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...
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...
ENERAL philosophy claims to be the critical subject which lays down for all of us what we may be allowed to think, and yet it has played no part whatever in the great revolutions of human thought of the present century-those connected with relativity and the quantum theory. It might have been expected that the scientists would have been constantly consulting the philosophers as to the legitimacy of their various speculations, but nothing of the kind has happened. Since no one can dispense with some sort of metaphysic, each scientist has made one for himself, and no doubt they contain many crudities, but it would seem that a deep interest in metaphysic is a disadvantage rather than an advantage to the physicist-at least I have the impression that those of my friends who are most inclined to speculate on the ultimate things appear to be the ones whose scientific work is most hampered by doing so. Now I propose to risk a similar indiscretion. I want to embody in it the practical philosophy of a physicist, and I do not mean it as an attack on the pure philosophers, who are very reasonable people, only chargeable with the minor offence of not having made me want to read their books! I had better begin by stating shortly the ideas I intend to discuss. There is a notable contrast between the way we think about things and the way we think we ought to think about them.
The relation between Physics and Philosophy brings to mind the proverbial marriage of high drama; the parties do not approve of each other, but separated they cannot live. Philosophers find physicists shallow, and many physicists claim that they find philosophic speculations useless or worse. Mostly both display a lack of knowledge and understanding of the methods and goals of the other. A few researchers have tried to bridge this gap and explore the worlds of both parties. Michael Redhead has worked in this borderland, and when he retired from his chair in Cambridge, a symposium was arranged to honour him. The talks presented on this occasion are now published in a volume presenting much food for thought to both philosophers and physicists. The essays in this publication do not offer easy reading; not too many readers will have the preparation to penetrate the technical arguments offered. The authors are well acquainted with both philosophical argumentation and mathematical formalism, and, following the lead of Professor Redhead, they combine these in intricate and suggestive ways. Only a close reading can offer understanding of the points of view taken by the various authors. Browsing and mere reading defines the scenery, exploring it demands much more. Many of the nine essays included investigate the meaning of terms used loosely in physics contexts: locality, beables, symmetries and time in relativity. All essays utilize the mathematical structures of physics, but the approach is mainly philosophical; concepts like reality and metaphysics are applied. Some writings are more physical in their treatment of technical questions relating to modern quantum theory. Bohmian mechanics, localized quantum states and gauge symmetries are discussed in detail. It is, however, found that these present interpretational problems that are usually glossed over in purely physical treatments. For an old sceptic like myself, it is quite refreshing to find that many assertions, taken for granted in our textbooks, are indeed doubtful and offer conceptual or technical difficulties. This insight is what a philosophical analysis can offer the working physicist; future progress may well arise from such realizations. However, the results offered by philosophical analysis are usually found unsatisfactory; the hope that philosophy can suggest novel directions for the theory remains unfounded. Philosophers can learn that modern physics rests on a very shaky conceptual foundation. The theory has evolved by a combination of serendipity and opportunism. The beast that finally has emerged is neither well founded nor internally consistent. Its only merit is that it works. That offers the ultimate philosophical problem of modern physics. If the present book can help the philosopher to behold this challenging but overwhelming wilderness, then it serves a useful purpose indeed. But the prospective researcher has to learn to master the difficult language used by the natives, who are not always friendly. I enjoyed reading the book immensely, but the technical difficulty of the text made my understanding remain mostly superficial. I hope to have the time to return some of the essays, and look into the references and issues involved. The work is genuinely what it promises: a guide From Physics to Philosophy .
