geoffrey Thomas Aug 26 '18 at 12:52
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In a very compressed nutshell, modern logic is concerned with relations of implication, contradiction, independence and the like between propositions and predicates.

In contrast Hegel's logic operates not on propositions or predicates but on 'notions', Begriffe, or (roughly) concepts. On his account certain concepts are more adequate to the nature or expression of reality than others. The concept of determinate being, for example, is more adequate to, more informative about, reality than the mere concept of being; and being, distinguished as finite or infinite, is more adequate than merely determinate being.

He moves up through concepts - very many more than these - until he teaches absolute being, the whole of reality or the Absolute, than which no other concept can be more adequate to reality.

So Hegel is not doing badly something that later logicians are doing better; he is doing something different. This isn't to say that he does not use propositions or predicates to formulate his logic but his logic is not about them. Nor is it to say that his logic is without internal faults. Not all the rungs of Hegel's ladder are secure.

To stress the contrast from a different angle ...

What modern logicians are concerned to formalise are, to repeat, relations of implication, contradiction, independence and the like between propositions and predicates. Hegel's logic of concepts is off-beam from this concern, answerable as it is to the admittedly unusual idea of adequacy to reality - for which, moreover, Hegel has his own criteria. There is also the problem that it is hard to disentangle Hegel's logic of concepts from his metaphysics and epistemology. Unlike modern logicians, Hegel connected logic explicitly with metaphysics and epistemology. All three are interwoven in his philosophy. Or to change the metaphor, they make up a kind of triptych. We are apter to keep things separate. Moreover, the three comprise a philosophy of Absolute Idealism which, for good reasons and bad, is held by few philosophers nowadays and even fewer symbolic logicians.

If for this reason Hegel does not offer a logic which squares with modern logic, he also repudiates the traditional Aristotelian logic and its Scholastic outgrowths. Logicians who are sympathetic to this traditional logic find little of relevance to them in Hegel's logic. Hegel falls between two stools of ancient and modern.

You still want to read Hegel ?

Hegel's Encyclopaedia of the Philosophical Sciences covers logic, nature, and spirit ('mind') in a relatively accessible way - relative, that is, to his Science of Logic and Phenomenology of Spirit. You can pick up logic, metaphysics and epistemology from all three. The part on logic, usually called The Lesser Logic, is probably the most accessible if you're new to Hegel.


References

G.W.F. Hegel, The Encyclopaedia Logic, G. W. F. Hegel, T. F. Geraets (translator), W. A. Suchting (translator), H. S. Harris (translator). ISBN 10: 0872200701 / ISBN 13: 9780872200708 Published by Hackett Publishing Company 1991-10-15, Indianapolis, 1991.

Online :

https://rosswolfe.files.wordpress.com/2015/05/georg-wilhelm-friedrich-hegel-encyclopedia-logic.pdf

Justus Hartnack, An Introduction to Hegel's Logic (Hackett Classics Series). ISBN 10: 0872204243 / ISBN 13: 9780872204249 Published by Hackett Publishing Company, Inc.,1998.

  • 'no other concept can be more adequate to reality' why isn't this a "proposition" – user34654 Aug 26 '18 at 11:35
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    @user3293056 it isn't formal proposition, which is what I take out to be the main different between Hegel's Era of logic and contemporary logic. – Yechiam Weiss Aug 26 '18 at 17:46
  • Hi GT, I would love to ask though as a sort of minor follow up question, is the sort of interwoven logic-metaphysics-epistemology that Hegel (and, as far as I understand it, Kant and Decartes) use have any relevance to contemporary philosophy? – Yechiam Weiss Aug 26 '18 at 17:48
  • @Yechiam Weiss. Hello again ! I think it does but more in French & German philosophy than in the Anglo-American analytical tradition. Badieu, Ricoeur, and of course Heidegger. – Geoffrey Thomas Aug 26 '18 at 17:55
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    @YechiamWeiss Well, Girard, the creator of linear logic, claims that his formalism vindicates "Hegel's contradictory foundations", and that his colleagues misinterpret Hegel by taking his negation as alethic rather than game-theoretic. His semantic programme is called "transcendental syntax", and yes, Kant is his even greater inspiration. I have to say that analytic logicians are not at all innocent of mixing logic with metaphysics, take Lewis, Kripke or Williamson. – Conifold Aug 28 '18 at 5:36
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Hegel's logic lies almost completely in the part of logic that modern logicians no longer study -- how discovery and the evolution of ideas work as a process, rather than as a set of rules.

