Dialectical Reasoning is a very interesting and neglected topic because of its association with Marxism and Communism. There are many good books on the topic however because there has been a kind of fascination with it as the only alternative to Analytical Philosophy. Continental Philosophy takes for granted Dialectical processes because most of the french philosophers of note were all Marxists of one kind or another. An excellent book is Critique of Dialectical Reason by Sartre which tries to make Dialectics itself Dialectical instead of mechanical as most Marxist treatments tend to be. Fredrick Jameson has recently written a reappraisal of Dialectics in the wake of Post-modern philosophy trying to salvage the idea. Biut what you should know is that Kant assumes that Synthesis happens a priori and thus is hidden from us. Besides making reasoning dynamic, and putting it in history, Hegel is also making synthesis a visible process, that is made explicit in his Logic.
Quora answer: How would one explain dialectical reasoning in layman’s terms?
I have read a lot of books on Dialectics over the years, basically every one I could get my hands on. But something I found when I finally got through Phenomenology of Spirit is that in that book Hegel defines not just Dialectics but Trialectics as well. It comes up when he treats the nature of work, just before the transition into Spirit. He first defines work as Circumstance, Purpose and Means. This is not thesis, anti-thesis and synthesis. Rather we have context, goal, and the way to realize the goal given the situation. The means mediates between circumstance and goal. There is a third element in the equation as an active mediating element. We can see this third element as circumstance mediating means and ends. Or we can see goals mediating beween circumstances and means. But all three of these elements give rise to the synthesis of work performed. Once you realize that there are trialectics possible this puts dialectics in a different light, and suggests there might be quadralectics and pentalictics which I develop in my dissertation to explain Emergent Design.
Mediation does not just mean that thesis and anti-thesis are absorbed in the aufhebung (uplifting) into a greater synthesis, but we can actually experience the mediation as a third element that relativizes all three theses that become part of the higher order synthesis by which work produces its product.
The simple answer then is that there is a series of multi-lectics starting with monolectics (dogmatism) and leading to more and more complex synthese. Dialectics is the second stage which through aufhebung (uplifting) produces the synthesis that allows both thesis and synthesis to be absorbed in a higher unity despite their diversity and conflict or dynamic at the lower level before the synthesis is realized. But it is also possible to have active mediation in which case you get a trinity of elements (called a triality in mathematics) in three way complementarity. Arkady talks about this as a possibility in his work Complementarities.
Understanding that dialectics is in a series I think demystifies the subject, because it says that there is a whole family of these X-lectics which more or less develop in the kind of progression that we have seen with numbers etc. Why this has not been noted before in any work I have seen on Dialectics, I assume that is because of the mechanistic interpretation of Dialectics by Marxism.