"Dialectics, so-called objective dialectics, prevails throughout nature, and so-called subjective dialectics (dialectical thought), is only the reflection of the motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites and their final passage into one another, or into higher forms, determines the life of nature."
-- Freidrich Engels, Dialectics of Nature
The materialist dialectic is the theoretical foundation of Marxism from the writings Karl Marx and Friedrich Engels, and elaborated by lefty poster boys Plekhanov, Lenin, and Stalin. The exact term 'Dialectical Materialism' was coined by Karl Kautsky and popularised in the Second International after the death of Marx and Engels
Put simply, dialectical materialism is a combination of Hegel's theory of Dialectics, and materialism. The notion of dialectics expresses the view that development depends on the clash of contradictions and the creation of a new, more advanced synthesis from these clashes.
Materialism rejects idealist explanations of social and other phenomena and suggests that everything is material, rather than metaphysical.
Marx's use of this notion was generally limited to accounting for social and historical events. As Marx saw it, the " history of all hitherto existing society is the history of class struggles" - a clash of opposites based on material grounds.
Engels extended the scope of dialectical analysis as to establish it as a general law of development that applied equally in social, natural and intellectual spheres. He believed both that the real world, whether of society or nature, developed according to dialectical sequences of contradiction and synthesis, and that dialectical logic was the means by which one could comprehend any development.
Use of the principle of dialectical materialism in history and sociology is sometimes called historical materialism.
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