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Leonardo, Vol. 8, pp. 167-180. Pergamon Press 1975. Printed in Great Britain BOOKS Readers are invited to recommend books to be reviewed. Only books in English and in French can be reviewed at this stage. Those who would like to be added to Leonardo’s panel of reviewers should write to the Founder-Editor, indicating their particular interests. The Paradoxical Nature of Reality. George Melhuish. St. Vincent’s Press, Bristol, 1973. 196 pp. Reviewed by Eric Toms* From time to time in the development of thinking about the universe, a sudden startling halt has been called by the appearance of a serious paradox. In ancient times Zeno’s paradox of motion was the most troublesome. In recent times Kant’s famous ‘antinomies’ were posed. Kant used these contradictions to support his doctrine that knowledge of reality as a whole is impossible and that genuine knowledge is possible only in the sciences and mathematics . But following Russell’s discovery of the logical paradox of classes early in the present century, paradoxes descended in an avalanche and science and mathematics came under threat too. Mathematicians have been hard put to it to save face and have split into three schools according to the way in which they have tried to avert contradictions. The resulting impression is that through knowledge one is incapable of getting to the heart of things; knowledge is only a system of subjective concepts, useful for handling this or that particular subject matter. But the obvious conclusion surely is that human beings themselves have raised the question as to the impossibility of knowledge. The lesson of history seems to be that reality is paradoxical and, therefore, that, if the principles of thinking were remodelled to take account of paradox, knowledge of reality would no longer be put in doubt. Hegel, coming after Kant, went some way in this direction. Where Kant used contradiction negatively to criticize human knowledge, Hegel used it positively to characterize reality. George Melhuish wants to go further. He proposes that paradox is not only a positive feature of reality, to be finally allotted a subordinate place, but that it belongs to the heart of reality. In my opinion the first chapter of his book is by far the best argued and most substantial. In it he claims that in order to understand experience we need a conceptual system radically different from the traditionally accepted one. The traditional system is based upon the law of identity (any given subject matter is simply itself) and the law of non-contradiction (any given subject matter is not both present and absent). This system he calls the ‘tautological system’. Its effect is to define any subject matter of experience in a way that precludes any principle of change. The new system maintains laws opposite to these. He calls it the ‘non-tautological system’. It defines the ‘vehicle’ of a subject matter, by contrast with the subject matter itself. The vehicle embodies the coalescence of the presence and absence of the subject matter. Presence and absence are still, however, logically incompatible and the result is therefore a state of logical unrest, aptly called the ‘paradoxically energetic state’. In it is to be found the principle of change impossible within the tautological system. The latter system is not, however, discarded, for ~~ * 9 Campsie Drive, Milngavie, Glasgow G62 8HX, Scotland. 167 experience still requires a subject matter comprehensible only in terms of the traditional logical laws. The old laws are therefore retained alongside the new ones but subsidiary to them. This merely extends the paradox already admitted. Melhuish leads up to this general result in three stages. The first depends upon a consideration of Zeno’s paradox of motion. He considers in turn the traditional ways of solving it, showing that they are all involved in contradiction (see especially pp. 10, 13-16). The conclusion is that motion and change are of such a nature as to elude the tautological system. In the second stage of the argument he shows that an unchanging experience is unintelligible . It now follows that experience, like change, cannot be understood in terms of the tautological system. This brings us to the third stage and final...

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