Dialectics is a system of logic based on the idea that reality involves continuous change. All continuous change i.e. movement is fundamentally contradictory. If we take any body in motion, for example a falling ball, it is impossible to define its position exactly, because any such attempt involves trying to identify its position at a point in time. However, because time is continuous, there can be no such thing as a point in time, because however small we attempt to make this point, it will always have some duration – a beginning and end. Consequently, it will always be true that the ball will be at one position at the beginning of this time period, and somewhere else at the end.
The only point in time where this would not be the case would be one that had no duration, no dimension, a zero in time. But, in the real world there is no such thing as a zero of time. Time by its essence is continuous. Consequently, when we reduce reality down to these quantum levels we find that it is contradictory. We find that for any period or point of time, the ball is at two different positions.
This is at odds with Aristotelian Logic based on the syllogism, which insists that no such contradiction can exist. It is based on the fundamental proposition A = A, and consequently A does not = not A (-A). Trotsky in A Petit-Bourgeois Opposition In The Socialist Workers Party sets out what is wrong with this when he challenged the adoption of syllogistic logic by Burnham and Shachtman.
“I will here attempt to sketch the substance of the problem in a very concise form. The Aristotelian logic of the simple syllogism starts from the proposition that “A” is equal to “A.” This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalizations. But in reality “A” is not equal to “A.” This is easy to prove if we observe these two letters under a lens – they are quite different from each other. But, one can object, the question is not of the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar – a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is this true – all bodies change uninterruptedly in size, weight, color, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself “at any given moment.” Aside from the extremely dubious practical value of this “axiom,” it does not withstand theoretical criticism either. How should we really conceive the word “moment”? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that “moment” to inevitable changes. Or is the “moment” a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom “A” is equal to “A” signifies that a thing is equal to itself if it does not change, that is, if it does not exist...
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...
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.”
This contradiction can be seen in many different spheres. For example, a central postulate of geometry is based upon the tangent. A tangent touches the circumference of a circle at a point. At this point, therefore, the angle of the circle is equal to the angle of the tangent. But, the tangent is a straight line. Its angle is 180 degrees. So, how can the circle be equal to a straight line? Geometry avoids this contradiction, by theorising a point as a zero point, but a zero point in space is in reality as meaningless as a zero point in time. It can only exist in the world of ideas, as an abstraction, not in the real material world. Everything materially existing in space has dimension, just as much as everything existing in time. Indeed, thanks to Einstein we know that space and time are interchangeable as part of the space-time continuum.
The same contradiction can be seen in the fact that light can be both a wave and a particle. Quantum mechanics has demonstrated that at a quantum level the certainty required by syllogistic logic does not exist, and instead we have the Uncertainty Principle.
This may be true for time at a quantum level too. For example, we accept that the Arrow Of Time points only in one direction. However, it is possible that reduced to a quantum level, time's arrow too may be uncertain. It could move forward or backward with varying probabilities. Consequently, any concept of a point in time at this level would incorporate in itself, the basic idea of the dialectic that the present is itself a contradictory unity of the past and future, in the process of resolution of this contradiction, the resultant being forward motion.
Hegel based his dialectic on his Idealist philosophy. That is that the material world is merely a reflection of the world of ideas. The logical conclusion of Idealism is in fact Solipsism. If there is no such thing as the material world outside what the human mind creates, then that applies equally to every material thing including other human beings. Indeed that would extend to our own physical bodies. So we are left with a reality in which all that exists is our own mind!
Hegel believed that the Dialectic was the unfolding of The Idea, and its manifestation in the material world. The Idea (or God) established the rules, which could be uncovered. Philosopher Kings uncovered these rules, and in doing so the Idea was revealed. The Philosopher Kings (The Prussian State for Hegel) then applied these rules in the material world, so that the material world itself mirrored the unfolding of the idea. The unfolding of The Idea was itself a process of movement, and, therefore governed by the Dialectic.
Marx as a Materialist rejected this mysticism. He and Engels both recognised independently that the material world existed whether or not the human mind existed. Indeed, the human mind was a physical element, a material thing itself. But, both also recognised that it was the nature of this material reality that was itself contradictory, precisely because the nature of matter is that it exists in time, and is continuously, therefore, changing. Rather than it being The Idea, which is unfolding, and then being reflected in the material world, it is the other way around. Material reality is constantly changing, and this causes Men's Minds to change, their perception of that reality to change, and consequently their ideas to change.