Scottish Philosophy and British Physics, 1740-1870: A Study in the Foundations of the Victorian Scientific Style 9781400872497

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Scottish Philosophy and British Physics 1750-1880

Scottish Philosophy and British Physics 1750-1880

A Study in the Foundations of the Victorian Scientific Style

Richard Olson

Princeton, New Jersey Princeton University Press

Copyright © 1975 by Princeton University Press Published by Princeton University Press, Princeton and London All Rights Reserved Library of Congress Cataloging in Publication data will be found on the last printed page of this book Publication of this book has been aided by a grant from The Andrew W. Mellon Foundation This book has been composed in VIP Caledonia Printed in the United States of America by Princeton University Press, Princeton, New Jersey

ACKNOWLEDGMENTS

T H I S WORK grew out of a biographical dissertation on John Leslie done under the guidance of I. Bernard Cohen of Harvard University, to whom I am deeply indebted. The critical advice of Robert E. Schofield of Case Western Reserve encouraged me to undertake a vastly expanded study of Common Sense science. And conversations and/or correspondence with Geoffrey Cantor of the Uni­ versity of Leeds, Tom Cook of North Carolina University at Charlotte, Ed Morse of California State University at Sonoma, and Roger Hahn and John Heilbron of the Uni­ versity of California at Berkeley have provided me with continual support by helping me focus on new questions and recognize n e w sources of information. Travel, microfilming, and other reproduction expenses have been generously provided for through the course of several years by faculty research grants from the Univer­ sity of California at Santa Cruz, and a National Endow­ ment for the Humanities Younger Humanist Fellowship provided me with the time to complete work on a first draft of this manuscript. T h e stenographic services of Crown College at the University of California at Santa Cruz have provided clerical support throughout the proj­ ect. My work in Great Britain was facilitated by the active interest and encouragement of Mr. Alexander Leslie and Professor Charles Waterston and by the librarians at The National Library of Scotland, T h e British Museum, The Royal Society of London, University College, London, and the Universities of Edinburgh, St. Andrews, Glasgow, Aberdeen, Cambridge, and Oxford. Special thanks go to The Royal Society of London, T h e National Library of Scotland, St. Andrews University, and Edinburgh Uni­ versity for permission to cite from documents in their possession. ν

ACKNOWLEDGMENTS

I have discussed some of the concerns in this book elsewhere in different form, and I am indebted to the History of Science Society and the publishers of Journal of the History of Ideas, The American Journal of Physics, and Annals of Science for permission to reprint small portions from "The Reception of Boscovich's Ideas in Scotland," Isis, 60(1969):91-103; "Sir John Leslie and the Laws of Electrical Conduction in Solids," American Journal of Physics, 37 (1969):190-194; "Count Rumford, Sir John Leslie, and the Study of the Nature and Propaga­ tion of Heat at the Beginning of the Nineteenth Century," Annals of Science, 26 (1970):273-304; and "Scottish Philosophy and Mathematics: 1750-1830,"Journal of the History of Ideas, 32 (1971):29-44. Finally, I am indebted to my wife, Kathleen, and to Ms. Jacqueline Barnhart for editorial help and criticisms. Santa Cruz, California January, 1974

CONTENTS

Acknowledgments Prologue

ν 3

PART I: T H E G R O W T H O F A C O M M O N S E N S E PHILOSOPHY O F S C I E N C E

Chapter 1: T h e Integration of Moral Philosophy and Natural Philosophy in Scottish Academia Chapter 2: The Origins of Common Sense Philosophical Concern with the Nature of Science: Bacon and New­ ton Revisited in the Light of Hume Chapter 3: Common Sense Concerns with the Nature of Mathematics Chapter 4: A Change in Mood: Dugald Stewart, Thomas Brown, and the Acceptance of Hypothetical and Analogical Methods in Science Chapter 5: Thomas Brown and William Hamilton: T h e Relativity of Scientific Knowledge and the Triumph of Simplicity a n d Analogy

11

26 55

94

125

PART II: T H E I N F L U E N C E O F C O M M O N S E N S E IDEAS ON T H E EXACT S C I E N C E S IN BRITAIN

Chapter 6: Common Sense Reflections in the Natural Philosophy of John Robison and John Playfair Chapter 7: Common Sense Elements in Scientific Re­ views: 1790-1840 Chapter 8: John Leslie and Henry Brougham: Model Common Sense Scientists of the First Generation Chapter 9: Common Sense Concerns Once Removed: James D. Forbes and John James Waterston Chapter 10: Sir John Herschel's Preliminary Discourse on the Study of Natural Philosophy and the Common Sense Tradition Chapter 11: T h e Methodological Writings of William John Macquorn Rankine Chapter 12: Culmination of the Tradition: Metaphysics and Method in the Works of James Clerk Maxwell Epilogue Index VIl

157 169 194 225

252 271 287 323 337

Scottish Philosophy and British Physics 1750-1880

PROLOGUE

SlNCE the publication of Pierre Duhem's La Theorie

Physique: Son Objet, Sa Structure in 1906, historians and philosophers of science have been intrigued by the im­ pact of disparate cultural styles on the study of the exact sciences during the nineteenth century. Duhem claimed that throughout the century Continental scientists em­ phasized analytic mathematical techniques and abstract, extremely general theories, whereas British scientists were more inclined toward geometrical—or at least pic­ torial—imagery and techniques, and that they were more willing to use models and analogies with limited ranges of applicability. 1 The present study was motivated by Duhem's contentions and by the suggestions of George Elder Davie (The Democratic Intellect: Scotland and Her Universities in the 19th Century, Edinburgh, 2nd ed., 1964) that Scottish scientists and mathematicians, at least, were strongly influenced by the epistemological and pedagogical teachings of their academic colleagues in Moral Philosophy. Its aim is to investigate the extent to which Duhem's delineation of British Science might be accounted for through an understanding of the interac­ tions between the British scientific tradition and the Scot­ tish Philosophy of Common Sense as taught by Thomas Reid and Dugald Stewart and modified by Thomas Brown and Sir William Hamilton. 1 Pierre Duhem, TheAim and Structure of Physical Theory, translated from the 2nd (1914) French edition by Philip P. Wiener (New York; Atheneum Press, 1962, from Princeton University Press edition of 1954), ch. 4, "Abstract Theories and Mechanical Models," pp. 55-104. Duhem's arguments respecting the character of Victorian British physics have been reinforced by Robert Kargon in "Model and Analogy in Victorian science: Maxwell's Critique ofthe French Physicists,"Journal of the History of Ideas, 30 (1969), pp. 423—436, and more recently in David B. Wilson, "The Thought of Late Victorian Physicists: Oliver Lodge's Ethereal Body," Victorian Studies, 15 (1971), pp. 29-48.

PROLOGUE

When we isolate those British scientists of the midnineteenth century who seem most clearly to exemplify Duhem's stereotype—James Clerk Maxwell, William M. Rankine, J J . Waterston, Lord Kelvin, etc.—it becomes clear that a very large percentage were Scots who obtained their early training in the Scottish university system. Furthermore, almost all these men devoted significant effort to explicit discussions of their scientific methodology; and their discussions mirror very closely the writings of the Scottish Common Sense philosophers, Dugald Stewart, Thomas Brown, and Sir William Hamilton. These Scottish philosophers were particularly concerned with analyzing and emphasizing the roles played by analogies and models in the creation of scientific theories. While they consciously emphasized the heuristic value of models, they dissociated the models and the theories arising from them from any ontological content. In addition, they stressed the value of visualizable, geometrical mathematical approaches. Thus, it is clear that the characteristics of nineteenth-century British physics were at least consonant with the principles of Common Sense Philosophy in their major concern with heuristic models and in the tendency to use geometrical arguments in spite of the acknowledged efficiency of analytic mathematical techniques. A close investigation of (1) the philosophy of science derivable from the tradition of Common Sense philosophers, (2) the line of possible transmission of the ideas of the eighteenth-century moral philosophers to the nineteenth-century scientists, and (3) both the explicit methodological statements and the implicit methodology actually used by several important British natural philosophers tends to establish that the relationships between Scottish philosophy and British physics were more than coincidental. Such an investigation also accounts for certain characteristcs of British physics—like the bitter early rejection of the wave theory of light among some 4

PROLOGUE

British scientists—which were not emphasized by Duhem; and it points to the need for modifications in the Duhem-Poincare interpretation of British scientific style. In particular, it shows that underneath the surface appear­ ance of a naive use of mutually contradictory models lay a sophisticated drive toward extremely abstract and general theories, especially by Scottish theoreticians. A detailed look at the interaction between Scottish metaphysics and epistemology and the exact sciences in Britain, moreover, raises interesting questions about the relative importance of other philosophical traditions —particularly of the German Idealist tradition devolving from Immanuel Kant, which has been emphasized by L. Pearce Williams. 2 The Scottish tradition placed great em­ phasis on the key roles of imagination and conceptualiza­ tion in the development of scientific theory, on the drive for simplicity and the reduction of the number of funda­ mental elements involved in theory construction, and on the encouragement of conceptual developments which led to the adoption of field theories. All of these develop­ ments have been attributed principally to Kantian influ­ ences on British physics and must be reassessed in light of an independent native philosophical tradition. Perhaps most importantly, the interactions between philosophy and science which are examined raise a more general question about the relation of epistemology and methodology to each other and to any attempt to come to grips with "physical reality." Because there has been no satisfactory investigation of the philosophy of science as expounded by Common Sense philosophers I have had to precede my discussion of the interaction between Common Sense methodology and the exact sciences with a discussion of the Scottish methodological tradition within academic philosophy; thus this study falls into two fairly distinct parts. In Parti, I have attempted to discuss the close intellectual connec2 See, for example, L. Pearce Williams, Michael Faraday, New York; Basic Books, 1965, especially chs. 2, 9.

PROLOGUE

tions between natural philosophy, mathematics, and moral philosophy in the Scottish academic setting and to analyze the historical development of a Common Sense philosophy of science from the naive Baconianism of Os­ wald and Beattie in the 1750's to the highly critical sophis­ ticated notions of Stewart and Hamilton in the early nineteenth century. Part II then deals with the adoption of elements from this philosophical tradition by members of the scientific community. In Part II, after a short discussion of Common Sense elements in the works of two eighteenth-century scien­ tists, John Playfair and John Robison, I deal extensively with the work of a group of Scottish scientists of the early nineteenth century whose attitudes toward the exact sci­ ences were directly influenced by their contacts with Common Sense Philosophy—Henry Brougham, David Brewster, John Leslie, James David Forbes, and J. J. Waterston. I show how Common Sense considerations influenced their concern with hypotheses and analogies, their emphasis on geometrical mathematics, their at­ titudes toward subtle fluids and the luminiferous ether, and their tendency to embrace Boscovichian point atom­ ism, and later, the quite different substantial atomism associated with John Dalton. Next, I analyze the Common Sense elements in the methodological writings ofSir John Herschel, one of the most influential English scientist philosophers of the early nineteenth century. And finally, I deal with two later nineteenth-century Scottish scien­ tists, James Clerk Maxwell and William Macquorn Rankine, who carried important philosophical precepts de­ rived from the Scottish tradition into the main stream of British physics. In particular, I deal with their insistence upon the value of physical analogies and their lingering tendency to value visualizable, geometrical arguments in spite of their expertise in analysis. There are two significant and intentional limitations to this study. The first has to do with the absence of any analysis of the ideas of William Thomson (Lord Kelvin).

PROLOGUE

Duhem clearly saw Kelvin as the exemplar of Victorian scientific style. Kelvin was a Scot and an extremely impor­ tant Victorian scientist; moreover, his methodological ideas almost certainly owe a substantial amount to Com­ mon Sense considerations. Thus it may seem odd or per­ verse that he is ignored in what follows. Kelvin stands apart from all figures dealt with in this study (except Herschel) in that he was not associated with the Univer­ sity of Edinburgh nor did he have direct personal contact with any of the major Common Sense philosophers early in his career. The men I deal with formed a closely inter­ connected set from which Kelvin was excluded geo­ graphically and socially (except through correspondence and occasional meetings). Furthermore, to the extent that Kelvin was explicit or self-conscious about his method­ ological commitments, they come most directly from the French proto-positivist, Joseph Fourier or from John Herschel, rather than from his Scottish colleagues. In Herschel's case I argue for a close connection with Com­ mon Sense Philosophy, and in Fourier's it may be possi­ ble to do so through the mediation of Pierre Prevost, who drew upon Dugald Stewart and from whom Fourier drew in turn. But to discuss adequately the complex genealogy of Kelvin's methodology would demand almost another book. In spite of such complications, it would be inexcusable to ignore Kelvin if he were the principle figure in the diffusion of those characterisitics which we identify with Victorian scientific style. But such is not the case. The force of James Clerk Maxwell's personality together with the striking clarity and sophistication of his methodologi­ cal arguments and examples made him a more central figure than Kelvin in calling the attention of other Vic­ torian scientists to dominant methodological issues.3 Thus I feel justified in leaving a discussion of Lord Kelvin to another time and place. 3 In his "Model and Analogy in Victorian Science: Maxwell's Critique of the French Physicists,"Journal of the History of Ideas, 30 (1969), pp.

PROLOGUE

The study's second limitation is its exclusive concentra­ tion upon Scottish philosophy. In France, Germany, Swit­ zerland, and England, as well as in Scotland, eighteenthand early nineteenth-century natural philosophers were deeply concerned with clarifying and exploring the philosophical presuppositions and implications of their work. One need only think of such men as George Louis Le Sage, Pierre Prevost, Christian Wolff, Immanuel Kant, Dennis Diderot, Jean D'Alembert, Pierre Maupertuis, David Hartley, and Joseph Priestley, to get a sense of how universal such concerns were. 4 Yet I have made little attempt to compare and contrast developments within the Scottish tradition of methodological writ­ ings with those in other countries or to investigate the interactions between Scottish and Continental phi­ losophy except where it seemed absolutely essential to an understanding of the Scottish tradition. Only such an approach has allowed me to achieve my principal goals —clarifying the character, development, and importance of a reasonably coherent and relatively self-contained methodological tradition—in a monograph of tolerable length.

423-436, Robert Kargon points up the central ity of Maxwell's writings in spreading the Victorian style. 4 Laurens Laudan, "Theories of Scientific Method from Plato to Mach," History of Science, 7 (1968), pp. 1-63, points up the very strong interest in methodology among late eighteenth- and early nineteenthcentury scientists of all nations.

