**Alan Woods **and** Ted Grant, ***Reason in Revolt: Marxist Philosophy and Modern Science*, Wellred Publications, London, 1995, pp443

THE MOTTO of this book could be: ‘There is but one theory of everything, dialectical determinism is its name. Hegel, Marx and Engels are its Prophets.’ Those who have read *An Introduction to the Philosophy of Marxism* by RS Baghavan, published by Socialist Platform in 1987, will already be familiar with much of the approach. Indeed, many of the examples and quotations are the same.

Just as Christians argue that the wondrous complexities of nature testify to the hand of God, so our evangelists for the dialectics of nature point to developments in science to support their beliefs. Using science to argue that philosophy and logic reached their apogee in the nineteenth century with Hegel and Marx indicates an essentially religious frame of mind. Engels, living during the revolution in scientific thinking that occurred during the late nineteenth and early twentieth centuries, and already under the influence of Hegel and Marx, may have had some excuse for uncritical enthusiasm. But Marxist philosophers who wish to dabble in science at the end of the twentieth century should ask themselves: what, precisely, has the method of dialectical determinism contributed to the physical sciences? Not a lot — well, nothing really, though Grant and Woods suggest that physicists would have made even better progress and resolved some of their present difficulties if they had read Hegel and Engels!

The theories of relativity and quantum mechanics, seeming to fly in the face of common sense, caused a degree of philosophising even amongst the physicists. But it is important not to confuse the science with the philosophising. In the special theory of relativity two observers moving at different speeds will record different times on their stopwatches when timing the same jointly observed event. The authors are clearly unhappy with this, as they feel it can lead to subjectivism on the part of the observers in any philosophising they may do. They insist on another, objective, notion of time. Time, calculated according to the Lorentz transformation in relativity theory is clear enough, but to explain this ‘objective’ time of the materialist we get quotes from Engels. But just how do you measure it? Or feel the quality?

Heisenberg’s uncertainty principle in quantum mechanics states that the position and velocity of an electron are described by two interrelated probability density functions — the more certain you are of its position, the more uncertain you must be of its velocity. The authors argue that Heisenberg extrapolated from this to a subjectivist philosophy and to justify his Nazi sympathies. This should be a warning against silly philosophy, that the laws governing the motion of electrons can be borrowed to describe the development of political events. Our authors can only rather pathetically point out that others who also contributed to quantum mechanics didn’t share his extra-curricular views. Quite so.

The authors also take sides in the debate concerning the origins of the universe, if any — big bang, steady state, or what? Grant and Woods are very critical of the big bangers’ ‘singularity’, their inability to describe the situation that would have existed before the bang. But such singularities are not uncommon in physical theories. No matter how many measurements a hydrodynamicist may make of flow conditions downstream of a hydraulic jump, ask him to describe the conditions upstream of it by means of his flow equations and back analysis, and he will say: ‘Sorry, guv, don’t know much.’ But the authors will not let cosmologists pull that stunt — the holy grail of the theory of everything is at stake. They are also criticised for too much mathematical modelling. But exploratory satellites cost huge sums of money, and take a long time to circumnavigate the solar system. So why shouldn’t the big bangers play with their maths in the meantime? Differential equations, the opium of the technological classes? Mine is football.

Grant and Woods’ problems with singularities and the associated problem of the infinite also cause them to have a tilt at mathematicians and logicians. The calculus of Leibnitz and Newton led to errors because it was based on an intuitive concept of the infinite. It suffered from the paradoxes described by Zeno two millennia earlier. They ridicule those who dispensed with notions of infinity and argued from the basis of finite numbers, albeit very small or very big ones. But it was this approach pioneered by Cauchy (1789-1857) and Riemann (1826-1866) which succeeded in providing a rigorous theory of calculus, and made it such a potent tool in every branch of science and engineering. The authors’ partisan support for Hegel causes them to misrepresent and falsify the history of this subject.

Ironically, mathematics did develop a theory of transfinite numbers, and, contrary to the authors’ assertions, it is possible for such numbers to be countable, that is, denumerable, and ordered in size. Concepts of the infinite have developed since Hegel, but since he and Engels are prophets and already had the answers, Grant and Woods cannot be expected to pursue that subject. Transfinite numbers make an appearance in the subject of mathematical logic. The authors belittle Frege, Russell and Whitehead for their attempts to develop logic in this area. What they were trying to do in *Grundlagen der Arithmetik* and *Principia Mathematica* was to show that all mathematical knowledge can be developed from logic. Ultimately they failed, but they had begun an attempt in a field which was to yield important results. The authors cite Gödel whilst poking fun at Russell’s notation, but the devil is in the detail, and it was Gödel who demonstrated in his theorem proofs that applying rules to a given set of initial assumptions would not yield mathematics as a consistent body of knowledge. Apparently, there is no holy grail for mathematicians either, but investigations in this subject led to Turing’s ‘machine’, which provided the theory for reading the ‘Enigma’ codes and for compauter science. Strangely, amongst the 250 branches of science dealt with in this book, the latter is not included amongst them.

The history of science is a far more fascinating subject than this awful book would indicate. But its study requires integrity and honesty towards the subject matter. It cannot be chopped, tailed and stuffed into someone’s philosophic bean-bag, as has been done here.

To those who feel an urge to write an opus on the dialectics of nature, I would put before them the example of Barré St Venant. As a student at the École Polytechnique, he came under military command, and served as a sergeant of artillery. When called upon to fight for Napoleon in 1814, he stepped forward from the ranks and denounced Napoleon as a usurper. He was dismissed from the school as a deserter, but continued his scientific studies. He never published any books, but in his correspondence with and editorial work for others, he laid the foundations of the theory of elasticity. Today, when engineers design aeroplanes, machines and bridges, they call on knowledge first given real coherence by this great scientist. Apart from his courage, integrity and mastery of his subject, I would most strenuously recommend his reluctance to write a book.

**Bill Thompson**