It has also been rolled up into systems that we wish to disown as science and which modern science has decided are unlikely to discover anything or evolve. Excluding the materialist offspring of Hegel's logic is what motivated Popper to try to define the boundary around the sciences. And the sciences themselves have largely accepted his demarcation criterion in the work they do to police themselves.

So you will seldom find modern logicians that engage this theory at all. Since the advent of the modern analytic approach in the 'linguistic turn' things like motivation and evolution of a train of thought, like dialectic, are not logic anymore. They are considered something closer to politics or rational psychology.

Rational psychology has been largely displaced by concerns about science, since modernism set in, and the philosophical discipline of politics has become sociology.

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    I wonder why this has been downvoted? Ideally it would have references but it's def accurate. – Canyon Aug 26 '18 at 0:46
  • I upvoted it. Russell himself led the charge against Hegel, and he had some fun with Hegel's logic. (Russell had studied Hegel early on and he was a "fan".). But Russell was also a socialist, according to his archivist, which is no surprise to me. Kenneth Blackwell, The Spinozistic Ethics of Bertrand Russell. – Gordon Aug 26 '18 at 0:57
  • What I am saying is that Rusell was perfectly capable of keeping another logic, like Hegel's "logic", in the background. – Gordon Aug 26 '18 at 1:15
  • Walter Kaufmann (Philosopher and Translator of Popper) on Popper's Hegel. marxists.org/reference/subject/philosophy/works/us/kaufmann.htm – Gordon Aug 26 '18 at 1:45
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    @ everyone freak out about a down vote, I down voted this answer for the same reason I always do when I do down vote an answer by jobermark, the answer contains no citations, there are a lot of conjectures which, even if they are true, are still conjectures with no appeal to any sort of argument, and because it's handwavy. "So you will seldom find modern logicians that engage this theory at all.", this is the perfect example. "You will seldom find", well, that means sometimes you will find it, and the OP asked for examples, so why phrase what you're saying this way? It's a lazy answer. – Not_Here Aug 26 '18 at 5:27
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I only know of one mathematician who engaged seriously with Hegel---William Lawvere, in, for instance, his paper on the unity of opposites in physics. I can't say if it's correct, because I don't understand nearly enough category theory, and, of course, I don't understand Hegel.

Lawvere's work has inspired at least one further attempt to model Hegel in category theory: this absolutely insane formalization of the Science of Logic. Again, I can't make too much of it, because I don't understand category theory. But since it starts at a more fundamental level it was possible to follow along at least a bit, and that bit seemed superficially correct.

And yet I don't recommend treating Hegel with the tools of modern logic. The above formalization seems to me to do incredible violence to Hegel's ideas. Some comments in the Lesser Logic, section 19, addition 2, shed light on his view:

Anybody can think, it is believed, without the study of logic, much as one can digest food without having studied physiology. And even if one has studied logic, one thinks just as one did before, perhaps more methodically, but otherwise with little difference, or so it seems. If logic had no other business than to familiarize us with the activity of merely formal thinking, then it would indeed produce nothing one would not have otherwise been doing just as well all along. The earlier logic was in fact reduced to this position.

Mathematical logic, it seems to me, can only ever "familiarize us with the activity of merely formal thinking". The truly essential philosophical elements are all already presupposed in the form of axioms and rules of inference. Hegel appears to want to change the way we think, not merely formalize it. So logic, as we conceive of it nowadays, has very little to do with Hegel's project. It's not surprising, then, that there's so little formal logical work on Hegel.

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