PART I

The Growth of a Common Sense Philosophy of Science

CHAPTER 1

The Integration of Moral Philosophy and Natural Philosophy in Scottish Academia DURING THE eighteenth and early nineteenth centuries an intense interaction grew between natural and moral philosophy within the institutional framework of the Scot­ tish universities. Scottish scholars, like those of other countries, sought to extend the triumphs of the methods of natural science into morality, theology, and social and aesthetic concerns. David Hume's great classic, A Trea­ tise of Human Nature: An Attempt to Introduce the Ex­ perimental Method of Reasoning into Moral Subjects (1739) symbolized this scholarly attempt. 1 And as a schoolboy, Henry Brougham, later Lord Chancellor of England, attested to the scholars' success in convincing students that mental and social phenomena should be subject to the same kind of scientific analysis as mathe­ matics and physics, by proposing the establishment of an "Academy of Physics"—a student society which would study "the Newtonian Philosophy, comprehending every subject to which induction and reasoning can be applied: 1 Humes clearest statement of his intent in the Treatise appears in An Absract of A Treatise on Human Nature (London, 1740), which was written as an advertisement for his own book. He writes: ". . . tis at least worthwhile to try if the science of man will not admit of the same accuracy which several parts of natural philosophy are found susceptible of. . . . This seems to have been the aim of our late philosophers, and among the rest, of this author. He proposes to anatomize human nature in a regular manner, and promises to draw no conclusions but where he is authorized by experience."

GROWTH OF COMMON SENSE PHILOSOPHY

1. Mathematics, pure and mixed, 2. Physics, 3. Mind, 4. History. . . ." 2 But in Scotland, as elsewhere, there was a second—and for our purposes, more important—side to this Enlight­ enment interaction between natural and moral philos­ ophy. Ideas, often initially introduced into moral phi­ losophy from natural philosophy, were sifted, refined, and transformed by the moralists, epistemologists, and metaphysicians. Then they were reintroduced into the mathematical and physical sciences, bringing about changes in the nature of scientific method and in the character of the intellectual constructs which form the subject matter of the natural sciences. 3 This reflux of ideas from moral philosophy was unusually important and per­ vasive in Scotland because of the peculiar institutional characteristics of university education there. Unlike the English university pattern of studies in which early specialization (in classics at Oxford and in mathematics at Cambridge) presumably provided the 2 Henry Brougham to James Reddie, 17 December 1796; National Library of Scotland Ms. 3704. The infusion of scientific methods into Scottish moral and social con­ cerns is particularly well told by Gladys Bryson in her Man and Society: The Scottish Inquiry of the 18th Century (Princeton; Princeton Univer­ sity Press, 1945). A more detailed study of David Hume, who is perhaps the central figure in this movement is Mary S. Kuypers, Studies in the Eighteenth-Century Background of Hume's Empiricism (New York; Russell and Russell, 1966). 3 Studies of this return influence of moral philosophy, epistemology, and metaphysics upon the physical sciences in the eighteenth and nineteenth centuries are as yet infrequent. Interesting but halting be­ ginnings are represented in H. A. M. Snelders1 "Romanticism and Naturphilosophie and the Inorganic Natural Sciences 1797-1840: An Introductory Survey," Studies in Romanticism, 9 (1970), pp. 193-215; Thomas L. Hankins, Jean D'Alemert: Science and the Enlightenment (Oxford; The Clarendon Press, 1970); L. Pearse Williams' work growing out of his Michael Faraday (New York; Basic Books, 1965); and }. W. Herivel, "Aspects and French Theoretical Physics in the Nineteenth Century," British Journalfor the History of Science, 3 (1966), pp. 109132.

MORAL AND NATURAL PHILOSOPHY

basis for a later broadening of scope, the university curriculum in Scotland was organized from the mideighteenth to the mid-nineteenth century to provide a broadly based philosophical foundation for later specialized study. In order to ensure a sufficient breadth of vision—a liberal education—Scottish students were ordinarily required to attend a two-year course variously called Humanities, Rhetoric and Logic, or Moral Philosophy. 4 This course was almost universally taught in such a way as to emphasize that an understanding of the activities of the human mind was a prerequisite for all other studies, and to enable a student to keep his later specialized interests in proper perspective. David Hume, though often seen by the moral philosophers as an opponent rather than an ally, because of his skepticism and overt irreligious attitudes, nonetheless set the tone for the Scottish contention that all other branches of endeavor depended on an insight into human nature by writing: 'Tis evident that all the sciences have a relation, greater or less, to human nature, and that, however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural 4 J. B. Morrell has taken issue with the basic thesis I am trying to establish on the grounds that "very few students followed the full degree program. It is therefore rash to assume, for instance, that all students of the natural philosophy class automatically attended that of moral philosophy." See " T h e University of Edinburgh in the late Eighteenth Century: Its Scientific Eminence and Academic Structure," Isis, 62 (1970), p. 168. Morrell, in fact, argues that it was the effective Lehrenfreiheit available within the Scottish context that accounts for the high productivity of scientists. He may be correct with regard to the production of technically trained personnel in general—especially that of proto-engineers and chemists. But of those who went on to be important academic natural philosophers, almost all attended the moral philosophy course. When they did not, they either audited the course or read widely in the standard moral philosophy texts. This is true for John Leslie, David Brewster, Henry Brougham, James D. Forbes, J. J. Waterston, W.J.M. Rankine, J. C. Maxwell, and P. G. Tait among others.

13

GROWTH OF COMMON SENSE PHILOSOPHY

Philosophy, and Natural Religion are in some measure dependent on the science of Man, since they lie under the cognizance of men and are judged by their powers and faculties. It is impossible to tell what changes and improvements we might make in these sciences, were we thoroughly acquainted with the extent and force of human understanding and could explain the nature of the ideas we employ and of the operations we perform in our reasonings. 5 Nearly all the Scottish philosophers following Hume agreed with this statement and sought to demonstrate how an understanding of man's cognitive faculties, his feel­ ings, and his desires formed the basis for specialized forms of knowledge. With respect to natural philosophy in particular, the Scottish philosophers did precisely and explicitly what John Dewey claimed that modern phi­ losophy has been attempting since the time of Kant—they reversed the historic relationship between the theory of knowledge and the theory of nature. 6 While thinkers from Greek times had explained the nature of knowledge on the basis of what they believed about the nature of the universe, the Scottish philosophers, like most modern academic philosophers, argued that one must begin with an understanding of the nature of human knowledge and develop an understanding of the universe as a derivative procedure. Dugald Stewart presented the general argument for using epistemology as a foundation for specialization par­ ticularly clearly: When our views are limited to one particular science, to which we have been led to devote ourselves by taste 5 Quoted from the introduction to the Treatise on Human Nature by Dugald Stewart in the first dissertation in Dissertations on the History of Metaphysical and Ethical, and Mathematical and Physical Science (Edinburgh; Adam and Charles Black, 1835). 6 See John Dewey, The Questfor Certainty: A Study of the Relation of Knowledge and Action (New York; Minton, Balch and Co., 1929), espe­ cially pp. 40-41 but passim.

MORAL AND NATURAL PHILOSOPHY

or accident, the course of our studies resembles the progress of a traveler through an unexplored country, whose wanderings from place to place are determined merely by the impulse of occasional curiosity, and whose opportunities of information must necessarily be limited to the objects which accidentally present themselves to his notice. It is the philosophy of the mind alone which, by furnishing us with a general map of the field of human knowledge, can enable us to proceed with steadiness, and in a useful direction. . . . 7 This contention was certainly not new. The Scottish school, for example, attributed it to Francis Bacon and to John Locke, their widely acclaimed mentors. But it gradually took on a great importance because the Scots came to question the naive empiricism of Bacon, because they integrated metaphysical and epistemological concerns in an interesting and fruitful way, and above all because their commanding place in the academic system allowed them to push their scientific colleagues to reevaluate and analyze the foundations of their disciplines and to modify their methods and concepts accordingly. Since the holders of all Scottish chairs of mathematics and natural philosophy were educated within the closed, philosophically oriented system, they responded not by envying or discrediting the philosophers but rather by becoming more philosophical themselves. 8 Over and over again we find Scottish scientists writing works on the philosophical and psychological background 'Dugald Stewart, The Collected Works ofDugald Stewart, Sir William Hamilton, ed., (Edinburgh; Thomas Constable and Co., 1859), II, p. 79. 8 See, for example, James Hutton, An Investigation of the Principles of Knowledge and the Progress of Reason from Sense to Science and Philosophy (Edinburgh; A. Straham and T. Cadell, 1794); Thomas Beddoes, Observations on the Nature of Demonstrative Evidence; with an Explanation of the Difficulties Occurring in the Elements of Geometry (London; n.p., 1793) John Leslie, Philosophy of Arithmetic (Edinburgh; W. and C. Tait, 1819), James Gregory, Essay on the Difference between the Relation of Motive and Action and that of Cause and Effect: on

15

GROWTH OF COMMON SENSE PHILOSOPHY

of their subjects 9 and including metaphysical and epistemological concerns even in their scientific monographs and textbooks. Forexample 5 John Leslie's monograph, An Experimental Investigation into the Nature and Propaga­ tion of Heat, included a twenty-page note on the problem of cause and effect. And the very definition of dynamics given by John Robinson in his textbook, The Elements of Mechanical Philosophy, points up the philosophical bent of Scottish scientists and their emphasis on the human element in science: "Dynamics . . . contain the abstract doctrine of moving forces; that is, the necessary results of our thoughts concerning motion and the causes of its production and change." 10 He goes on to explain in more detail what he means by analyzing Newton's famous three laws: ". . . [they] are in reality, not descriptions of ex­ ternal nature, but of the proceedings of the human mind in contemplating or studying it. Being independent of all experience of a thing beyond our own thoughts, they form a body of demonstrative truths." 11 These few examples illustrate only that lip service was paid by Scottish natural scientists to their society's in­ terest in philosophical matters. It will be one of the major tasks of this book to describe the extent to which such concerns were truly integral to their science and deter­ mining factors in the directions that it took. In addition to an emphasis on the psychological and epistemological foundations of scientific disciplines, there was a second characteristic of Scottish phiPhysical and Mathematical Principles (London; W. Creech, 1792), Wil­ liam M. Rankine, "On the Use of Mechanical Hypotheses in Science, and Especially in the Theory of Heat," Proceedings of the Glasgow Philosophical Society, 5 (1864), pp. 126-132. 9 John Leslie, An Experimental Inquiry into the Nature and Propaga­ tion of Heat (London; J. Mawman, 1804), pp. 115-136. 10 John Robison, Elements of Mechanical Philosophy: Being the Sub­ stance of a Course of Lectures on that Science (Edinburgh; Archibald Constable and Co., 1804), p. 88. 11 Ibid, p. 157.

MORAL AND NATURAL PHILOSOPHY

losophy—especially of the Philosophy of Common Sense which was dominant between 1750 and 1850—that was closely related to the pursuit of scientific studies. The highest tribute to an enlightened Scot was to be known as a "man o' parts," meaning not only an extremely capable man in his field but also a man of wide-ranging interests and abilities. The primary aim and object of all education was thus, "to cultivate all the various principles of our nature, both speculative and active, in such a manner as to bring them to the greatest perfection of which they are susceptible. . . . 12 Since all human capabilities were valued, narrow specialism was consciously to be avoided: It ought not be the leading object of anyone to become an eminent metaphysician, mathematician, or poet; but to render himself happy as an individual, and an agreeable, a respectable, and a useful member of society. A man who loses his sight improves the sensibility of his touch: but who would consent, for such recompense, to part with the pleasures which he receives from the eyes? 1 3 We must constantly be aware of this emphasis on the necessity for breadth of vision within the Scottish tradition in order to assess many of the comments of Scots (both philosophers and scientists) on the nature of science. This is particularly true when we come to assess the very important Scottish analysis of the uses and abuses of analogy within the sciences. The Scots almost universally condemned narrowly based attempts to force phenomena from one field into patterns analogous to those in other fields. Adam Smith, for example, complained in his History of Astronomy of those who, 12 Dugald Stewart, "Elements of the Philosophy of the Human Mind" in Collected Works, n, p. 59. 13 IbJd, p. 61.

17

GROWTH OF COMMON SENSE PHILOSOPHY

have written parallels of painting and poetry, of poetry and music, of music and architecture, of beauty and virtue, of all the fine arts; systems which have universally owed their origin to the lucubrations of those who were acquainted with the one art, but ignorant of the other; who therefore explained to themselves the phenomena in that which was strange to them, by those in that which was familiar; and with whom, upon that account, the analogy, which in other writers gives occasion to a few ingenious similitudes, became the great hinge upon which everything turned. 1 4 H e was no more enamored of those who generated scientific systems in a similar way—the chemists with t h e i r narrow e x p e r i e n c e of t h e furnace, or the Pythagoreans who wanted to reduce all to conformity with numerical patterns. But Smith and his philosophical and scientific colleagues did not deny the importance of analogical reasoning founded in broad experience and subject to the limitations which a widely experienced man could bring to it. In fact, as we shall see, they emphasized its great importance. The Scots' emphasis on philosophical training had an additional important influence on the sciences in connection with its demands for sufficient breadth in the foundations of scientific theory. Like the medieval theory which held that science and philosophy were only handmaidens for theology, the Scots' theory of moral philosophy held that all specific subjects of study should serve principally to forward one's liberal education and to develop man's intellectual powers. Thus, it demanded that, if the sciences were to take a place in academia, they justify themselves as elements in a liberal education and as mindtraining disciplines. Once more, the scientists—at least until the early nineteenth century—were often willing to adopt the 14

Adam Smith, The Early Writings ofAdam Smith, J. R. Lindgren, ed., (New York; Augustus M. Kelley, 1967), pp. 83-84.

18

MORAL AND NATURAL PHILOSOPHY

philosopher's point of view and to see their disciplines as somehow ancillary to the main ends of education. Though the great geologist, James Hutton, was not a professional educator himself, he put in strongest terms what was a common feeling among Scottish scientists at the end of the eighteenth century when he wrote: Philosophy surely is the ultimate of human knowledge, or the object at which all science properly should aim; every step in science, therefore, ought to be valued, in some measure, as it tends to bring about that end. Science, no doubt, promotes the arts of life; and it is natural for human wisdom to promote these arts. But, what are all the arts of life, or all the enjoyments of the a n i m a l n a t u r e , c o m p a r e d w i t h t h e art of h u m a n happiness—an art which is only to be attained by education, and which is only brought to perfection by philosophy! Man must learn to know himself; he must see his station among created things; he must become a moral agent; and he must enquire after that system in which he had been intended either for happiness, or for misery, as an end. This is what he has to learn; but it is only by studying things in general that he may arrive at this perfection of his nature. It is impossible to form the idea of generals except upon a knowledge of the particulars; and it is upon particular physical and mathematical truths that natural philosophy must found its principles. . . . The truths of science are to philosophy what the beams of wood, and the hewn stones, are to a building. 1 5 Hutton was careful to point out in including this statement in the introduction to his Dissertations on Light, Heat, and Fire that it was not just something tacked on to fill out his book, but that it was a central thesis for which the scientific content of the book was only exemplary 15 James Hutton, Dissertations on Light, Heat, and Fire (Edinburgh; Cadell, Junior and Davies, 1794), pp. v-vii.

