Immanent critique, also called dialectic or dialectics, is a mode of philosophical argumentation that grasps each thought as an incomplete moment in a further unfolding of truth. Contrary to what we're used to in logic, its aim is not to ascribe fixed truth values to propositions, but instead to understand the way in which these propositions and their implied structures of understanding aim to make sense of the world. As Engels puts it, it "comprehends things and their representations, ideas, in their essential connection, concatenation, motion, origin and ending."
Dialectical method is characterized by the prevalence of contradiction, something which formal logic usually tries to avoid. Contradicting ideas or aspects of things are juxtaposed and allowed to interact with each other to develop a deeper sense of them. This may happen in various ways. Views may get abandoned and replaced with more sophisticated ones, or they may be revealed to actually be compatible with each other. Most interesting, however, is when we discover that the contradiction constitutes a gap inherent to the subject at hand. One that we cannot simply skip over, but that has to be integrated in the way we think about the subject. We may also find that two opposite concepts naturally necessitate each other, which is resolved by a move Hegel called sublation.
Thus dialectics attempts to involve in every thought an apprehension of its own failure. In Hegel's words, dialectics combines "in our process of inquiry the action of the forms of thought with a criticism of them." Since the critique is itself a thought, it cannot stand apart from the object of inquiry. This means the modes of thought "are at once the object of research and the action of that object." This aspect is referred to as immanent critique.
Modern dialectics was first developed by Hegel, and then adapted to materialism by Marx and Engels.
The Prehistory of Dialectics
The most ancient dialectical method can arguably be found in Plato's dialogues. In these texts, Plato places his teacher Socrates in a debate on some philosophical issue, often as a mouthpiece for Plato's own positions. Characteristic for these dialogues is the use of Socratic irony. Instead of claiming to know the truth, Socrates claims ignorance and asks the other to explain their position. This position is then examined and inevitably loses its credibility, often by leading to some contradiction with the interlocutor's opinions. This reduction of a premise to a falsehood in order to disprove it is called reductio ad absurdum. The position is then revised, or some other person comes in with an alternative, and Socrates again subjects it to his line of questioning. Paradoxically, Socrates turns out to be the wiser because only he understands how limited his understanding is.
In most dialogues, Socrates will end up constructing his own (or rather Plato's) opinion on the matter. This process of repeated questioning leading to the refinement of the understanding (or the admission that it is flawed) is referred to as the Socratic method, and is a primitive instance of dialectical reasoning. When it simply has the aim of discovering ignorance, the Socratic method is called elenchus. This process aims at aporia, a state of philosophically useful puzzlement.
Hegel discusses the Socratic method in his lectures on the History of Philosophy. 
In medieval Europe, dialectic returns to play a prominent role in the Scholastic school of philosophy,
For Immanuel Kant, "dialectic" was a false way of thinking, whose purpose consisted only in demonstrating the limits of reason itself. He uses the term to refer to "in general a logic of appearance." Nevertheless "there is [...] a natural and unavoidable dialectic of pure reason – [...] that which is an inseparable adjunct of human reason, and which, even after its illusions have been exposed, does not cease to deceive, and continually to lead reason into momentary errors, which it becomes necessary continually to remove." As such, the dialectic has to be studied carefully, which Kant does in the second division of the "transcendental logic" in his Critique of Pure Reason, named the "transcendental dialectic."
[On transcendental ideas]
[On the antinomies]
Idealist (or Hegelian) Dialectics
Marx's dialectical method
The Marxist dialectic, Marx’s Dialectical method or immanent critique, is a sustained inquiry into a subject matter, using its own internal logic, and by locating the internal contradictions, the origins of said internal contradictions become revealed, as well their fate, I.E. how they might be resolved and lead to a transformation of the subject matter.
Any internal contradiction exists as a unity of two opposites, that is, one opposite necessitates the other. Each one of these poles revealed within a contradiction must ungergo self-sublation (sublation is a translation of the technical German word aufheben, which means both to cancel and to preserve something) and pass into its negation, the opposite pole. The opposite pole contains the original pole in its definition, hence preservation and the cycle continues.
