George Novack on "negation of the negation"

From the glossary in George Novack's Polemics in Marxist Philosophy

negation of the negation - one of the basic laws of dialectics, flowing from the unity and struggle of opposites and the transformation of quantity into quality.  Every object or condition is characterized by internal contradiction between a positive and a negative pole - that which exists and that which is coming into being.  At the first dialectical leap, or negation, the old framework is broken, the previously subordinate quality or object in the relationship becomes dominant, and a new framework is established with a new set of internal contradictions.  In both Hegelian and Marxist dialectics, this rupture is referred to as transcendence, rather than mere empty negation of the previous status quo, because there is an element of continuity and development as well as destruction.  The concept of the negation of the negation traces this element of transcendence over a longer period of time.  It is the logical means of conceptualizing evolution over time, on the premise that natural and social processes are sufficiently determinate to show long-term cyclical patterns.  Common examples given include the life cycles of living species, where birth represents the breakup of the previous unity of the parent organism for the first negation, with the stage where the progeny reach reproductive age representing the second negation, or the negation of the negation.  In social evolution, a common example is the negation of primitive social property by the rise of private property and class society, followed by the eventual emergence of the proletariat, which moves toward the second stage, the negation of private property and the reestablishment of social property on a higher level, for a negation of the negation.  From these examples  it can be seen that Marx's concept is not purely cyclical but more like a spiral in which the conclusion of the complete process also involved evolution and progress toward a higher level of organic or organizational complexity, and not mere repetition.

from Polemics in Marxist Philosophy [Pathfinder, 1978] page 315.