19

GROWTH O F COMMON SENSE PHILOSOPHY

material. While Scottish scientists as a group may not have gone as far as Hutton in allowing such an overwhelming primacy to philosophy, few escaped the influence of this point of view. It clearly influenced the presentation of scientific results in Scotland, calling forth at least some general philosophical remarks in nearly all scientific monographs. And it undoubtedly accounts, at least in part, for the extremely elementary level of science teaching in the Scottish universities; since most science courses were explicitly designed to serve the needs of non-specialist students. 1 6 In most sciences it is difficult to establish that the role of science in general education had an appreciable effect on the conceptual content of science or on the way in which scientific investigations were conducted. But in mathematics there was a direct and fundamental impact. Because the pursuit of geometry was seen by many of the notable Scottish philosophers as leading to an improve16 The elementary and philosophical nature of Scottish natural philosophy course is very nicely dealt with in George E. Davie, The Democratic Intellect (Edinburgh; Edinburgh University Press, 1959), especially ch. 1, " T h e Presbyterian Inheritance," and ch. 8, "The Humanistic Bias of Scottish Science." But nowhere can a better impression be gained than from looking at students' notebooks from these classes. When one looks at Balfour Stewart's notes on James Forbes's natural philosophy lectures (Edinburgh University Library Archives, shelf number Dc. 101-107) one is struck by the fact that as late as 1845-1846, Forbes was forced to alternate his lectures between technical, mathematical subjects and popular, non-mathematical ones in order to maintain the interest of students in his classes. And to maintain interest was of supreme importance then, for professors still gained most of their livelihood from class fees paid directly to the professor by each student taking a course, and students rebelled at taking courses which seemed too technical. T h e same situation can be seen in reading the notes taken down by John Russell in 1811-1812. Young Russell manfully compiled notes on most lectures which were carefully delivered in an elementary style; but occasionally Playfair went beyond the range of his listeners' abilities and a few lectures are tersely summarized with the comment "too mathematical." (Edinburgh University Library Archives, shelf number Dc. 3.21).

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MORAL AND NATURAL PHILOSOPHY

m e n t o f the intellect, whereas algebraic analysis was not, Scottish mathematical research was skewed significantly away from the analytical techniques being developed on the Continent and toward ancient geometrical techniques. The essential justification for the pedagogical superiority of geometry over algebraic analysis is contained in the following comment about Robert Simson written by John Robison, his student, for the Encyclopedia Britannica: . . . he preferred the ancient method of studying pure geometry, and even felt a dislike for the Cartesian method of substituting symbols for operations of the mind, and still more was he disgusted with the substitution of symbols for the very objects of discussion, for lines, surfaces, solids, and their affections. . . . And he came at last to consider algebraic analysis little better than a kind oimechanical knack, in which we proceed without ideas of any kind, and obtain a result without meaning and without being conscious of any process of reasoning. . . . 17 According to the Scottish philosophers, we must be aware of the intellectual processes and their functioning in order to train them effectively. Geometry keeps us aware of the steps of reasoning involved in a mathematical argument and algebra does not; therefore, geometry is better than algebra for training the intellect. William Hamilton, Dugald Stewart's heir to the deanship of Scottish philosophy, indicated his feelings about the relative merits of the two methods explicitly in his "Letter to the Lord Provost" of 1838 which was written when there was a movement to emphasize analytical mathematics in the university course. Hamilton said: " Q u o t e d from William Hamilton, "On the Study of Mathematics as an Exercise of the Mind," Discussions of Philosophy, 2nd edn. (London; Longman, Brown, Green and Londmans, 1853), p. 317. The emphasis is Robison's.

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The mathematical process in the symbolical method [i.e., the algebraical] is like running a railroad through a tunnelled mountain; that in the ostensive [i.e., the geometrical] like crossing the mountain on foot. The former causes us, by a short and easy transit, to our destined point, but in miasma, darkness, and torpidity, whereas the latter allows us to reach it only after time and trouble, but feasting us at each turn with glances of the earth and of the heavens, while we inhale the pleasant breeze, and gather new strength at every effort we put forth. 18 In light of this statement and that of Simson, we can well understand the general attitude of Scottish philosophers which was expressed by Dugald Stewart's contention that: . . . mathematics is peculiarly calculated to strengthen the power of steady and concatenated thinking—a power which, in all the pursuits of life, w h e t h e r speculative or active, is one of the most valuable endowments we can possess. This command of attention, however, it may be proper to add, is to be acquired, not by the practice of modern methods, but by the study of the Greek geometry. 1 9 Although it might seem that this way of looking at mathematics as an ancillary discipline would have been unpalatable to mathematicians, it was embraced wholeheartedly by some and in part by almost all. 20 In the pref18 Quoted by George Davie, Democratic Intellect, p. 127. The brackets are Davie's. 19 Dugald Stewart, Collected Works, iv, p. 201. 20 See Florian Cajori, Mathematics in Liberal Education (Boston; Christopher Publishing house, 1928), for a fascinating (but unfortunately superficial) historical analysis of the opinions regarding the theory in question. Cajori reports (p. 161) that of 110 mathematicians of the seventeenth, eighteenth and nineteenth centuries whose works he perused, 108 at some point wrote a declaration emphasizing the important role of mathematics in a liberal education—i.e., in favor of mathematics as a mind-training discipline.

22

MORAL AND NATURAL PHILOSOPHY

ace to his Elements of Geometry. . . of 1809, for instance, John Leslie indicated its influence by stating that: The study of mathematics holds forth two capital objectives; while it traces the beautiful relations of figure and quantity, it likewise accustoms the mind to the invaluable exercise of patient attention and accurate reasoning. Of these distinct objects the last is perhaps the most important in a course of liberal education. For this purpose, the geometry of the ancients is the most powerfully recommended, as bearing the stamp of that acute people, and displaying the finest specimens of logical deduction. Some of the propositions, indeed, might be reached by a sort of algebraic calculation; but such an artificial mode of procedure gives only an apparent facility, and leaves no clear or permanent impression on the mind. 2 1 Since statements like this appear most often in the prefaces to mathematical works, there is a tendency to pass over them as rationalizations in a pejorative sense rather than valid justifications for work done. In the case of the Scottish academician-mathematicians, and of Leslie in particular, however, these statements do mirror a theme which seems to have been important in motivating much of what they did. If we go far from textbook prefaces to look at Leslie's "Dissertation Fourth on the History of Mathematical and Physical Science," where he freely discussed his philosophical views, we again see that he emphasized the pedagogical philosophy expressed above as a motivating factor for his work on the restoration of ancient geometrical methods. In his article he spoke of the general run of mathematical texts available; then he went on to say: . . . the works now mentioned might suffice for the instruction of practical or professional men; but the 21

John Leslie, Elements of Geometry, (Edinburgh, 1809), pp. v-vi. Emphasis mine.

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pursuit of a liberal education aspires to great attainments. The main object is to sharpen the faculty of perception, and investigate by due exercise, the tone of the intellectual powers. For contributing to that effect, the fullness and circumspection of the ancient mode of demonstration are admirably calculated. It seemed, therefore, an estimable task to select the scattered wrecks of the Greek analysis, and dispose them into a form accessible to ordinary students. . . . 22 The emphasis on mathematics as an integral part of a liberal education and the feeling of a need to relate mathematics to general culture was very strong in Leslie; it even led him to try to teach arithmetic from the same point of view that he used for geometry. 23 The pedagogical theory was thus more than ad hoc justification for studies which would have been done even had this reason not been present. In the late eighteenth century, then, moral philosophy, natural philosophy, and mathematics were integral parts of an academic system which ensured that natural scientists and mathematicians had a great intellectual background in common with the philosophers and that they would listen when the philosophers had something to say about the nature and methods of science. Furthermore, the scientists produced in this milieu tended to take an explicit interest in the philosophical foundations of their 22

Dugald Stewart, et al., Dissertations, pp. 582-583. In The Philosophy of Arithmetic: Exhibiting a Progressive View of the Theory and Practice of Calculation, 2nd. ed., (Edinburgh, 1820), p. i., Leslie wrote: "Arithmetic is deduced from its principles, and treated as a branch of liberal education. The object proposed was not merely to teach the rules of calculation, but to train the young student to the invaluable habit of close and patient investigation. . . . In seeking to unfold the natural progress of discovery, I have traced the science of numbers, through the succession of ages, from its earliest germs, till it acquired the strength and expansion of full maturity. This species of history, combining solid instruction with curious details, cannot fail to engage the attention of inquisitive readers." 23

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MORAL AND NATURAL PHILOSOPHY

subjects, and, at least in the case of mathematics, the Scottish scientists' philosophical upbringing tended to influence the very content of scientific texts and investi­ gations.

C H A P T E R

2

The Origins of Common Sense Philosophical Concern with the Nature of Science: Bacon and Newton Revisited in the Light of Hume I N THE last chapter I passed over the discussion of a "scientific" element within Scottish moral philosophy in order to emphasize the basically humane nature of all Scottish academic thought and to demonstrate the extent to which moral philosophy formed the core of university education. To understand how the Scottish moral philosophers d e v e l o p e d ideas which w e r e specifically applied to the natural sciences, however, we must return to consider their interest in scientific method and scientific concept formation. For it was out of the reworking of notions initially imbibed from the scientists themselves that the Scottish philosophers—especially the Common Sense philosophers, Thomas Reid (1710-1796), Dugald Stewart (1753-1828), Thomas Brown (1778-1819), and William Hamilton (1788-1856) 1 —developed doctrines which influenced the subsequent direction taken by mathematical and physical as well as psychological and moral studies in Britain. With regard to its views on scientific method in particular, Common Sense Philosophy underwent important developments between 1750 and 1840; so that on such important topics as the proper role of hypotheses and the importance of analogy, Hamilton's views seem almost H a m i l t o n is not usually considered a Common Sense philosopher, but he explicitly saw himself as a member of the school, and for my purposes, his most important work was as an expositor and developer of Common Sense doctrines.

26

CONCERN WITH T H E NATURE O F SCIENCE

completely antithetical to the earlier views of Reid and his comtemporaries. At each stage in its development, however, Common Sense Philosophy had considerations of lasting value to offer on scientific method; and some of the more influential concerns of Stewart and Hamilton can be fully understood only in relation to the earlier and less sophisticated discussions of Reid and Beattie. Scottish Common Sense Philosophy grew out of the discussions of a private literary society, The Philosophical Society of Aberdeen (also known as the Wise Club) which met twice monthly from 1758 to 1773. This group heard and discussed papers on a wide variety of philosophical questions, designating as philosophical, "every principle of science which may be deduced by just and lawful induction from the phenomena either of the human mind or of the material world; all observations and experiments that may furnish materials for such induction; the examination of false schemes of philosophy and false methods of philosophizing: the subserviency of philosophy to the arts, the principles they borrow from it, and the means of carrying them to their perfection." 2 The two most active and influential members of the group, Thomas Reid, Professor of Philosophy at Kings College, Aberdeen, and James Beattie, poet and Professor of Moral Philosophy at Marischal College, became the founders of the Scottish Common Sense School of Philosophy. But several other members, especially George Campbell, principal of Marischal College, and Dr. John Gregory, who taught medicine and natural philosophy at Aberdeen before becoming Professor of Medicine at Edinburgh in 1764, also played a significant role in clarifying some of the school's doctrines. While Common Sense Philosophy had the same encyclopedic scope as the interests of the society in which it 2 From the "Rules" of the Philosophical Society of Aberdeen quoted by Lloyd F. Bitzer in his introduction to George Campbell, The Philosophy of Rhetoric (Carbondale; Southern Illinois University Press, 1963), pp. xi-xii.

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arose, it began principally as a critical response to the philosophical writings of David Hume. 3 And even though much of Reid's work dealt with the establishment of a positive philosophy of the human mind (very similar to what we now call psychology), one of the main thrusts of early Common Sense Philosophy—of Reid's and Gregory's as well as of Beattie's—was to defend the religious beliefs and moral tenets of moderate Scots' Presbyterianism against the corrosive influences of atheistical skepticism (personified in David Hume) on the one hand and against necessitarian materialism (personified in David Hartley and later in Joseph Priestley), on the other. John Gregory expressed the fears of the group as a whole when he wrote from Edinburgh in 1767, urging Beattie to publish his views: Atheism and materialism are the present fashion. If one speaks with warmth of an infinitely wise and good Being, who sustains and directs the frame of nature, or expresses his steady belief of a future state of existence, he gets hints of his having either a very weak understanding, or of being a very great hypocrite—But what hurts me most is the emphatic silence of those who should be supposed to hold very different sentiments on these subjects. The world supposes that no man will tamely bear sentiments ridiculed which he holds as the most deeply interesting and sacred, without expressing such dissatisfaction as would effectually prevent any gentleman of tolerable good breeding from repeating the insult, or at least, that he would endeavor to retort 3

Both Reid and Campbell saw Hume as their principal teacher as well as their principal antagonist. In fact, both men sent copies of their major early works—Reid's An Inquiry into the Human Mind on the Principles of Common Sense (1764) and Campbell's The Philosophy of Rhetoric (1776)—to H u m e for criticism before publication. James Beattie and John Gregory, on the other hand, carried their distaste for Hume's skeptical philosophy into a personal dislike for the man; and Beattie refused to acknowledge the considerable debt of Common Sense Philosophy to Hume.

28

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the ridicule, if he was not conscious of the weakness of his cause. Till within these last thirty years, the wit was generally on the side of religion. I do not remember any man of the least pretensions to genius in Britain, who ever thought of subverting every principle of natural religion till of late [Hume is the obvious referent here ]. And if the present spirit is not very speedily checked, I am confident it will give the finishing stroke to that corruption of heart and principles which makes such alarming progress. . . . 4 Skeptical philosophy was the first-order enemy, for it was "destructive of genuine philosophy, as well as of religion and virtue," and skeptical philosophers were, "the corrupters of science, the pests of society, and the enemies of mankind. " 5 But materialistic determinism was a very close second, since moral liberty provided the very possibility of virtue, and without some freedom from the uniform laws of the material universe, moral liberty could be nothing but an illusion. In Beattie's words, That I am a free agent, is what I not only believe, but what I judge to be of such importance, that all morality must be founded on it, yey, and all religion too. To vindicate the ways of God to man, is not so difficult a thing when we acknowledge human liberty; but on the principles of fatality, it seems to me absolutely impossible. 6 The foundation for all Common Sense responses to skepticism and materialism depended upon the assertion that both philosophies lead to conclusions which contradict "certain principles . . . which the constitution of our nature leads us to believe, and which we are under a 4

John Gregory to Dr. Beattie, Edinburgh, 16 June, 1767, reprinted in William Forbes, An Account of the Life and Writings of James Beattie, (New York; Brisban and Brannan, 1807), pp. 73-74. 5 James Beattie, quoted in William Forbes, Life and Writings of Beattie, p. 92. 6 Beattie to D. Blacklock, Aberdeen, 27 May, 1770. Ibid., p. 119.

