From A Notebook on Dialectics : Part Three [extra to text]
All mathematical equations are formalised statements of dialectical relations.
For example, take Newton’s Law, F = ma
This equation expresses an identity between distinct variables or a distinction between variables in their identity as represented by the ‘=’ sign.
Force is identified as the product of mass and acceleration. But mass and/or acceleration are not force. It is only in their relation that they constitute force. The fact that different variables (representing real entities) appear on opposite sides of the equal sign itself implies identification of distinct variables.
The very existence of the equation itself denotes the distinctions within the identity and articulates the dialectics of the relation but articulated in a formalised mathematical expression. If there were no distinction and opposition in the identity, there would be no need for the equation itself. Force is the product of mass and acceleration and yet it is more than simply this product.
To assert that Force is absolutely identical with the product of mass and acceleration is akin to asserting that the whole is absolutely identical to the sum and product of its component parts without the distinction in which the whole is also greater than the summation and product of its parts. In other words, for practical purposes, the equation is only a formal approximation which does not fully embrace the dialectics of the relation but, in spite of this, it does remain an approximated and formalised expression of the dialectics of the variables representing real entities.
The ‘formal logician’ sees all identity and no distinction or all distinction and no identity. He always misses the distinction within the identity and vice versa. In other words, the positivist, empiricist, pragmatist, etc, would deny this latter principle (call it “illogical” or “contradictory of logic”, etc) but the dialectician would acknowledge its existence in thought as an intrinsic part and expression of all forms of development and would recognise it expressed in the workings and equations of Physics and Mathematics. Christopher Zeeman’s and Rene Thom’s work on Catastrophe Theory, for example, is a demonstration of dialectics in higher mathematics as Darwin’s work was in Biology.
The equation presents an identification of different variables in a specific relationship with each other which reflects the real character of a relationship in Nature. Accordingly, even in the mathematical formulae of Physics, etc, the humble dialectic rears its ubiquitous head and haunts the enunciations of formal logic, regardless of its current forms or lineage. They cannot escape its universality. Hence, formal logic as a limiting case of dialectical logic. Every mathematical equation is a formalised statement of dialectics, however well disguised those relations may be within the formula itself.
Needless to say, if ‘formal logic’ is beginning, in today’s forms, Frege, Kripke, etc, to articulate the dialectics of the world, then it is in process of ceasing to be ‘formal’ and indeed becoming dialectical. This is the dialectics of the evolution of logic itself and an implicit recognition of the dialectical character of the cosmos. Why else would it be compelled to move in such a direction?
Moreover, relative to this, if we recognise dialectics as having a heuristic function then this, once again, is an implicit acknowledgement of this dialectical character of the cosmos. If we are using dialectics as a means of investigation and discovery then it would be absurd to use it if the world itself were not dialectical in its actual relations. It would be counter-productive as well as counter-intuitive, revealing an absence of insight. The empiricist protests and directs us to ‘evidence’ alone
Philosophically, if we proceeded on the basis of ‘evidence’ alone – which is the hallmark of the empiricist – the whole of the Marx’s project would not have come into being. One of the sources for Marx was, of course, the ’empirical’ but the source of Marx’s theory as a whole was not ‘evidence’ alone. But for the empiricist, ‘evidence’ is the gold standard of knowledge.
In the end, the whole question of dialectics is not as complex as some think. The dry, dense and impenetrable language and terminology of Hegel is a problem and ‘turn off’ for many. However, in the finality of the question, there are two fundamental bifurcations on the whole journey. One : either the cosmos (embracing Nature, Humanity, Mind) is in a constant state of development, of evolution, arising and vanishing determinations and negations or it is not. If you think it is not, you will tend to walk down the road of formalistics which, sooner or later, leads to political conservatism and/or reaction. Two : once we have accepted the proposition that the cosmos is in constant development we reach another fork in this road : either, (a) all this evolution, this life and vitality, is producing and produced by conflicts and contradictions i.e. the cosmos, including Man’s relations to it, is inherently dialectical without the need for gods, ghosts or ghouls. This is the first step onto the revolutionary road. Or (b) we fall into the loving embrace of the Heavenly Father and accept that the ultimate cause behind all this evolution is divine impulse and intervention. As with Newton the Unitarian. And as with Hegel the Theist, the high tide of historical development of Idealism. We then embrace the religious, theistic, call it what you like. This is the road to the monastery, to mysticism or to the theosophical seminary. Or for intellectuals and postmoderns who wish to throw the paper darts of philosophy at each other and egoistically pleasure and congratulate themselves on making a “hit”.
If you reject materialist dialectics, you also reject the philosophical basis of Marx’s theory. You may use all manner of subtlety, conceptual evasion and sophistry to reject it. All the back alleys, shortcuts, refuges and hiding places of the philosophical fugitive, Kantianism being the usual one. But there are others, of course. Including Hegel’s sophisticated form of transfigured theology. But by rejecting Marx’s materialism, you automatically reject Marx’s theory and the tradition which has arisen therefrom. No matter how “dialectical” and sophisticated you may appear to be in your elaboration of the “concept”, etc. You cannot reject the underlying method and then claim to be in accord with its results and findings. It is as simple as that. There is nothing ‘complex’ about it. You may reject materialist dialectics as a comprehensive outlook in one breath then refer to yourself as a “Marxist” in the next breath. Sorry. Logically impermissible. Cannot be a whitewasher and chimney sweep simultaneously. Sophistics. Useless for the coming revolution.