Hegel’s dialectics "refers to the particular dialectical method of argument employed by the German philosopher, G.W.F. Hegel, which, like other “dialectical” methods, relies on a contradictory process between opposing sides. Whereas Plato’s “opposing sides” were people (Socrates and his interlocutors), however, what the “opposing sides” are in Hegel’s work depends on the subject matter he discusses. In his work on logic, for instance, the “opposing sides” are different definitions of logical concepts that are opposed to one another."
Hegel provides the most extensive, general account of his dialectical method in Part I of his Encyclopaedia of Philosophical Sciences, which is often called the Encyclopaedia Logic [EL]. The form or presentation of logic, he says, has three sides or moments (EL §79). These sides are not parts of logic, but, rather, moments of “every concept”, as well as “of everything true in general” (EL Remark to §79). The first moment—the moment of the understanding—is the moment of fixity, in which concepts or forms have a seemingly stable definition or determination (EL §80). The second moment—the “dialectical” (EL §§79, 81) or “negatively rational” (EL §79) moment—is the moment of instability. In this moment, a one-sidedness or restrictedness (EL Remark to §81) in the determination from the moment of understanding comes to the fore, and the determination that was fixed in the first moment passes into its opposite (EL §81). [...] The third moment—the “speculative” or “positively rational” (EL §§79, 82) moment—grasps the unity of the opposition between the first two determinations, or is the positive result of the dissolution or transition of those determinations (EL §82 and Remark to §82). Here, Hegel rejects the traditional, reductio ad absurdum argument, which says that when the premises of an argument lead to a contradiction, then the premises must be discarded altogether, leaving nothing.
See also the discussion of the “textbook example” regarding Being-Nothing-Becoming:
closely connected to the traditional idea that Hegel’s dialectics follows a thesis-antithesis-synthesis pattern, which, when applied to the logic, means that one concept is introduced as a “thesis” or positive concept, which then develops into a second concept that negates or is opposed to the first or is its “antithesis”, which in turn leads to a third concept, the “synthesis”, that unifies the first two [with ref to McTaggert]. On this reading, Being is the positive moment or thesis, Nothing is the negative moment or antithesis, and Becoming is the moment of aufheben or synthesis—the concept that cancels and preserves, or unifies and combines, Being and Nothing.
Hegel’s categorial triads [in the science of Logic] appear to repeat Kant’s own triadic way of articulating the categories in the Table of Categories (Critique of Pure Reason A80/B106) in which the third term in the triad in some way integrates the first two. (In Hegel’s terminology, he would say that the first two were sublated [aufgehoben] in the third—while the first two are negated by the third, they continue to work within the context defined by it.)
See Hegel on Science of Logic as well as Karin de Boer, Hegel's Account of Contradiction in the Science of Logic (2010).
Disclaim: I'm not an Hegel's scholar. For people like me, not versed into Idealism and trained with anlytic tradition, can be necessary trying to understand in what sense Hegel's Logic is a "logic".
I think that the comparison with Aristotle ("the deepest and also the most
comprehensive thinker of antiquity", Hegel's The Philosophy of History) is still useful.
For both thinkers logic is the ground of method and thus of knowledge (science). But while for Aristotle logic is formal, for Hegel a real understanding is impossibile without managing the opposition between form and content.
Compare Aristole: "Since a definition is said to be an account of what a thing is, it is evident that one type will be an account of what the name, or a different name-like account, signifies (Post.An.)" and:
"If what is signified by the name and by the account are not the same,
clearly the account given will not be a definition (Top)", with Hegel's Science of Logic (Preface to the 2nd edition): "Some [German] words possess the peculiarity of having not only different but opposite meanings so that one cannot fail to recognize a speculative spirit of the language in them".
With a catch-phrase: contradictions are in the language while oppositions are in the world.
See Ermanno Bencivenga, Hegel’s Dialectical Logic (Oxford University Press, 2000).