29

GROWTH OF COMMON SENSE PHILOSOPHY

necessity to take for granted in the common concerns of life." 7 Such principles, the Principles of Common Sense, are both impossible to disbelieve and impossible to prove; so they must be accepted as ultimate principles in much the same way that the axioms of geometry must be accepted as unproven first principles. No amount of reasoning, no matter how subtle, can either justify or undermine genuine principles of common sense. Consequently, if they are contradicted by some philosophical system, that system must be in error. Basic principles of common sense were controverted or questioned both by materialists—who denied the common-sense intuition of man's moral free agency—and by skeptics and idealists—who denied (among other things) the common-sense belief that we can know the existence of an external world. Thus materialism, skepticism, and traditional idealism were all in error. For our purposes, Common Sense Philosophy became interesting only after these errors had been detected through the use of the fundamental principle; for then the key problem became—at least for Reid and his followers—to determine where the other philosophies went wrong and to establish the basis for uncontaminated knowledge. And this problem led directly to an intense interest in scientific methodology and concept formation. For a few of the early propounders of Common Sense Philosophy, especially for James Oswald, author of An Appeal to Common Sense in Behalf of Religion (1766), and to a lesser extent for James Beattie andjohn Gregory, it was an overtly anti-intellectual movement which decried all "metaphysical" discussions—whatever their intent—because they seemed to undermine religious beliefs and moral values. The very act of reasoning with 'Thomas Reid, An Inquiry into the Human Mind, On the Principles of Common Sense in The Works of Thomas Reid, D. D. Now Fully Collected with Selections from his Unpublished Letters, Sir William Hamilton, ed., 6th edition, (Edinburgh: McLachlan and Stewart, 1863), I, p. 108.

30

CONCERN WITH T H E NATURE O F SCIENCE

atheists as though they might have valid arguments was unwise and ill-advised, according to Oswald, since it was bound to give the multitude the impression that the truths of religion were still unsettled. 8 We should simply affirm the religious truths known intuitively by common sense. Similarly, Beattie warned that "to suppose that everything may be made a matter of dispute is an exceedingly false principle," 9 and he argued that a "metaphysical" spirit—meaning the kind of questing for philosophical certainty typified in Hume's writing—"has a bad effect on the human faculties, and tends not a little to sour the temper, to subvert good principles, and to disqualify men for the business of life." 10 This anti-intellectual facet of Common Sense Philosophy obviously leads to a dead end, as Joseph Priestley was quick to point out in his blisteringExammfliion of Dr. Reid's Inquiry.11 With the exception of Oswald, however, the members of the Common Sense school were far from being mere naive cavaliers against the sophistry of intellectuals. George Campbell and, to an even greater extent Thomas Reid, were as much the philosophical disciples of David Hume as they were his religious enemies. In accepting many of Hume's critical and methodological insights they were clearly anti-rationalist insofar as they denied that reason alone could provide the basis for any significant knowledge either of the material or of the spiritual world. They did not, however, take refuge in a primitive appeal to the feelings of the mob. Instead, they built upon Hume's empiricist foundations a highly sophisticated critical philosophy which, in spite of some 8 Oswald, An Appeal to Common Sense in Behalf of Religion (Edinburgh: A. Kincaid and J. Bell, 1766), p. 316. 9 Beattie to William Forbes, Aberdeen, 30 January, 1766 in Forbes, Life and Writings of Beattie, p. 60. t0 Beattie to Dr. Blacklock, Aberdeen, 9 January, 1769. Ibid., p. 92. ''Joseph Priestley, An Examination of Dr. Reid's Inquiry into the Human Mind on the Principles of Common Sense; Dr. Beattie's Essay on the Nature and Immutability of Truth, and Dr. Oswald's Appeal to Common Sense in Behalf of Religion. (London: J. Johnson, 1774).

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great differences, bears a number of similarities to the Kantian critical philosophy developed on the same foundations. Like Kant, the Scots saw in certain aspects of mathematics and natural philosophy domains of knowledge which did not seem so seriously challenged by skeptical considerations as were moral and religious concerns. They, like Kant, sought to analyze and understand the characteristics of natural science and to apply the precepts learned in that study in order to build a science of the mind and subsequently a practical science of morality and a foundation for religious faith that had the same claims on belief as the natural sciences. Hume, of course, had set the tone for this endeavor in his Treatise of Human Nature which he touted as an attempt, "to try if the science of man will not admit of the same accuracy which several parts of natural philosophy are found susceptible of."12 Hume saw himself as one of a long line of empiricist seekers after a knowledge of human nature, mentioning Francis Bacon, Lord Shaftesbury, Bernard de Mandeville, Francis Hutcheson, and Samuel Butler as his predecessors. Hume's extreme emphasis on method, however, changed the character of the endeavor in fundamental ways. John Gregory, a full-time scientist himself, as well as Thomas Reid, whose early interests had been centered on mathematics and Newtonian natural philosophy, 1 3 were quick to take up Hume's suggestion that all branches of philosophy should be made rigorously scientific. 12 David H u m e , An Abstract of A Treatise on Human Nature: 1740: A Pamphlet hitherto unknown by David Hume Reprinted with an Introduction by J. M. Keynes and P. Saffa. (Cambridge; Cambridge University Press, 1938), p. 6. 13 Dugald Stewart's Account of the Life and Writing of Thomas Reid reprinted in The Works of Thomas Reid discusses Reid's early connection with the mathematician, John Stewart, his important "Essay on Quantity" of 1748, and his role as professor of mathematics and physics as well as logic and ethics at Aberdeen. See especially The Works of Thomas Reid, I, pp. 4-6.

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Even the least scientifically inclined and most antiHumian among the Common Sense philosophers, James Beattie, was enthusiastic about using the natural sciences as a model for mental and moral philosophy. Beattie ad­ mitted that by establishing careful criteria for what was to count as truth, mathematics and natural philosophy have become of all sciences the most respectable in point of certainty. I am encouraged to hope that if the same criterion were uni­ versally adopted in the philosophy of the mind, the science of human nature, instead of being, as it is at present, a chaos of uncertainty and contradiction, would acquire a considerable degree of certainty, perspicuity, and order. If truth be at all attainable in this science, (and if it is not attainable, why should we trouble our heads about it?) surely it must be attained by the same means as in those other sciences. 14 In seeking to establish a boundary marking off the proper domains of reason and common sense, Beattie again as­ serted his dependence on the scientific model: The sciences in which this boundary has been long settled and acknowledged, are mathematics and natural philosophy; and it is remarkable that more truth has been discovered in those sciences than in any other. Now there is not a more effectual way of learning the rules of any art, than by attending to the practice of those who have performed it most successfully. . . . 15 Thus Beattie explained one important motivation for deep Common Sense interest in analyzing scientific method. Common Sense Philosophy was by no means the only attempt to apply scientific methods in the mental and moral spheres. Almost all Enlightenment philosophers 14 James Beattie, Essay on the Nature and Immutability of Truth in Opposition to Sophistry and Skepticism, 2nd edition, (Edinburgh; A. Kincaid and J. Bell, 1770), p. 127. 15 Ibid. pp. 101-102.

GROWTH OF COMMON SENSE PHILOSOPHY

accepted this as a goal. In particular, both the major schools attacked by the Common Sense philosophers felt that they were doing the same thing. We have already spoken of Hume; and the materialists Hartley and Priest­ ley were no less insistent on applying scientific method to the problem of man's nature. In fact, Priestley claimed that Hartley's scientific approach "has thrown more use­ ful light upon the theory of the mind than Newton did upon the theory of the Natural World. 16 What distin­ guished the early Common Sense philosophers from their opponents in this attempt to develop a science of mind was their desire to adopt a particularly rigorous form of empiricism harking back to a method which they believed was first expounded by Bacon and more fully developed by Newton. 17 Reid was certain that both Hume and the materialists went wrong because they paid too little attention to the dictates of Bacon and because they misinterpreted Newton's "Rules of reasoning in Philosophy" laid down in the Prtncipia. One of the most perceptive recent stu­ dents of Common Sense Philosophy, S. A. Grave, has put Reid's criticism of all the other philosophical schools av­ owing a scientific approach in the following way: "The [ir] error is fundamentally an error of method: hypotheses where there should be severe induction, analogies where the facts should be left to their uniqueness, and a vacuum in the place of first principles." 18 And Reid's insistence on the careful interpretation of scientific method became the keystone of Common Sense Philosophy. 16 Joseph

Priestley, Examination . . ., p. 3. L. L. Laudan, "Thomas Reid and the Newtonian Turn of British Methodological Thought," in Robert Butts and John W. Davis, eds., The Methodological Heritage of Newton (Toronto; University of Toronto Press, 1970), pp. 103-131, for the argument that Common Sense indebt­ edness to Bacon was largely second-hand. While the argument makes sense for Reid, I think that it does not for other members of the school. 18 S. A. Grave, The Scottish Philosophy of Common Sense, (Oxford; The Clarendon Press, 1960), p. 131. 17 See

CONCERN WITH THE NATURE OF SCIENCE

Reid's followers modified his interpretation of proper scientific method; but they continued to emphasize its importance. Dugald Stewart, Reid's student and succes­ sor as head of the Common Sense movement, spoke of "how much the powers of invention and discovery may be assisted by the study of method" and wrote that "in all the sciences, without exception, whoever employs his genius with a regular and habitual success, plainly shows that it is by means of general rules that his inquiries are conducted." 19 And Thomas Brown, who followed Stewart, continued the tradition in his first important work, Observations on Dr. Darwin's Zoonomia (1796), which was exclusively devoted to a critique of Erasmus Darwin's methodology, and in his lectures on moral philosophy, of which a large segment was devoted to the philosophy of the natural sciences. 20 Even Sir William Hamilton, whose methodological concerns were diffused widely through his works and never made the focus of an organized and coherent discussion, was deeply con­ cerned with method. Later we shall see that one of his greatest lasting influences was on the methods used by James Clerk Maxwell in his physical investigations. The remainder of this chapter will be devoted to follow­ ing Thomas Reid and John Gregory in their attempts to isolate and correct the methodological errors of Hume and Hartley and to clarify their own views on the proper methods for a science of the human mind; for it was in the course of this endeavor that a Common Sense philosophy of science arose. THE INITIAL ANTAGONISM TOWARD HYPOTHESES Reid's most frequent methodological criticism was that his opponents engaged in too many unsubstantiated and Stewart, Collected Works, π, p. 288. See Thomas Brown, Lectures on the Philosophy of the Mind, 19th edition, (Edinburgh; Adam and Charles Black, 1851). 19 Dugald 20

GROWTH OF COMMON SENSE PHILOSOPHY

imaginative hypotheses about natural phenomenon. In this attitude he showed his great debt to Bacon, reiterating Bacon's ladder metaphor for human knowledge and warn­ ing of men's fruitless desire to skip directly from bottom to top: Human knowledge is like the steps of a ladder. The first step consists of particular truths, discovered by observation or experiment: the second collects these into more general truths: the third into still more gen­ eral. But there are many such steps before we come to the top. Ambitious of knowledge, and unconscious of weakness, we would fain jump at once from the lowest to the highest. But the consequence of this is that we tumble down and find that our labor must begin anew. 21 Even more than Bacon, however, Newton provided the precedent for Reid's impatience with hypothetical reasoning, and Reid referred over and over again to the famous General Scholium of Book 3 of the Principia where Newton discussed gravitational phenomena and wrote: But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame [feign] no hypotheses, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards ren­ dered general by induction. 22 Reid's vilification of hypothetical reasoning knew al­ most no bounds, for it was a hypothesis, the so-called "doctrine of ideas" which, in his mind, led modern 21 Reid, Letter to Lord Kames, 1 October, 1775, The Words of Thomas Reid, p. 53. 22 Isaac Newton, Principia, Cajori edition, (Berkeley: University of California Press, 1934), n, P. 547. Reid's references can be found in The Works of Thomas Reid, pp. 211, 236, 250.

CONCERN WITH THE NATURE OF SCIENCE

philosophy into the skepticism that threatened to triumph over the dictates of common sense. 23 He admitted that many of the most brilliant phi­ losophers had developed hypotheses, and referred to De­ scartes' vortex cosmology as a prime example. In fact, he acknowledged that men of great genius and imagination alone are able to produce plausible and convincing hypotheses. But he went on then to decry the role of genius in philosophy, writing: It is genius, and not the want of it, that adulterates philosophy and fills it with false theory. A creative imagination disdains the mean offices of digging for a foundation, of removing rubbish, and carrying materi­ als; leaving these servile employments to the drudges in science, it plans a design and raises a fabric. Inven­ tion supplies materials where they are wanting, and fancy adds colouring and every befitting ornament. The work pleases the eye, and wants nothing but solidity and a good foundation. It seems even to vie with the works of nature till some succeeding architect blows it to rubbish, and builds as goodly a fabric of his own in its place. Happily for the present age, the castle builders employ themselves more in Romance than in phi­ losophy. That is undoubtedly their province, and in those regions the offspring of fancy is legitimate, but in philosophy it is all spurious. 24 In spite of the fact that the hypothesis of ideas may be the most pernicious in its consequences, Reid could under­ stand how men were seduced into believing in the exis­ tence of a distinct class of entities called "ideas" and even how they failed to note the hypothetical character of these entities. In fact, Reid demonstrated almost a compassion for those misled into accepting "ideas" because they were unaware of what they were doing. But he showed no such compassion for the materialists—like David Hartley —who consciously chose to adopt hypotheses in their 23 Reid,

The Works of Thomas Reid, p. 98.

24 Ibid.

p. 99.

GROWTH OF COMMON SENSE PHILOSOPHY

reasonings. For these men not only erred but explicitly directed others into errant ways. 25 When we try to discover what reasons Reid had for denying the hypothetical road to science other than the personal authority of Bacon and Newton and his heartfelt opposition to the effects of specific hypotheses, we must keep in mind his desire for certainty in philosophy—his need to defend every statement against the critical skepti­ cism of Hume. It is on this point that he broke with Hart­ ley and Priestley and claimed to follow Newton more closely than they did, and with very good reason. Both Hartley and Priestley were quite willing to accept what Priestley called a "reasonable degree of evidence" rather than a "plenary assurance" for philosophical proposi­ tions. 26 Speaking of Locke's discussion of the reality of the external world in particular, Priestley said: Mr. Locke would not, indeed, pretend to such an absolute demonstration of the reality of an external world as Dr. Reid pleads for [Priestley uses demonstra­ tion here in a loose way, implying certainty]; but neither is that strict demonstration necessary. It is quite sufficient if the supposition be the easiest hypothesis for explaining the origin of our ideas. The evidence of it is such that we allow it to be barely possible to doubt of it, but that it is as certain as that two and two make four, we do not pretend. 27 And Hartley justified his belief in the ether, stating that "if it serves to account for a great variety of phenomena, it 25 Reid writes: "It is a pity that a man of Dr. Hartley's knowledge and candour should have followed the multitude in this fallacious tract [Observations on Man], after expressing his approbation of the proper method of philosophizing, pointed out by Bacon and Newton. The last considered it as a reproach when his system was called hypothesis; and says, with disdain of such imputation, Hypothesa nonfingo. And it is very strange that Dr. Hartley should not only follow such a method of philosophizing himself but that he should direct others in their inquiries to follow it." Reid, The Works of Thomas Reid,, pp. 249-50. 26 Priestley, Examination, p. 64. 27 Ibid., pp. 57-58. Emphasis mine.

