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BOOK REVIEWS 425 sense is concerned, mathematical logic distorts and hides the nature and role of the proper method or organon of philosophical knowledge; and, with its technical formal symbolism, simply obstructs the language of such reasoning. No important point in logic itself, or in any branch of philosophy , is illumined simply by being formulated in the symbolism of mathematical logic. And the major part of logic, logic considered on the part of matter, is necessarily a closed book to the formalism of mathematical logic. Philosophy and mathematical logic are not really made for each other; incompatibility would necessarily follow from their marriage. But it is quite otherwise with respect to the role mathematical logic plays in experimental science. It is the appropriate tool experimental science needs for its investigation of the quantitative and relational aspects of things. It is the calculus needed for the dialectical exploration of the experimental scientist. It is as such a calculus that mathematical logic really works and where its fruitful application is realized. Divorced from the role it plays for experimental science, mathematical logic seems to become merely a game of arbitrarily constructed systems of purely formal rules of procedure within the web of mathematical imagination. Such a formulation of what the excellence of mathematical logic consists in (as well as what it does not consist in) is certainly open to further investigation and consideration. In any case, it seems to me that both traditional and mathematical logicians would benefit seeing the proper excellence of each rather than trying to have one simply obliterated by the other. Of one thing, nevertheless, I am certain: serious traditional and mathematical logicians should read Professor Veatch's book for a thorough, conscientious, and able discussion of the relation and contrast between traditional and mathematical logic. It is a necessary step in achieving a balanced judgment and evaluation of both, the indispensable prerequisite for any fruitful discussion. JoHN A. OEsTERLE College of St. Thomas St. Paul, Minnesota Philosophic Problems of Nuclear Science. By WERNER HEISENBERG. Translated by F. C. Hayes. New York: Pantheon Books, 19M~. Pp. HW. $!il.75. This little volume contains eight lectures which were delivered at different places and times between the years 1934 and 1948. The message which it contains is noteworthy both because of the great authority of the author in the field of theoretical physics and because it is full, frank and informative statement of the historic aims of mathematical physics and a critical account of the present achievement of this science. 426 BOOK REVIEWS Although the so-called classical physics originated chiefly from the work of Galileo and Newton in the seventeenth century, the author of these lectures sees the whole development of modern physics as an effort to solve the problem first posed by the ancient Greek philosophers who asked: what are all things made of? Pythagoras was first to realize the mathematical order in musical notes, and Democritus said that all things are made of atoms. These are the terms of the historic problem and of its solution through mathematical physics. The ancient physicists were seeking a single material principle by which everything might be explained and understood in the clear light of mathematical formulation. Modern science has accepted from antiquity the idea of a pattern in the world which is capable of mathematical description . But we must not think that pure theoretical understanding is the only goal. Such an understanding is humanly unsatisfying, and seeks an outlet in technical applications. The mathematical formulation is itself an abstract control of things, and it enables man to make nature serve his own purposes. Furthermore, it gives a real insight into the interrelations of things, and will help man to appreciate his appropriate position in nature. Here in two words, understanding and control, we have the aims of this type of science. The understanding must be crystal clear, that is, mathematical in form. It must be a universal understanding, attaining to the principle of all things and revealing the real interrelations of things and man's position in the universe. Control also must in a sense be universal , that is, sufficient to enable man to make nature serve his own purpose...

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