The negation of the negation
In order to break this cycle, the poles must be grasped as a whole and to criticise the unity of these two opposites, causing the unity of two opposites in its one-sideness to self-sublate again. This generates a new subject matter that both preserves and cancels out the original matter itself, but in fact is a subject which contains within its definition the original concept and its negation. This method starts with the simpler ideas and eventually leads to more complex ones, which within them, still contain the simpler ideas. The unity discovered from the negation of the negation are not the dialectic themselves, but simply the result of the dialectical method. For examples of these results, see the path of argument used in Capital Vol. I.
"Not only has a state of general anarchy set in among the reformers, but everyone will have to admit to himself that he has no exact idea what the future ought to be. On the other hand, it is precisely the advantage of the new trend that we do not dogmatically anticipate the world, but only want to find the new world through criticism of the old one. Hitherto philosophers have had the solution of all riddles lying in their writing-desks, and the stupid, exoteric world had only to open its mouth for the roast pigeons of absolute knowledge to fly into it. Now philosophy has become mundane, and the most striking proof of this is that philosophical consciousness itself has been drawn into the torment of the struggle, not only externally but also internally. But, if constructing the future and settling everything for all times are not our affair, it is all the more clear what we have to accomplish at present: I am referring to ruthless criticism of all that exists, ruthless both in the sense of not being afraid of the results it arrives at and in the sense of being just as little afraid of conflict with the powers that be." 
Under the umbrella of "dialectical materialism" are subsumed a number of efforts at systematising Marx's dialectical method into a science.
Engels' materialist dialectic
Engels defines dialectics as the systematic inquiry into universal interconnections of all processes in nature:
“It is precisely dialectics that constitutes the most important form of thinking for present-day natural science, for it alone offers the analogue for, and thereby the method of explaining, the evolutionary processes occurring in nature, inter-connections in general, and transitions from one field of investigation to another.”[old preface to Anti-Duhring: On Dialectics]
This worldview of universal interconnection is in staunch contrast with reductionism and metaphysics which holds an alienated worldview that ignores interconnection and thus considers objects to be isolated until proven otherwise. Engels points out the artificial character of the distinction men have drawn between not merely between 'organic and inorganic', vertebrates and invertebrates, liquids, and gases, but also between different fields of human knowledge such as economics, history, and natural science. [dialectics of nature: preface by JBS Haldane] The ignoring of interconnections, especially across disciplinary boundaries has been the main source of error in complex fields of applied biology such as public health, epidemiology, embryology, epigenetics, agriculture, environmental protection (see climate change) and resource management and cause the stagnation of theory in these areas.
Laws of dialectics:
The laws of dialectics are abstracted from the history of nature and human society. These laws are nothing but the most general laws of these two aspects of historical development. Engels reduces this statement to three general laws:
- The law of transformation of quantity into quality and vice versa
- The law of the interpenetration of opposites
- The law of the negation of the negation [Aufhebung, sublimation]
Since these laws are really laws of development of nature, they are also valid for theoretical natural sciences and as well to thought itself. The mistake of Hegel was that he considered these laws as deriving from mind laws and projected them onto nature and history, instead of deducing these laws from historical development of nature.
More Recent Developments
Dialectics in the USSR
Adorno's Negative Dialectic
Attempts at Formalization
- ↑ Engels, Socialism: Utopian and Scientific Part 2 §10 (on MIA)
- ↑ 2.0 2.1 Hegel, Shorter Logic IV 2 §41 n1 (on MIA)
- ↑ Phaidros, 276e
- ↑ Hegel, HoP Part I. 1st Per. 2nd Div. B. 1. (on MIA)
- ↑ Immanuel Kant, Critique of Pure Reason, "Transcendental Dialectic", translation by J. M. D. Meiklejohn (On MIA)
- ↑ Karl Marx, 1843 Letter to Arnold Ruge (on MIA)