CONCERN WITH T H E NATURE OF SCIENCE

will have an indirect evidence in its favor by this means." 2 8 Reid clearly acknowledged the impossibility of attaining absolute certainty in natural philosophy in the sense that the truths of natural science are contingent rather than necessary truths; nonetheless he believed that the degree of probability attainable went far beyond Priestley's vision of a reasonable degree of evidence. He countered Priestley's sentiments with his own statement that, be they ever so plausible, it is evident in the very nature of conjectures that they are uncertain; and it is difficult to determine how much weight to give to the indirect evidence for a hypothesis based on its coherence and conformity to a necessarily limited range of experience. In fact, Reid argued, we have good reason to suspect that any human conjecture about the causes of natural phenomena will be wrong. The wisdom of God exceeds that of the wisest man to a greater degree than that by which the wisdom of the wisest man exceeds that of a small child. If a child were to speculate on how to fortify a city, or draw a battle plan, or govern a state, he would have little chance to guess correctly. How then, could we expect a human being to guess correctly how God chose to move the planets or to make our minds and bodies interact? If a thousand of the greatest wits that ever the world produced were, without any previous knowledge in anatomy, to sit down and contrive how, and by what internal organs, the various functions of the human body are carried on, how the blood is made to circulate and the limbs to move, they would not, in a thousand years, hit upon anything like the truth. 29 Only the accurate observations of anatomists could possibly lead to scientific knowledge in this case, and as far as 28

Quoted by Reid, The Works of Thomas Reid, p. 250. Ibid., p. 235. Reid's argument is by no means original. In a slightly different form, it was the central argument of the Roman Catholic C h u r c h against the Copernican hypothesis. 29

39

GROWTH OF COMMON SENSE PHILOSOPHY

Reid was concerned, as long as men continue to be mortal rather than divine, their attempts to discover the structure of God's works by speculation will be vain. Only in one very limited set of circumstances—not, according to Reid, like those under which Hartley and Priestley justified the use of hypotheses—could conjec­ ture play a significant role in establishing the kind of certitude in natural philosophy which Reid sought. Reid clarified these circumstances in response to a letter from Lord Kames, one of his frequent correspondents. Kames argued that, "Never to trust to hypotheses and conjectures about the works of God, and being persuaded that they are more likely to be false than true, is a discouraging doc­ trine, and damps the spirit of inquiry." 30 And Reid re­ sponded by saying that he did not really intend to keep men from conjecturing but rather to keep them from mis­ taking speculations for knowledge. Speculation even had a place in natural philosophy: Attending to ... a phenomenon, I conjecture that it may be owing to such a cause. This may lead me to make the experiments or observations proper for discovering whether that is really the cause or not; and if I can discover either that it is or is not, my knowledge is improved; and my conjecture was a step into that improvement. 31 It is important to realize, however, that proving that a supposed cause is sufficient to produce an effect is not evidence that it really does so. Descartes' supposition that the planets are carried around the sun in a vortex of subtle matter might have accounted for the planetary motions, but it could not even then have been accepted as knowl­ edge about the universe unless some kind of direct evi­ dence for the existence of the vortex had been produced. Reid amplified his attitude on this topic by referring to Newton's "first rule of philosophy," which demands that 30Ibid.,

p. 56.

31Ibid.,

pp. 56-57.

CONCERN WITH THE NATURE OF SCIENCE

causes of natural events should be admitted only if they are "both true and sufficient to explain the appear­ ances." 32 The rule in fact, reads, "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." Newton used it primarily to argue against the multiplication of causes, and he wrote of the rule, "to this purpose the philosophers say that Nature does nothing in vain and more is in vain when less will serve; for Nature is pleased with simplic­ ity, and affects not the pomp of superfluous causes." For most Newtonians, as for Newton himself, the rule thus served principally as a restatement of the law of par­ simony, and little attention was paid to what, if anything, Newton might have meant by this demand that a cause be not only sufficient to explain the event, but also true. Reid, however, changed the interpretation of this rule, emphasizing the demand for truth—i.e., in this case, for direct empirical verifiability. In his words, If a philosopher, therefore, pretends to show us the cause of any natural effect, whether relating to matter or to mind, let us first consider whether there is sufficient evidence that the cause he assigns does really exist. If there is not, reject it with disdain, as a fiction which ought to have no place in genuine philosophy. If the cause really exists, consider, in the next place, whether the effect it is brought to explain necessarily follows from it. Unless it has these two conditions, it is good for nothing. 33 Only if we assume that Reid meant to demand of "causes" an existence verified independently of the effect 32 Newton,

Principia, p. 398. The Works of Thomas Reid, p. 236, see also p. 250 for a reiteration of the dual requirement: "When men pretend to account for any of the operations of Nature, the causes assigned by them ought, as Sir Issac Newton taught us, to have two conditions... .First, they ought to be true, to have a real existence and not to be barely conjecturted to exist without proof. Secondly, they ought to be sufficient to produce the effect." 33 Reid,

GROWTH OF COMMON SENSE PHILOSOPHY under consideration does this whole argument make any sense at all. Thus it appears that Reid took a position very similar to that of later positivists who refused to consider the use of intermediate variables which were not directly observable as portions of an acceptable physical theory. As we shall see, it is precisely such a refusal that underlay Reid's rejection of "ideas" as intermediaries between ex­ ternal reality and "internal" mind and that provided one of the important bases for an almost universal tendency among Scottish natural philosophers to reject the Newto­ nian "aetherial media" which were so popular during the late eighteenth century.

REID'S NOTIONS OF CAUSATION AND THE AIMS OF SCIENCE To state that Reid wanted to demand that the existence of causes be proved independent of their effects is il­ luminating as long as we conceive of causes in the old Aristotelian sense of "efficient" causes, i.e., as agents which produce an effect. Reid would probably have ac­ cepted such an interpretation in the context which we have been discussing, since he felt that the "doctrine of ideas" and the hypothesis of an ether were both attempts to discover the efficient causes of phenomena. Moreover, in connection with mental philosophy in particular, Reid was concerned with retaining a notion of active agency or "efficient cause." But our statement of the preceding sec­ tion is misleading in fundamental ways, for Reid's under­ standing of the term "physical cause" was significantly different from that of his materialist opponents. It was much more closely related to Hume's notion of causality, and it precluded the possibility of discovering "efficient" causes of the kind envisaged by those who speculated about the functions of the ether. For Reid, as for all Common Sense philosophers before Hamilton, our basic belief in the notion of causation was a

CONCERN WITH THE NATURE OF SCIENCE

dictate of common sense or a law of human thought. 34 We simply cannot avoid believing that every change or event must have a cause. From the standpoint of metaphysics, Reid believed that the term "cause" shoud be reserved for a being which has the power to produce an effect and exerts that power for that purpose. 3 5 Our only notion of power comes from the consciousness of our own exertions; because our power is exerted by will, Reid claimed that only intelligent beings can be causes in the proper sense of the word. Thus Reid managed to exclude the "proper" notion of cause from all natural philosophy. 3 6 There was, however, a widely accepted sense in which the term "cause" was used by modern philosophers who acknowledged that "we have no ground to ascribe efficiency to natural causes." 3 7 This sense, most carefully articulated by David Hume, includes no implications other than temporal priority and constant spatial conjunction. In spite of the fact that Reid felt it to be an abuse of the term to give the name of causation to the mere contingent spatiotemporal relation between connected physical events, he nonetheless agreed to use the term "physical cause" (often shortened to "cause") to indicate no more than a descriptive law of nature discovered by repeated experience. He did this both because such laws "have by prescription acquired a right to that name," 3 8 and because it is absolutely necessary to have some accepted name for a relation which, in his view, is the ne plus ultra in natural philosophy. Even Bacon, Reid's great culture hero, was mistaken in believing that men might 34 Reid, The Works of Thomas Reid, p. 75; Beattie, Essay on Truth, pp. 66-67; Campbell, Philosophy of Rhetoric, p. 40; John Gregory, Observations on the Duties and Offices of a Physician; and on the Method of Prosecuting Enquiries in Philosophy (London; W. Strahan, 1770), pp. 96-98. 35 Ibid., p. 65. 36 In this belief he follows George Berkeley. See The Works of George Berkeley, Bishop of Cloyne, ed., A. A. Luce and T. E. Jessop (London; Thomas Nelson and Sons, 1948-57), iv, pp. 31-33. 37 38 Reid, The Works of Thomas Reid, p. 76. Ibid., p. 73.

43

GROWTH OF COMMON SENSE PHILOSOPHY

discover the efficiency by which natural causes produce their effects. But, according to Reid, Newton was able to see that we could never attain this end within the limits of natural philosophy. Newton, more enlightened on this point has taught us to acquiesce in a law of nature according to which the effect is produced, as the utmost that natural philosophy can reach, leaving what can be known of the agent or efficient cause to metaphysics or natural theology. This I look upon as one of the great discoveries of Newton; for I know of none that went before him in it. It has new-modelled our notion of physical causes. 39 Of course Reid was interpreting Newton in light of the Humian discussion of causation. While Newton and even Galileo before him demonstrated that natural philosophy was capable of outstanding successes when it concentrated on developing descriptive laws of natural phenomena, neither was clearly convinced that a deeper search for traditional causes was hopeless. 4 0 It was Hume's gift to the Scottish philosophers which fully turned discussions of causation in the physical world away from essential causes and toward a concern with contiguity in space and succession in time; i.e., in some sense, it turned the aims of natural philosophy from explanation to pure description. For Reid and his Common Sense colleagues, then, the true aim of natural philosophy is no more than to discover connections between phenomena and to express them as general rules called laws of nature. 4 1 The natural philosopher is not, however, content to drop his investigation 39

Ibid„ p. 76. See Newton's attempts to explain gravity. One such attempt is presented in I. B. Cohen, ed., Isaac Newton's Papers and Letters on Natural Philosophy (Cambridge, Mass.: Harvard University Press, 1958), pp. 249-254. 41 See John Gregory, Observations, pp. 103-104, and Reid, The Works of Thomas Reid, pp. 260-261. 40

44

CONCERN WITH THE NATURE OF SCIENCE

when he has discovered a large number of laws of nature, each applicable to a specific situation. The phenomena of nature are infinite in number, and human capacities, especially the memory, are very limited; consequently, if the first general principles discovered were not somehow subsumable under more general laws, our attempts to philosophize would be of little use. 42 Fortunately, God has created the world in such a way that it does operate according to exceedingly general, regular laws and he has given men an inherent drive to discover them. Thus: . . . after we have arrived at the knowledge of some general laws, by an accurate comparison and arrange­ ment of observations, we may, by comparing these laws together, discover laws of a more general nature, and, thus, by a slow and cautious induction we make ad­ vances to a knowledge of the most general laws that regulate the system of nature, in all the different de­ partments of the arts and sciences. 43 Ultimately, then, according to Gregory and Reid, the natural philosopher seeks to develop general theories which use the minimum necessary number of basic laws of nature to connect up the maximum possible number of natural phenomena, the nature of the connections going no deeper than the description of causal connections in Hume's very limited sense of cause. This kind of theory, later called "abstractive" by William M. Rankine, 44 or "reticular" by the modern philosopher of science, Rom Harre, 45 continued to be the ultimate goal sought by later Common Sense philosophers like Dugald Stewart and 42 Gregory,

Observations, p. 103. p. 104. 44 See W. M. Rankine, Miscellaneous Scientific Papers from the Transactions and Proceedings of the Royal and other Scientific and Philosophical Societies and the Scientific Journals, ed. W. J. Millar (London: Charles Griffin, 1881), p. 316. 45 R. Harre, Matter and Method (London: MacMillan Co. Ltd., 1964), pp. 9ff. 43 Ibid.,

GROWTH OF COMMON SENSE PHILOSOPHY

William Hamilton, and by their scientific followers, because it was the only form of theory which carried a guarantee of certainty based on metaphysical first principles. Such theories depend on no other assumption or principle than that the natural connections that we have observed in the past will continue to hold in the future—i.e., that God governs nature by temporally immutable laws. This principle, the so-called inductive principle, was for Reid and his followers, one of those "principles of common sense" which cannot b e rationally or empirically proved but which cannot be doubted. Thus it could provide the basis for reasoning in natural philosophy. As Reid stated: Upon this principle of our constitution, not only acquired perception, but all inductive reasoning, and all reasoning from analogy, is grounded; and, therefore, for want of another name, we shall beg leave to call it the inductive principle. It is from the force of this principle that we immediately assent to that axiom upon which all our knowledge of nature is built, that effects of the same kind must have the same cause: for effects and causes, in the operations of nature, mean nothing but signs and things signified by them. We perceive no proper causality or efficiency in any natural cause; but only a connection established by the course of nature between it and what is called its effect. Antecedently to all reasoning, we have, by our constitution, an anticipation that there is a fixed and steady course of nature; and we have an eager desire to discover this course of nature. We attend to every conjunction of things which presents itself, and expect the continuance of that conjunction. And, when such a conjunction has been often observed, we conceive the things to be naturally connected, and the appearance of one, without any reasoning, or reflection, carries along with it the belief of the other. 46 46

Reid, The Works of Thomas Reid, p. 199.

