The deficiencies of traditional logic have been grasped by other philosophers, who are very far from the dialectical standpoint. In general, in the Anglo-Saxon world, there has traditionally been a greater inclination towards empiricism, and inductive reasoning. Nevertheless, science still requires a philosophical framework that will enable it to assess its results and guide its steps through the confused mass of facts and statistics, like Ariadne’s thread in the labyrinth. Mere appeals to “common sense”, or the “facts”, will not suffice.

Syllogistic thinking, the abstract deductive method, is very much in the French tradition, especially since Descartes. The English tradition was altogether different, being heavily influenced by empiricism. From Britain, this school of thought was early on imported to the United States, where it sunk deep roots. Thus, the formal-deductive mode of thought was not at all characteristic of the Anglo-Saxon intellectual tradition. Trotsky wrote shortly before his assassination:

On the contrary, it is possible to say that this [school of] thought is distinguished by a sovereign-empirical contempt for the pure syllogism, which did not prevent the English from making colossal conquests in many spheres of scientific investigation. If one really thinks this through as one should, then it is impossible not to arrive at the conclusion that the empirical disregard for the syllogism is a primitive form of dialectical thinking.

Empiricism historically played both a progressive role (in the struggle against religion and mediaeval dogmatism) and a negative one (an excessively narrow interpretation of materialism, resistance to broad theoretical generalisations). Locke’s famous assertion that there is nothing in the intellect which is not derived from the senses contains the germ of a profoundly correct idea, but presented in a one-sided way, which could, and did, have the most harmful consequences on the future development of philosophy. In relation to this, Trotsky explained:

‘We do not know anything about the world except what is provided through experience.’ This is correct if one does not understand experience in the sense of the direct testimony of our individual five senses. If we reduce the matter to experience in the narrow empirical sense, then it is impossible for us to arrive at any judgment concerning either the origin of the species or, still less, the formation of the earth’s crust. To say that the basis for everything is experience is to say too much or to say nothing at all. Experience is the active interrelationship between subject and object. To analyse experience outside this category, i.e., outside the objective material milieu of the investigator who is counterpoised to it and who from another standpoint is a part of this milieu – to do this is to dissolve experience in a formless unity where there is neither object nor subject but only the mystical formula of experience. ‘Experiment’ or ‘experience’ of this kind is peculiar only to a baby in its mother’s womb, but unfortunately the baby is deprived of the opportunity to share the scientific conclusions of its experiment.[59]

The uncertainty principle of quantum mechanics cannot be applied to ordinary objects, but only to atoms and subatomic particles. Subatomic particles obey different laws to those of the “ordinary” world. They move at incredible speeds, close to the speed of light. They can move in different directions at the same time. Given this situation, the forms of thought which apply to everyday experience are no longer valid. Formal logic is useless. Its black and white, yes-or-no, take it or leave it categories have no point of contact with this fluid, unstable and contradictory reality. All we can do is to say that it is probably such and such a motion, with an infinite number of possibilities. Far from proceeding from the premises of formal logic, quantum mechanics violates the law of identity by asserting the “non-individuality” of individual particles. The law of identity cannot apply at this level, because the “identity” of individual particles cannot be fixed. Hence the lengthy controversy over “wave” or “particle”. It could not be both! Here “A” turns out to be “not-A”, and “A” can indeed be also “B”. Hence, the impossibility of “fixing” an electron’s position and velocity in the neat and absolute manner of formal logic. That is a serious problem for formal logic and “common sense”, but not for dialectics or for quantum mechanics. An electron has both the qualities of a wave and a particle, and this has been experimentally demonstrated.

In 1932, Werner Heisenberg (1901-76), a German physicist, suggested that the protons inside the nucleus were held together by something he called exchange force. This implied that protons and neutrons were constantly exchanging identity. Any given particle is in a constant state of flux, changing from a proton into a neutron and back again. Only in this way is the nucleus held together. Before a proton can be repelled by another proton, it changes into a neutron, and vice versa. This process in which particles are changed into their opposites takes place uninterruptedly, so that it is impossible to say at any given moment whether a particle is a proton or a neutron. In fact it is both – it is and is not.

The exchange of identities between electrons does not mean a simple change of position, but a complicated process where electron “A” interpenetrates with electron “B” to produce a “mix” of, say, 60 per cent “A” and 40 per cent “B” and vice versa. Later, they may have completely exchanged identities, with all “A” here and all “B” there. The flow would then be reversed in a permanent oscillation, involving a rhythmic interchange of the electrons’ identities, which goes on indefinitely. The old rigid, fixed Law of Identity vanishes altogether in this kind of pulsating identity-in-difference, which underlies all being, and received its scientific expression in Pauli’s principle of exclusion.

Thus, two and a half millennia later, Heraclitus’ principle “everything flows” turns out to be true – literally. Here we have, not only a state of unceasing change and motion, but also a process of universal interconnection, and the unity and interpenetration of opposites. Not only do electrons condition each other, but they actually pass into each other and become transformed into each other. How far removed from the static, unchanging idealist universe of Plato! How does one fix the position of an electron? By looking at it. And how to determine its momentum? By looking at it twice. But in that time, even in an infinitesimally small space of time, the electron has changed, and is no longer what it was. It is something else. It is both a particle (a “thing”, a “point”) and a wave (a “process”, movement, becoming). It is and is not. The old black and white method of formal logic used in classical mechanics cannot give results here because of the very nature of the phenomenon.

In 1963, it was suggested by Japanese physicists that the extremely small particle known as the neutrino changed its identity as it travelled through space at very high speeds. At one point it was an electron-neutrino, at another, a muon-neutrino, at another, a tauon-neutrino, and so on. If this is true, the law of identity, which has already been thoroughly battered, can be said to have received the final coup de grace. Such a rigid, black-and-white conception is clearly out of its depth when confronted with any one of the complex and contradictory phenomena of nature described by modern science.

  1. Trotsky, L Writings, 1939-40, pp. 401 and 403.