Dialectical and Historical Materialism

Begin with Trotsky's argument that A is never actually equal to A.  There are subtle differences or "deviations" that prevent things from equaling each other, even themselves at a given moment in time, which in itself is infinitely divisible.  DM addresses the processes of matter that are undergoing change at all times.  "Dialectical thinking analyses all things and phenomena in their continuous change, while determining in the material conditions of those changes; that critical limit beyond which A ceases to be A; a workers' state ceases to be a workers' state."  Trotsky.  "Dialectical thinking is related to vulgar thinking in the same way that a motion picture is related to a still photograph. The motion picture does not outlaw the still photograph but combines a series of them according to the laws of motion. Dialectics does not deny the syllogism, but teaches us to combine syllogisms in such a way as to bring our understanding closer to the eternally changing reality."  Id.  "We call our dialectic materialist since its roots are neither in heaven nor in the depths of our "free will" but in objective reality, in nature. Consciousness grew out of the unconscious, psychology out of physiology, the organic world out of the inorganic, the solar system out of nebula."  Id.