46

CONCERN WITH THE NATURE OF SCIENCE

The "inductive principle" warrants our belief in reticular theories generated by careful observation and induction; but as it obviously carries us no further toward a deeper understanding of a "necessary" or "essential" nature of causal relations, it can justify no other type of theory in natural philosophy. In spite of the lack of metaphysical rationale, a second type of theory, later termed "hypothetical" or "explanatory" or "reductionist," which was decried by Reid, came to play an increasingly important role in the methodological writings of successive Common Sense philosophers. These theories generally attempt to explain one set of facts in terms of another set of facts, which may or may not be directly observed. Such, for example, was Newton's explanation of gravitation in terms of the motions of a subtle ether and Hartley's attempt to explain mental phenomena in terms of physiological vibrations. Traditionally, such explanatory or hypothetical theories implied a deeper sense of causation or connection than that admitted by Hume and justified by the inductive principle, so they had no legitimate role in natural philosophy. As long as the primary philosophical concern with science remained focused on the process of justification rather than on the process of discovery—as it did in the work of Reid and his contemporaries because of their concern with the avoidance of error—little positive discussion of hypothetical methods could be expected. But when Common Sense Philosophy became less interested in defending traditional religious and moral positions and more concerned with developing a positive philosophy of the mind—as it did in the hands of Dugald Stewart—there was an increasing, if cautious, interest in investigating methods of gaining knowledge beyond the rigorously controlled induction of Bacon and Newton—as seen by Reid. We have already looked at Reid's reasons for opposing the use of hypothetical theories in the sciences. But Reid and John Gregory did devote a significant effort to ex-

47

GROWTH OF COMMON SENSE PHILOSOPHY

plaining why men were led into the error of hypothesizing, and their comments on this subject were developed and turned against them by later writers within the Common Sense tradition; consequently they demand some consideration here. ANALOGICAL R E A S O N I N G AND T H E P R I N C I P L E O F SIMPLICITY

Basically, according to the early Common Sense commentators, there are two major tendencies which turn men away from the sure inductive path toward knowledge: The anxiety and impatience of mankind to reduce all knowledge, and to refer all events to certain general laws, makes them unwilling to submit to this slow, but sure, method of investigation. They attempt, therefore, a shorter way of establishing those laws, in which they are misled either by a loose reasoning from imaginary analogies, or by supposing the laws of nature to be fewer and simpler than they really are. The consequences of which are, the hasty reduction of the sciences into systems, imperfect and corrupted in all their parts. 47 The problem of reasoning from analogy received Reid's greatest attention because the use of analogies between physical phenomena and mental phenomena lay at the basis of his old enemy—"the doctrine of ideas." Men naturally attempt to understand what is unfamiliar by relating it to what they know, said Reid: Thus if a man bred to the seafaring life and accustomed to talking only of matters relating to navigation enters into discourse upon any other subject, it is well known that the language and notions proper to his own profession are infused into every subject, and all things 47

Gregory, Observations, p. 105.

48

CONCERN WITH THE NATURE OF SCIENCE

are measured by the rules of navigation; and if he should take it into his head to philosophize concerning the faculties of the mind, it cannot be doubted that he would draw his notions from the fabric of the ship, and would find in the mind, sails, masts, rudder and compass. 4 8 Reid had been convinced, in part by his own investigations, and in part by the interesting arguments of George Campbell and James Beattie, his fellow members of the Aberdeen Philosophical Society, that the objects of external sense were the first concern of men, 4 9 so that when men turned to thinking of mental phenomena, they inevitably borrowed their terms and concepts from their knowledge of the material world: The condition of mankind, therefore, affords good reason to apprehend that their language and their common notions concerning the mind and its operations will be analogical and derived from the objects of the sense; and that these analogies will be apt to impose upon philosophers, as well as upon the vulgar and lead them to materialize the mind and its facilities. 50 Reid discussed three specific instances of such analogical thought which have misled philosophers into formulating the pernicious doctrine of ideas. First, "Thought is considered as analogous to motion in a body; and as bodies are put in motion by impulses, and by impressions made upon them by contiguous objects, we are apt to conclude that the mind is made to think by impressions made upon it, and that there must be some kind of contiguity between it and the objects of thought." 5 1 As an example of this conclusion, Reid quoted from Samuel Clarke, Newton's religious spokesman: 48

Reid, The Works of Thomas Reid, p. 202. See G. Campbell, Philosophy of Rhetoric, p. 304, and John Beattie, Essay on Truth, p. 97. 50 51 Reid, The Works of Thomas Reid, p. 202. Ibid., p. 470. 49

49

GROWTH OF COMMON SENSE PHILOSOPHY

Without being present to the images of the things perceived, it (the soul) could not possibly perceive them. A living substance can only there perceive where it is present, either to the things themselves (as the omnipresent God is to the whole universe) or to the images of things (as the soul of man is in its proper sensory). Nothing can any more act, or be acted upon, where it is not present, than it can be where it is not. We are sure the soul cannot perceive what it is not present to, because nothing can act or be acted upon where it is not. 52 Reid argued that several unsupportable implications about mental phenomena are hidden within this statement. First, the analogy between matter and mind leads us to assume that the mind can be spatially located like a physical object and to believe that it is seated in the brain. But no direct evidence can be adduced for either of these contentions, so they provide a very weak foundation for further philosophizing. 5 3 Second, the analogy demands what we might call a principle of cognitive contact analogous to the impact of material bodies in order for any interaction to take place. Since there must be cognitive contact and because the mind is located in the brain, we are forced to conclude that w e do not perceive phenomena in the external world directly, but that we perceive only through some mechanism which deposits "images" or "ideas" in the brain. Once more we can discover no direct proof of the existence of such images. Furthermore, it is a principle of common sense that we do perceive external objects; consequently something must be wrong with the analogy 54 —and by inference, therefore, we should not accept the validity of any argument based merely on analogy. Even if we could admit that perception cannot be accounted for except by some kind of mechanism which 52

Ibid., pp. 255-256.

53

Ibid., p. 256.

50

54

IbId., p. 257.

CONCERN WITH THE NATURE OF SCIENCE

involves ideas localized in the brain mediating between external object and mental precept, we must be on guard against accepting the implicit suggestions of the idealists' terminology, which is adopted from the physical science of optics. We cannot avoid this metaphorical or analogical language, for it is all we have, 5 5 but, "All analogical and figurative words have a double meaning; and if we are not very much upon our guard, we slide insensibly from the borrowed and figurative meaning into the primitive. We are prone to carry the parallel between the things compared further than it will hold, and thus very naturally fall into error." 56 When we speak of imagining, for example, the notion of "image" implies the real existence of that object of which an image exists. It is essential, however, to Reid, that men be acknowledged to imagine what has never existed—at least in precisely the form that it is imagined. This is in fact what distinguishes imagination from memory. Consequently, the analogical terminology is seen to complicate and obfuscate what should be accepted as a clear and simple distinction between imagining and remembering. Similarly, there is a strong tendency to think of the process of conceiving an object as being like the process by which a painter produces a picture; since, when the painter finishes, there is a physical object which continues to exist—the painting—there is a tendency to believe in the continued existence of a mental object, the conception. 5 7 But once more there is no warrant for such a belief, and it tends to raise spurious and complicating questions, like "Where is the conception stored when it is not present in consciousness?" All Reid's successors, including Stewart and Hamilton, agreed with Reid's rejection of the "ideal theory" and argued for a theory of "natural realism" in which external objects are directly perceived by the mind with no mediating objects or phenomena. But whereas Reid used 55

Ibid., p. 362.

56

IbId., p. 362.

51

"Ibid., pp. 362-363.

GROWTH O F COMMON SENSE PHILOSOPHY

its implication in the ideal theory to impugn virtually all analogical reasoning, 58 his successors found a way to reject the particular analogies which led to idealism without rejecting all analogical thought. In fact, as we shall see, starting from Reid's admission that analogical reasoning formed the initial phases of nearly all philosophizing, and that metaphorical language was fundamentally unavoidable, they built up a theory in which analogical reasoning—always carefully m o n i t o r e d and controlled —became one of the principal keys to advancement in all the sciences. Closely associated in Reid's mind with the tainted technique of analogical reasoning was the second major source of error in philosophy, "the love of simplicity, which disposes us to reduce things to a few principles, and to conceive a greater simplicity in nature than there really is." 5 9 Reid had complete faith that God governs the world in conformity with simple laws. But because he emphasized the disproportion between divine and human intellect, he could not admit that men were capable of determining what is truly the simplest mode of governance of the universe. The problem seen by Reid was closley related to the problem of evil in what was presumably the best of all possible worlds. Apparent complexity (or evil) in one context might very well be a necessary aspect of a more inclusive simplicity (or good). Consequently, men deceived themselves if they guided their researches by assuming some special principle of simplicity. 60 Basically, then, Reid believed that simplicity would be discovered in nature as evidence was collected and as nature was "put to the question in well contrived experiments," 6 1 but at the same time, he was convinced 58

Reid did allow that analogy was useful for one purpose—i.e., for answering objections against truths which have other evidence. Such, for instance, was Butler's use in The Analogy of Religion. See Reid, The Works of Thomas Reid, p. 237. 59 Ibid., p. 470. e0 61 Ibid., pp. 206-207, 470-472. Ibid., p. 472.

52

CONCERN WITH THE NATURE OF SCIENCE

that all attempts to impose some human criterion of simplicity were bound to lead to errors. In particular, the love of simplicity drove men to reduce the number of natural laws beyond what was legitimate. Thus, Descartes thought to build a complete system of material and spiritual philosophy upon two axioms, the "cogito," and the conservation of the initial quantity of notion in the material world, 62 and Newton sought to make all of the phenomena of the material world depend on attracting and repelling forces in particles of matter. 63 But subsequent investigations have demonstrated that neither of these simple systems was correct: We see, then, that although in the structure of the world, there is, without doubt, all the beautiful simplicity consistent with the purposes for which it was made, it is not so simple as the great Descartes determined it to be; nay it is not so simple as the greater Newton modestly conjecture it to be. Both were misled by analogy, and the love of simplicity. One had been much conversant about extension, figure, and notion; the other had enlarged his views to attracting and repelling forces; and both formed their notions of the unknown parts of nature from those with which they were acquainted. 6 4 Reid's attitude toward the principle of simplicity, like his attitude toward analogy, was determined largely by his need to find a metaphysical justification for statements in natural philosophy. But as was the case with his considerations of analogies, Reid's success in calling attention to the way in which the principle of simplicity had historically provided a guide to discovery in spite of its tendency to lead into error turned his successors' attention to the positive role of the principle of simplicity. Thus, as we shall see, Reid's comments provided the stimulus for the later development of a much different attitude toward the principle of simplicity than he would have encouraged. 62

IbId., p. 206.

63

IbId., pp. 206-207.

53

64

IbId., p. 207.

GROWTH OF COMMON SENSE PHILOSOPHY

With respect to the immediate issues facing Reid and his contemporaries, the love of simplicity with its consequent tendency to push men into analogical thinking seemed to have two particularly grave consequences. It led their materialist opponent, Hartley, to formulate a pernicious theory of the mind based solely on one principle, the association of ideas (which was analogous to Newton's law of attraction). But even more importantly, it led large numbers of men to expect that all laws of nature, including those of mind, should be formulatable in simple mathematical terms. Reid was particularly bothered by the attempt to mathematicize all knowledge typified in Francis Hutcheson's Inquiry Into the Origins of Our Ideas of Beauty and Virtue, 65 and he devoted great effort to distinguishing between appropriate and inappropriate objects of mathematics. This distinction depended on extensive considerations of the nature of mathematics and mathematical concepts, considerations which are important and complex enough to form the subject of the following chapter. 65

Francis Hutcheson, Znqwry Into the Origins of Our Ideas of Beauty and Virtue (London; J. Darby, 1725).

54

CHAPTER 3

Common Sense Concerns with the Nature of Mathematics MATHEMATICAL concepts and systems provided touch­ stones for several very important aspects of Common Sense Philosophy; and although there were major dis­ agreements among Common Sense philosophers regard­ ing the basic foundations of mathematical knowledge, all, with the possible exception of Hamilton, agreed on four fundamental propositions: (1) that mathematics provided one of the best historical models of how a system of know­ ledge should be organized to insure the greatest possible certainty; (2) that mathematical systems offered a con­ vincing precedent for the very notion of common-sense principles—i.e., principles at once unquestionable and unprovable; (3) that the formation of mathematical con­ cepts provided a key to understanding the nature and limitations of universal terms in all forms of discourse through an analysis of the distinctions and similarities between the concepts of mathematics and those of other fields; and (4) that mathematical knowledge differed in critical ways from knowledge of the physical and moral worlds, so that any attempt to formulate natural and moral philosophy had to take into account these differences. Mathematics was universally seen by first-and secondgeneration Common Sense philosophers as that branch of human knowledge which most successfully avoided the kind of sectarian disputes that curtailed progress and led to skepticism in other domains. For this reason, the Common Sense School (especially Thomas Reid and Dugald Stewart) diverged from its Baconain foundations to adopt an almost Cartesian stance with respect to the primacy of mathematics as a paradigmatic science. That is,

GROWTH OF COMMON SENSE PHILOSOPHY

from an analysis of the sources of mathematical certainty they sought to infer a set of criteria against which the concepts and basic principles of all other forms of reason­ ing could be measured. Reid wrote, it is in this science only, that, for more than two thousand years since it began to be cultivated, we find no sects, no contrary systems, and hardly any disputes; or, if there have been disputes, they have ended as soon as the animosity of parties subsided, and have never again been revived. The science, once firmly estab­ lished upon the foundations of a few axioms and defini­ tions, as upon a rock, has grown from age to age, so as to become the loftiest and most solid fabric that human reason can boast. 1 Mathematics, he granted, dealt with objects which were far easier to conceive of than those treated by the other sciences, but, he continued, "as this difficulty is not in­ superable, it affords a good reason, indeed, why the other sciences should have a longer infancy; but no reason at all why they must not at last arrive at maturity by the same steps. . . ." 2 If natural philosophy and the philosophy of the mind were organized and displayed in the same format as mathematics, with the whole system "reduced to axioms [or first principles], definitions, and deductions," 3 —as they certainly would be— great advantages would accrue to the critical philosopher as well as to the practitioners of the sciences themselves. They could then judge of the validity of each definition and principle and demonstra­ tion individually, and avoid the incredible complexity of judging "a mass in which they are kneaded together with­ out distinction." 4 Over and over Reid stated that if the definitions and first principles of each science were clearly pointed out and considered,"we should be better 1 Reid, 2 Ibid.,

The Works of Thomas Reid, p. 436. 3 Ibid., p. 437. 4 Ibid., p. 437. p. 437.

CONCERN WITH THE NATURE OF MATHEMATICS able to judge what stress may be laid upon the conclusions of that science." 5 If the principles were certain, as in mathematics, and the demonstrations just, then the con­ clusions would be certain. If the principles were merely probable, then one could judge the degree of probability and assent with appropriate assurance. And if they were false, dubious, or obscure, one could withhold assent and demand a revision or reassessment of the principles of the science. In fact, Reid optimistically argued that under such circumstances all human differences could be re­ duced to divergences over first principles. The reduction could then be of immense value in cutting down the vast number of disagreements among men and in locating cru­ cial areas for critical analysis. 6 THE AXIOMS OF MATHEMATICS, PRINCIPLES OF COMMON SENSE, AND FIRST PRINCIPLES OF NATURAL PHILOSOPHY The great emphasis placed on the axiomatic basis of mathematics by Euclid and by the early eighteenthcentury Scottish geometer Robert Simson provided one key to the intense Common Sense interest in mathemat­ ics. The axioms of mathematics, in fact, became the pri­ mary models for the Principles of Common Sense and for the first principles of other sciences. The two fundamental assumptions of Common Sense Philosophy—that (1) there are certain common concepts and first principles which neither need nor admit of ra­ tional justification or proof, and that (2) "all knowl­ edge got by reasoning must be built upon [these] first principles.'" 7 —are themselves unsupportable proposi­ tions, and cannot be proven in any ordinary sense of the word. Nonetheless, in seeking to convince their fellows, Beattie, Reid, and virtually all their followers needed at 5Ibid.,

p. 230.

