4. Formal Logic and Dialectics¶
Core Argument¶
This chapter argues that formal logic and dialectics are not eternal, divinely-given faculties but products of socio-historical development. Abstraction is indispensable to thought, yet formal logic’s abstractions are one-sided and static, adequate only for everyday, simple phenomena. They fail to capture movement, change, contradiction, or the transformation of quantity into quality. Dialectical thinking, by contrast, grasps the object as a living, contradictory whole, with all its interconnections. The syllogism, formal logic’s core device, is a triad of premises and conclusion where the conclusion is already contained in the premises; it concerns form, not content, and was rightly ridiculed by Kant and Hegel. Hegel subjected formal logic to thorough critique and developed a dynamic logic encompassing contradiction. Dialectics does not claim to teach people to think—as Hegel noted, logic no more teaches thinking than physiology teaches digestion. The process of cognition moves from concrete to abstract (analysis) and back to concrete (synthesis), combining analysis with synthesis, induction with deduction.
The first law of the dialectical method is absolute objectivity: laws of motion must be discovered by studying phenomena from every point of view, not by forcing facts into rigid preconceptions. Engels insisted categories must be derived from facts, not imposed upon them. Science generalises from experience, moving from particular to universal, with experiment as the sole judge of truth. Formal logic, unlike natural sciences, is not empirical but supposedly a priori, creating a contradiction between form and content. Kant argued logical forms must reflect objective reality, a position developed by Hegel and Marx: logical schemata relate to forms of thought, but these must be abstracted from the external world, not applied to it.
The basic laws of formal logic—identity, contradiction, excluded middle—have remained unchanged for over two thousand years. Trotsky argued the syllogism is an objective product of organic development, not an arbitrary convention. Formal logic is valid within limits, like Newtonian physics. However, the law of identity (“A” = “A”) is a tautology telling us nothing about concrete reality. Trotsky demonstrated that in reality “A” is never equal to “A”, as all bodies change uninterruptedly. The axiom holds only where quantitative changes are negligible; beyond certain limits, quantity changes into quality. Dialectical thinking relates to formal logic as a motion picture relates to a still photograph: it does not deny the syllogism but combines syllogisms to grasp eternally changing reality. Similarly, the law of the excluded middle breaks down when applied to organic beings, which are every moment the same and not the same.
Formal logic, rooted in a static view of reality, fails when applied to complex, changing, and contradictory phenomena. Only the dialectical method suffices for such turbulent processes. Empiricism, while progressive against dogma, is limited by its narrow interpretation of materialism. Trotsky argued that empirical disregard for the syllogism is a primitive form of dialectical thinking. Quantum mechanics violates formal logic’s law of identity, as subatomic particles exhibit non-individuality and contradictory properties, such as being both wave and particle. Heisenberg’s exchange force shows protons and neutrons constantly exchanging identity, being both what they are and are not. Modern symbolic logic, despite claims of innovation, merely rehashes Aristotelian principles—identity, non-contradiction, excluded middle—using symbols and jargon. It cannot handle the simplest judgment, which contains a contradiction (the particular is the universal). Formal logic has reached its limits; its axioms are tautologies valid only for simple, linear processes. For non-linear phenomena central to modern science, these laws break down.