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
is all about, and not bothering to familiarize themselves in specific detail with the vast accumulation of behavioral data upon which the conclusions ofpsychoanalysis are based. Though specialists in scientific method, they refuse to look through Galileo's telescope [p. 349]. Hospers examines with skill and calmness many of die totally illogical arguments used in this conference, permitting one to end the volume with a faintly restored faith that one day there will be "a free, critical interchange ofviews on die scientific status of psychoanalysis" between philosophers ofscience and psychoanalysts. Ifthere is any lesson to be drawn from this kind ofexhibition, it is that diere is no substitute for firsthand knowledge ofthe method and data ofa discipline as a prerequisite for any critical discussion ofits merit and validity. This may seem like an utterly banal dictum, yet the facts are that it is too often casually disregarded when it comes to the sciences ofhuman behavior. Any taxicab driver will freely volunteer opinions about reasons forjuvenile delinquency, sexual perversions, drug addiction, or dreams—but rarely about astral physics, genetics, or C14 dating. There is a good reason for this; all such matters touch one personally to varying degrees. But the philosopher (and, even more importandy, the physician) must be cautious not to confuse this personal interest and ¦ involvement with the scientific knowledge and detachment necessary for critical judgment . The latter come about only through long experience and diligent study. George L. Engel University ofRochester The Physicist's Conception ofNature. ByWerner Heisenberg.Translated from the German by ArnoldJ. Pomerans. New York: Harcourt, Brace & Co., 1958. Pp. 192. $3.75. This book, written by a famous German scientist, the founder ofquantum mechanics, die discoverer of die uncertainty relations, and die Nobel prize winner in physics for 1933, does not do much credit to die author. The first 67 pages comprise three chapters which apparendy represent an attempt to amalgamate the three speechesdelivered or three articles written on three different occasions at diree different times. It is difficult to date die first two chapters, but die diird one must have been written in 1948, since in it the author refers to a conversation which he had had "some diirty years ago" during die Communist revolt in Munich (1918). The first chapter of the book presents die idea of the three stages of die evolution ofhuman diought about the surrounding world. According to die author, during olden times (ofKepler, etc.) scientists saw die world as die work ofGod. During the nineteendi century die world was existing all for itself, independent ofman. Since the discovery of the uncertainty relations, die man looking at the surrounding world sees his own image in it. The second chapter represents a discussion ofuncertainty relations and contains several interesting ideas (for example, about past and future difference in die case ofvery short time intervals) which may be ofgreat interest to a person trained in die modern quantum theory but will pass unnoticed by a general reader. 158 Book Reviews Perspectives in Biology and Medicine · Autumn 1939 The third chapter discusses die relative advantages ofclassical (i.e., Greek grammar, etc.) and scientific education and presents arguments in favor ofdie former: "Thus, we may say in favour ofclassical education diat it is always a good diing to know the roots, even ifthey may not always be of practical use" (p. 52). However, by die end of the chapter (p. 67) die audior comes to die conclusion: "It does not matter whedier we prefer a classical or a scientific education. What alone matters is our unshakable faidi in the West." The remaining 115 pages ofthe text contain a masterful selection ofquotations from Kepler, Galileo, Newton, Oswald, De Broglie, and others which are supposed to illustrate die ideas ofdie author expressed in die first 67 pages. G. GAMOW University ofColorado The Autobiography of Charles Darwin, 1809-1882. Edited, with Appendix and notes, by his granddaughter Nora Barlow. New York: Harcourt, Brace & Co., 1959. Pp. 253. $4.50. Darwin's autobiography was written mainly in 1876, six years before his death, with additional material inserted during his last yean. When first published in 1887, as part ofthe Life and Letters ofCharles Darwin, edited by his son Francis, it...
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative
This talk is about quantum logic, and before we engage in the subject proper let me say how much I appreciate the invitation to deliver it that was extended to me by the Japanese Society for the Philosophy of Science.In particular because I feel that such a meeting is really the place that is most adequate for the discussion of these matters.Let us introduce the subject by mentioning a few general points.First of all, logics deals with propositions.Hence we shall be concerned with propositions.But in fact our interest will be exclusively focused on what is-or what should be the simplest type of propositions: the propositions by means of which a physicist expresses what he knows about a physical system.A priori, our subject should then be very simple.Indeed the elementary books about logic tell us that the rules concerning these propositions can be formalized.That, for example, the propositions can be combined by means of two rules, corresponding to and and to or, and that the resulting structure is just that of a Boolean Algebra.We would expect this to hold for any system.However, as you know, a major difficulty already creeps in at this point when we want to deal with atomic systems.This is because a very simple word such as "and" may well have no obvious meaning in that case.And when we try to force a meaning to it was sometimes encounter quite unpleasant surprises, exemplified by the Heisenberg relations.Among the founders of quantum physics the reactions to such a fact were quite varied as is well known.Some of them sort of hoped that the difficulty just came from our using the wrong concepts.For example, it is quite obvious that if we try to describe as a particle something which is really a wave, we are heading for trouble and we are bound to formulate some meaningless propositions.However, this remark did not lead to a satisfactory solution in the end.Other physicists notably the Copenhagen group took a very different standpoint.Substantially, what they said boiled to this: since we cannot "see" the elementary particles, let us refrain from formulating directly propositions bearing on them.Ultimately, there fore, all their propositions bear on the instruments; or should be interpreted in terms of such propositions.This is -it turned out a very good recipe.Of course, propositions bearing on instruments are propositions of classical, macroscopic physcis.As such, they fall -57-