6Ibid.,

p. 437.

7Ibid.,

p. 435.

GROWTH OF COMMON SENSE PHILOSOPHY

least some kind of plausible argument to support their assertions, and in spite of their explicit critiques of anal­ ogy, their favorite arguments came from the analogy be­ tween mathematics and all other forms of reasoning. Reid wrote: Mathematicians, before they prove any of the proposi­ tions of mathematics, lay down certain axioms or com­ mon principles, upon which they build their reason­ ings. And although those axioms be truths which every man knew before—such as, that the whole is greater than a part, that equal quantities added to equal quan­ tities make equal sums; yet, when we see nothing as­ sumed in the proof of mathematical propositions, but such self-evident axioms, the propositions appear more certain, and leave no room for doubt or dispute. In all other sciences, as well as mathematics, it will be found that there are a few common principles, upon which all the reasonings are grounded, and into which they may be resolved.8 Beattie even went on to make the historical argument that ancient Greek geometers consciously made the same dis­ tinction between Common Sense principles and reason­ ing which he and his colleagues wanted to make and that Aristotle's treatment of self-evident principles or Common Sentiments both borrowed from the ancient mathematicians and led directly to the Common Sense philosophers' distinction between common sense and reason.9 Mathematical precedents, moreover, were not confined to a general justification of appeals to a class of first princi8 Ibid., p. 230. For a nearly identical statement about the extension of geometrical patterns of reasoning to all other forms of reasoning see James Beattie, The Works of James Beattie (Philadelphia; Hopkins and Earl, 1809), ix, p. 275. 9 See James Beattie, An Essay on the Nature of Truth in Opposition to Sophistry and Skepticism (Edinburgh; Kincaid and Bell, 1770), pp. 24-25.

CONCERN WITH THE NATURE OF MATHEMATICS

pies. They were also used in numerous cases to turn aside skeptical doubts with regard to specific principles of common sense. Thus, for example, when Beattie came to refute David Hume's argument denying our ability to know our own identity, he wrote: It has been asked, how we can pretend to have full evidence of our identity when of identity itself we are so far from having a distinct notion, that we cannot define it. It might with as good reason be asked, how we come to believe that two and two are equal to four, or that a circle is different from a triangle, if we cannot define either equality or diversity. 10 Similarly, when Reid sought to justify his belief in the external existence of perceived objects, he likened the perception of objects to the apprehension of the axioms of mathematics, arguing that Simple perception has the same relation to the conclusions of reason drawn from our perceptions, as the axioms of mathematics have to the propositions. I cannot demonstrate that two quantities which are equal to the same quantity are equal to each other; neither can I demonstrate that the tree which I perceive exists. But by the constitution of my nature, my belief is irresistibly carried along by my apprehension of the axiom; and by the constitution of my nature, my belief is no less carried along by my perception of the tree. 1 1 Reid and his colleagues did agree that mathematical axioms might have a logically different status from that of the common-sense principles they wished to support. Some of the axioms of mathematics, they believed, were such that the denial of them implied a logical contradiction. Such was not the case, however, for the Principles of Common Sense. They acknowledged that it was logically 10

Ibid., p. 53. "Reid, The Works of Thomas Reid, p. 185.

59

GROWTH OF COMMON SENSE PHILOSOPHY

possible that Reid's principle of induction was wrong and that the course of nature might cease to follow the patterns it had taken in the past. Similarly, it was logically possible that there is no external world, so that our memories are no more than a delirium and our lives nothing but a dream. But, while these remained logical possibilities, such notions simply could not be seriously considered by any man in his right mind. If the Principles of Common Sense did not have quite the same status as mathematical axioms, this was even more true of the first principles of natural philosophy which still demanded assent. The first principles of natural philosophy are of a quite different nature from mathematical axioms; they have not the same kind of evidence, nor are they necessary truths, as mathematical axioms are. They are such as these: that similar effects proceed from the same or similar causes: that we ought to admit of no other causes of natural effects but such as are true and sufficient to account for the effects: these are principles which while they have not the same kind of evidence that mathematical axioms have: yet have such evidence that every man of common understanding readily assents to them and finds it absolutely necessary to conduct his actions and opinions by them, in the ordinary affairs of life. 12 George Campbell was the first of the Scottish school to state the common response to all critiques of their accepted principles: "Nothing can be juster than the reply given by Buffier, 'It must be observed,' says he, 'that to maintain propositions; the reverse of the primary truths of common sense doth not imply a contradiction it only implies insanity'. . . ." 13 The exact relationship perceived by the Common Sense philosophers between the axioms of mathematics 12 13

Ibid., p. 231. Campbell, Philosophy of Rhetoric, pp. 41-42.

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CONCERN WITH THE NATURE OF MATHEMATICS

and other kinds of first principles—including the Principles of Common Sense themselves—is difficult to analyze because the members of the school disagreed among themselves and because Reid and Stewart, who dealt most extensively with the problem, were often unclear and inconsistent. Yet their attempts to understand the similarities and differences between the definitions and axioms of mathematics and those of other forms of discourse were immensely important both within the context of moral philosophy and, later, in influencing the direction taken by mathematical study in Scotland well into the nineteenth century. The problem was crucial to the Common Sense philosophers because they needed critical techniques and criteria for analyzing the principles of sciences in order to determine both their degree of certainty and their primacy—i.e., their ability to resist resolution into more basic principles. In spite of their contention that first principles are selfevident and need no justification, Reid and all his colleagues (with the possible exception of Oswald) admitted that unless sufficient care was taken, a "vulgar prejudice" might be mistaken for a first principle. There was a remedy for the problem, however, Reid contended. "There are ways by which the evidence of first principles might be made more apparent when they are brought into dispute." 1 4 These ways could not, of course, involve demonstration. They could only involve providing proper perspectives and insightful comparisons, and no better objects for contrast and comparison existed than the certain and iireducible axioms of mathematics. It was widely agreed that one of the important criteria for certainty in mathematics depended upon the clarity, distinctness, and lack of ambiguity of the concepts or terms used in formulating mathematical propositions. If one could discover why mathematical concepts were so 14

Reid, The Works of Thomas Reid, p. 231. Emphasis mine.

61

GROWTH OF COMMON SENSE PHILOSOPHY

clear by looking at the way they were generated, then one could investigate the extent to which the procedure for determining the concepts of other domains approached or diverged from that operating in mathematics. Using this knowledge, one could then judge the probability and clarity of non-mathematical concepts. Thus, one of the important concerns of the Common Sense Philosophers was to analyze the generation of concepts in mathematics and in other fields and to compare the two processes. Two basically different attitudes toward the sources of mathematical concepts were developed among early Common Sense Philosophers; although both led to a rejection of the conflation of mathematical and philosophical reasoning which was pervasive among continental rationalists like the philosopher Malbranche and his scientific protege D'Alembert, they did so for very different reasons. One attitude completely separated the concepts and principles of mathematics from all other forms of thought and became preoccupied with criticizing virtually all attempts to apply mathematical criteria or modes of thought to other philosphical issues. The other acknowle d g e d important differences b e t w e e n mathematical knowledge and physical and moral knowledge but saw a much greater range of similarities. T H E COMPLETE D I S J U N C T I O N BETWEEN M A T H E M A T I C A L E V I D E N C E AND SENSORY E V I D E N C E — B E A T T I E , BROWN, AND H A M I L T O N

The first and simplest, but in many ways the least important, position was adopted by James Beattie and was modified only slightly by Thomas Brown and by William Hamilton. Basically, Beattie, Brown, and Hamilton separated the objects of human thought into two completely distinct categories, one containing mathematical (for Hamilton, logical) entities and the other containing objects of experience. In Beattie's words: "All the objects of the human understanding may be reduced to two classes, 62

CONCERN WITH T H E NATURE O F MATHEMATICS

viz. Abstract Ideas, and things really existing." Of abstract ideas and their relations, he said, "all our knowledge is certain, being founded on Mathematical Evidence (a) which comprehends (1) intuitive evidence, and (2) the evidence of strict demonstration." 1 5 Of things existing or supposed to exist, however, we can have only probable evidence of varying degrees of certainty. The reason that mathematical entities can be objects of certain reasoning is that they are completely divorcible from the physical existence of any object and are consequently not infected by the uncertainties which inhere in sensory objects. Brown stated the situation with respect to geometry as follows: It is from our ideas of figure that we reason, and it is of no consequence, whether these resemble real external existences. The uncertainty of other sciences is occasioned by the various qualities of objects, about which they are conversant, and by the imperfection of our organs of sense, by which we are unable to discern all of these qualities. 16 At first glance, it might appear that Beattie and Brown anticipated the twentieth-century notion that any arbitrary and supposedly self-consistent set of definitions and axioms provides a workable basis for a system of mathematics, the statements of which are demonstrably certain. That, however, was not the case. They would have agreed with Benjamin Pierce's later definition of mathematics as " t h e science which draws necessary conclusions." 1 7 "Necessary" for them, implied an absolute and exclusive claim to truth; it would have been inconceivable that two incompatible statements, each rigorously derived from a set of internally consistent first principles, could b e 15

Beattie, Essay on Truth, p. 35. '"Thomas Brown, Observations on theZoonomia of Erasmus Darwin, (Edinburgh; Mundell and Son, 1798), p. 200 note. 17 Benjamin Peirce, Linear Associative Algebra, (Washington, D . C ; National Academy of Sciences, 1870), section 1.

63

GROWTH OF COMMON SENSE PHILOSOPHY

equally true and certain. Euclid's geometry was the geometry not only because no one had chosen to present an alternative, but also because the concepts, axioms, and postulates of Euclidean geometry carried with them some special evidence of their validity. Beattie wrote, "they are simpler, perhaps, than any other, and in every case, their contraries are inconceivable." 1 8 Even though mathematical entities were considered hypothetical, the axioms of mathematics were by no means arbitrary; they could not be empirically verified, but their necessary status could be guaranteed by intuition, the ultimate arbiter of all disputes. Thus, the parallel postulate of Euclid was an absolutely incontestable truth directly intuited or, as Beattie thought more likely, logically reducible to some other first principle that would neither require nor admit of proof.19 Neither Beattie nor Brown was really able to go beyond the mere assertion of the intuitive certainty of mathematical concepts and axioms; Hamilton, borrowing in this case from his knowledge of Kantian philosophy, was able to push his analysis one step further. H e claimed that the notions of mathematics are modifications of the fundamental and necessary conditions of thought—i.e., space and time—and that this insured the necessary and certain c h a r a c t e r of m a t h e m a t i c a l p r i n c i p l e s . 2 0 H a m i l t o n ' s analysis had no material effect on the views delimited by his two predecessors, however, for it left mathematical concepts and axioms at once necessary and beyond the domain of experience. Since mathematical notions were totally independent of sensory evidence, mathematicians could not claim that such things as lines, planes, angles, triangles, etc., existed except as pure mental constructs. It was only the mutual relations and properties of these constructs which could be demonstrated. 18

19 Beattie, Works, ix, p. 275. Beattie, Works, I, p. 275. William Hamilton, Discussions on Philosophy and Literature, Education, andUniversityReform, (London; Longmans, 1853),pp.280-281. 20

64

CONCERN WITH THE NATURE OF MATHEMATICS

According to Beattie, Brown, and Hamilton, then, mathematicians purchase certainty in the development of their subject only by abdicating any claims that their con­ siderations are applicable to our concerns with the ex­ perienced world in which we live. Beattie, for example, was quite willing to acknowledge that "If. . . I were to attempt to prove, by the geometrical method, any truths in morality or in history, the attempt would be unsuccessful, and I should probably speak nonsense." 21 And Hamilton made the distinction between the domains of mathemati­ cal and other forms of scientific (philosophical) reason quite clear in stating: "Mathematics take no account of things, but are conversant solely about certain images; and their whole science is contained in the separation, conjunction, and comparison of these. Philosophy, on the other hand, is mainly occupied with realities; it is the science of a real existence, not merely of an imagined existence." 22 Hamilton, moreover, hammered home the implications of this dichotomy for the bright hopes of those who would pattern all methods on those of mathematics: "The truth of mathematics, is the harmony of thought and thought; the truth of philosophy is the harmony of thought and existence.—Hence the absurdity of all applications of the mathematical method to philosophy." 23 Thus, one of the Common Sense approaches to mathe­ matics ended in denying any applicability of mathemati­ cal methods to the natural sciences or to the science of the mind. For Beattie, Brown, and Hamilton, the fruitfulness of mathematics as a model science ended with its sugges­ tion that all sciences needed first principles. Their major concern with mathematics was to warn men against mak­ ing unwarranted inferences from mathematical systems to philosophical ones. 21 Beattie, Works, ix, p. 269. "Hamilton, Discussions, p. 279. 20 Ibid., p. 280.

GROWTH OF COMMON SENSE PHILOSOPHY HAMILTON'S ATTACK ON MATHEMATICS IN LIBERAL EDUCATION Neither Brown nor Beattie dealt with mathematics at all except in their discussions of varieties of evidence and in their arguments for the plausibility of first principles, but Hamilton became involved in a major controversy over the value of mathematical studies in liberal education. Hamilton was unique among Common Sense Phi­ losophers in his aggressive critique of mathematics, and his ideosyncratic attitudes toward mathematics as de­ veloped in this controversy had little influence on the scientists we shall be considering later. They do represent the logical extension of one Common Sense interpretation of the nature of mathematics, however, and to leave them out would be to distort the overall picture of Common Sense attitudes toward the sciences which it is one of my goals to present. In 1835, the Reverend William Whewell, who had joined John Herschel, George Peacock, and a small group of young mathematicians in introducing Continental analytic mathematics into the Cambridge tripos, pub­ lished a pamphlet entitled Thoughts on the Study of Mathematics as a Part of a Liberal Education. In this work, Whewell argued that mathematical studies (the study of algebraic or analytic mathematics as well as that of geometrical mathematics) is of paramount importance as a school for practical reasoning. In particular, he con­ trasted mathematics and logic as mind-training disci­ plines. He heavily favored mathematics and argued that the study of mathematics formed "logical habits better than Logic itself." Two major considerations moved Hamilton to write a confutation of this pamphlet in the form of a review article in the Edinburgh Review. 24 In the first place, Hamilton 2i Edinburgh Review, January, 1836, Vol. 62, pp. 409-455, reprinted in Discussions, pp. 263-340.

