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?
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.
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.
Within the realm of propositional calculus, there was an attempt to formalize Hegel's way of thinking by a four-valued logic called "directional logic" by a Polish logician L. Rogowski. Unfortunately, his two papers containing that idea were published in journals which no longer exist.
Regards, Maciej Janowicz
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.
Lenin said one must understand Hegel's Science of Logic to understand Marxism, but many doubt that he understood it at all. Kierkegaard admitted that he did not understand much of Hegel, but comforted himself that "neither did Hegel."
With a few exceptions, as noted by others, there is really very little overlap between modern logic and Hegel's system. In the the Kneale's 800-page tome "The Development of Logic," from Pythagoras to Godel, Hegel's name does not appear even once in the index.
I have a good companion book to "Phenomenology of Spirit" entitled "The Logic of Desire," and this is not a bad description of what Hegel is up to. He employs the thinking process we might call Logos, dialectic, or syllogism in a way that includes embodiment, purposes, desires, and, importantly, history. While formalisms like math or logic strive to be abstract, universal, and "timeless," Hegel sees "Logic" as a living teleological process that reflects on its own history. Ideas like "truth" or "justice" are thus historically contingent, yet undergo a continuous self-reflective development.
This process is true in the individual mind, in the development of philosophy as self-reflection, and in history itself. Because contradictions are both synthesized and preserved within the new synthesis "the identity of difference and identity" Hegel is far from the "either-or" distinctions employed in analytical logic. Distinctions collapse into one another in an evolutionary continuum. Generally, the murky, topsy-turvy development of his reasoning drives "logical" people crazy!
Definitely a slog. But Hegel is well worth studying and especially alongside Marx. As noted, the "Lesser Logic" is probably best, and some people think his early theological writings give you a good introduction to his dialectical "trinitarian" way of proceeding. "Phenomenology of Spirit," his most famous work, is supposed to be an introduction to his logic, but one can hardly call it "clarifying" or "introductory." While he was once totally excluded from the curriculum, he has returned to favor and there are many good companion books, including the famous lectures by Alexandre Kojeve that stirred up a Hegel revival.