CONCERN WITH THE NATURE OF MATHEMATICS

was a candidate for the Logic Chair at Edinburgh and probably hoped to gain support by defending logic against Whewell's attack. In the second place, his belief in the radical disjunction between mathematics and all other forms of reasoning made him particularly antagonistic to Whewell's claim that patterns of mathematical thought were specially suited to train men for thinking about philosophical matters whether those dealt with the physi­ cal, moral, or metaphysical aspects of the world. In fact, Hamilton's view of mathematics led him to argue that "an extensive study of the mathematical sciences does not only not prepare, it absolutely incapacitates the mind, for those intellectual energies which philosophy and life require. We are thus disqualified for observation, either internal or external—for abstraction and generalization,—and for common reasoning; nay dis­ posed to the alternative of blind credultiy or of irrational skepticism." 25 Hamilton did agree with his predecessors Reid and Stewart (as is discussed in chapter 1) that a limited study of geometry provided one desirable aspect of a liberal education and that mathematics might well be studied for its use in other sciences. Buthe acknowledged no value of analytic mathematics for training the mind and opposed the notion that even geometry should be emphasized as a major element in the kind of liberal education which sought to encourage the development of the whole man in all of his potentialities. Most of Hamilton's attack on WhewelI constituted an often intemperate compilation of authorities who con­ demned mathematics as a narrowing and desensitizing study. He borrowed from such disparate figures as Goethe—"the cultivation afforded by the Mathematics is, in the highest degree, one-sided and contracted" 26 —and Frederick the Great—"As for Mathematics, I confess to you, that I fear them; they tend too much to parch the 25 Hamilton,

Discussions, p. 282.

26 Ibid.,

p. 277.

GROWTH OF COMMON SENSE PHILOSOPHY

intellect." 27 Hamilton did, however, present several sub­ stantial criticisms of mathematics as a training discipline based on his theory of the nature of mathematical con­ cepts and systems. Mathematical reasoning is solely deductive in form. Contingent, practical, or probable reasoning, however, meets most of its difficulties in the formally inductive stage—i.e., in the process of discovering the premises from which subsequent deductions may be made. "In general reasoning, therefore," Hamilton writes, "the capacities mainly requisite, and mainly cultivated, are the prompt acuteness which discovers what materials are wanted for our premises, and the activity, knowledge, sagacity, and research able competently to supply them. In demonstration, on the contrary, the one capacity culti­ vated is that patient habit of suspending all intrusive thought. . . . of observation, experiment, induction, analogy, the mathematician knows nothing." 28 Mathemat­ ics not only fails to provide guidance in those forms of reasoning most necessary for the practical man but it also desensitizes him to the complexities which he should be trained to be constantly looking for. "Mathematics stand distinguished, not merely as affording us no aid towards alleviating the evils, but as actually inflaming the disease." 29 That is, mathematics encourages the passive acceptance of first principles in order to get on with the deductive program instead of encouraging the most searching care in establishing and criticizing its princi­ ples. So much for the help mathematics can provide with respect to the formal patterns of general reasoning. What guidance can one get with respect to the vehicle—i.e., the language of common discourse—from a study of mathematics? Again, according to Hamilton, the answer was essentially none. The problems which arise out of using ordinary language are brought on by the am27 Ibid.

28 Ibid.,

p. 291-292.

29 Ibid.

CONCERN WITH THE NATURE OF MATHEMATICS

biguities of terms, by the failure to develop terms which correspond closely enough to the real entities they signify, and by the connotations which ordinary terms carry with them. Mathematical language, on the other hand, is always precise and unambiguous, implying no more nor less than its definition. And it is perfectly identical with mathematical thought; it does not have to correspond to anything but itself. 30 Thus, mathematical language and its use provide no useful precedent for the vastly more complex vehicle of ordinary discourse. On this topic, Hamilton is in complete disagreement with Reid and Stewart, who saw in the development of mathematical language an ideal pattern for the generation of universal terms and an ideal of linguistic precision to be sought even though it might be unattainable in ordinary language. Finally, we come to the "object matter" of mathematics as it relates to that of other discourse. Because the relationships between mathematical objects are necessary while those between "real" objects are contingent, a special psychological problem faces the mathematician when he moves away from the mathematical sphere to talk about physical or spiritual problems. An exclusive concern with the necessary and certain statements of mathematics conditions him to expect either that necessity and certainty must be attainable in all realms of knowledge or that if such attributes are demonstrably absent from some domain, then no knowledge can be had about that domain and he must take the skeptical position. Hamilton is certain that an overemphasis on mathematics must lead to one of these positions, even though the student may have the best of intentions. As he argues: ". . . on the one hand, as we naturally believe to exist that only which we know to exist; and on the other, as all science tends to unity, reason forbidding us to assume, without necessity, a plurality of causes; consequently the mathematician, if he thinks at all, is naturally and ratio30

Ibid, p. 291.

69

GROWTH OF COMMON SENSE PHILOSOPHY

nally disposed to hold as absolutely universal, what is universal relatively to his own sphere of observation." 3 1 Since the universal characteristic of all rightly reasoned mathematical statements is necessity, mathematicians are in some sense warranted in attributing necessity to all rightly r e a s o n e d s t a t e m e n t s . H e n c e , s t u d e n t s of mathematics are led to adopt necessitarian determinism and to deny the free will and moral liberty which underly all ethics and religion. From the same source, Hamilton argues, the student of mathematics derives the unpleasant and unwarranted trait of intellectual arrogance. Quoting from the mystic, Poiret, he writes: Mathematicians are also infested with an overweening presumption or incurable arrogance, for, believing themselves in possession of demonstrative certainty in regard to the objects of their peculiar science, they persuade themselves that, in like manner, they possess a knowledge of many of the things beyond its sphere. Then, ordinating these with the former, as if demonstrated by equal evidence, they spurn every objection to every opinion, with the contempt or indignation they would feel at an endeavour to persuade them that two plus two are not four, or that the angles of a triangle are not equal to two right angles. 32 If by some miracle the student of mathematics avoids this form of the mathematical dilemma and comes to recognize that physical and moral phenomena cannot be treated with the same certainty as mathematical theorems can, then his training, which has led him to avoid and distrust all ambigous and uncertain reasoning, inevitably pushes him toward skepticism and ultimately to the associated sin of atheism. In sum, Hamilton derived from his theory of total disjunction between mathematics and "philosophy" a 31

Ibid., p. 307.

32

Ibid., p. 305.

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CONCERN WITH THE NATURE OF MATHEMATICS

sweeping condemnation of the centrality of mathematical studies in liberal education. It led him to believe that mathematics serves no useful purpose (with the minor exception of training the mind in deductive processes) while it leads to a variety of undesirable ends.

M A T H E M A T I C A L C O N C E P T S AS ABSTRACTIONS FROM E X P E R I E N C E : R E I D AND STEWART

It is easy to understand that men like Beattie and Brown, who came to philosophy with backgrounds as poets, or Hamilton, who started out as a classical scholar, could believe in the radical independence of philosophical and mathematical knowledge. But such a belief left unexplained an important fact which could not possibly be ignored by Reid or Stewart. Both of these men were initiated early in their lives into Newtonian Natural Philosophy. Reid taught natural philosophy and Stewart taught mathematics—including applied mathematics. Thus, both were constantly bombarded with evidence that the experienced world conforms in some of its very important properties to mathematical laws. No theory of the nature of mathematical concepts and principles which left the relationships between mathematics and natural science totally unaccounted for could have have been acceptable to them. At first glance, it may appear that they subscribed to the theories of Beattie and his followers. Stewart wrote, for example: Whereas, in all other sciences, the propositions which we attempt establish facts real or supposed—in mathematics, the propositions which we demonstrate only assert a connexion between certain suppositions and certain consequences. Our reasonings, therefore, in mathematics, are directed to an object essentially different from what we have in view, in any other employment of our intellectual faculties—not to ascertain truths 71

GROWTH OF COMMON SENSE PHILOSOPHY

with respect to actual existences, but to trace the logical filiation of consequences which follow from an assumed hypothesis. If from this hypothesis we reason with correctness, nothing, it is manifest, can be wanting to complete the evidence of the result, as this result only asserts a necessary connexion between the supposition and the conclusion. In other sciences, admitting that eveiy ambiguity of language were removed, and that every step of our deductions were rigorously accurate, our conclusions would still be attended with more or less of uncertainty, being ultimately founded on principles which may or may not correspond exactly with the fact.33 On the basis of this and similar statements alone, one could not differentiate between the Beattie-BrownHamilton schools of interpretation of mathematics and the Reid-Stewart school. But when we look more closely at the writings of Reid and Stewart, we see that they did not leave mathematicians the same freedom to define mathematical entities and formulate mathematical axioms as did their colleagues. For Reid and Stewart, the suppositions or hypotheses of the mathematician had to be suggested and controlled by experience. One can see this demand in looking at Reid's criticism of James Gregory's Essay on the Difference Between the Relation of Motive and Action, and that of Cause and Effect in Physics; on Physical and Mathematical Principles. Reid wrote to Gregory: What is said about the non-existence of the objects of geometry, I think, is rather too strongly expressed. I grant that they are things conceived without regard to their existence; but they are possible modifications of things which we daily perceive by our senses. We per33

Dugald Stewart, The Collected Works ofDugald Stewart, edited by Sir William Hamilton (Edinburgh; T. Constable and Son, 1854-60), in, pp. 114-115.

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CONCERN WITH THE NATURE OF MATHEMATICS

ceive length, breadth, and thickness: these attributes do really exist. The objects of geometry are modifications of one or more of these, accurately conceived and defined. 34 In a similar vein, Stewart emphasized the ultimate source of mathematical notions in experience: "The ideas of ex­ tension of a triangle, and of equality, presuppose the exer­ cise of our senses. Nay, the very idea of superposition involves that of motion, and, consequently, (as the parts of space are immovable), of a material triangle." 35 Reid and Stewart thus held what appear to be incompat­ ible beliefs: 1) mathematical entities are derived from and hence do correspond in some way to experienced objects, and 2) mathematical notions are not susceptible to the same kinds of uncertainties as others are, because they do not demand exact correspondence with fact. Both Reid and Stewart were aware of the seeming inconsistency of their attitude toward mathematics, and they developed a twofold line of reasoning to justify their beliefs. Neither aspect of the attempt was completely satisfactory, but together they led to interesting and important implica­ tions for the prospective student of mathematics in Scot­ land. Basically, Reid and Stewart argued that mathematical ideas are separated from their sensory context by a process of abstraction and generalization. This process allows mathematicians to construct mathematical concepts in such a way that they are not influenced either by the fact that physical objects may not exhibit perfectly such attri­ butes as straightness, circularity, and tangency, or by the fact that our senses may provide imperfect or uncertain information about many qualities of real bodies. Once this argument was made, they contended that the particular 34Reid, letter to James Gregory, published in Reid, The Works of Thomas Reid, p. 77. Emphasis mine. 35Stewart, Works, pp. 150-151.

GROWTH OF COMMON SENSE PHILOSOPHY

properties of bodies on which mathematical reasoning does depend (all other uncertain properties having been abstracted away) can be perfectly known and do correspond to the concepts constructed by the mathematicians.

ABSTRACTION AND CONCEPT FORMATION

The Reid-Stewart interpretation of mathematics depended upon a theory of the use of language and signs which was first developed among Common Sense philosophers by George Campbell in his Philosophy of Rhetoric and which was elaborated both by Reid and by Stewart. Theirs was basically a nominalist doctrine which argued that all general or "universal" terms, which provide the basis for most advanced human communication, are formulated by the human understanding to signify or represent classes of particular objects, qualities, events, or actions which are perceived to be similar in some way. Men have no experience except of particular or individual things, but they do have a remarkable ability to notice that two or more things, each of which must be in some sense unique, agree in some property or quality. Thus, men are able to classify objects, based on their similarities, into successively more general classes—traditionally termed species and genera.36 Classification, of course, depends upon our ability to separate certain aspects in which different entities agree from the rich and complex field of experience. This ability, Stewart called abstraction, and he wrote: ". . . as Abstraction is the groundwork of classification, without this faculty of the mind, we should have been perfectly incapable of general speculation, and all our knowledge must necessarily have been limited to individuals, and 36 See Campbell, Philosophy of Rhetoric, pp. 259-265; Reid, Works, pp. 390-391; Stewart, Works,u, pp. 162-163.

74

CONCERN WITH THE NATURE OF MATHEMATICS

some of the most useful branches of science, particularly the different branches of mathematics, in which the very subjects of our reasoning are abstractions of the understanding, could never have possibly had an existence." 3 7 The nature of the abstractive faculty and its implications for mathematics as understood by Reid and Stewart were clearly presented in an anonymous and undated essay on mathematics discovered among the Hume Papers at the Royal Society of Edinburgh. It begins: To reason abstractly is to reason from certain properties, affections or relations of objects, without regard to others of the same objects; whether these, we neglect, be, or be not, separable from those we regard . . . . When a carpenter examines a tree, he considers the hardness, strength, grain, colour, etc., of the wood, and concludes that it is better for this than for that kind of work. A physician, neglecting these properties, examines the taste, smell, and chemical analysis, its effects upon animal bodies, particularly the human, and from such examination determines its effects in medicine. The geometrician regards none of these, but confines himself to number, figure, length, breadth, and thickness. 3 8 T h e author of this essay goes on to acknowledge Hume's contention that men may never see perfectly straight lines or perfect right angles evidenced in the physical world and that they would have no way of knowing if they did so. But, he argues, this does not hinder them from developing a perfect geometry since the mind in some sense creates its own mathematical concepts based on (but not totally limited by) sensory considerations. Thus, he writes that in pure abstract geometry, while we "Stewart, Works, n, pp. 162-163. Lionel Grossman, "Two Unpublished Essays on Mathematics in the Hume Papers," Journal of the History of Ideas, 21 (1960), p. 446. 38

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GROWTH OF COMMON SENSE PHILOSOPHY

have our ideas of such things as lines and surfaces from real things, We reason neither from a real, nor an apparent, but a supposed construction. And we are satisfied that a dem­ onstration is just when the conclusion depends only on what is required in the supposition. To demonstrate that the sum of three angles of a triangle is equal to two right angles, a triangle is sup­ posed, and represented, perhaps on paper. And because the conclusion is drawn from the supposed figure only, not from what is real, or apparent, in the representation, therefore, we have full satisfaction without repeating the demonstration: on wood, marble, or metal. And be­ cause no determinate length, or position of the sides are required in the supposition, or referred to in the dem­ onstration, therefore, we are satisfied that the proposi­ tion is universal: without repeating the demonstration on triangles of various magnitudes and constructions. 39 Reid agreed in all essential points with this document, and in his own response to Hume's critique of the empiri­ cal foundations of mathematics he wrote: I agree with this acute author [Hume], that, if we could form no notions of points, lines, and surfaces, more accurate than those we see and handle, there could be no mathematical demonstration. But every man that has understanding, by analyzing, by abstracting, and com­ pounding the rude materials exhibited by his senses, can fabricate, in his own mind, those elegant and accu­ rate forms of mathematical lines, surfaces, and solids. 40 One very important point should be made about this doctrine of abstraction. It demands a very significant act of judgment, and the mathematical concepts which result 39 Ibid.,

pp. 447-448.

40 Reid, Works,

p. 452.

CONCERN WITH THE NATURE OF MATHEMATICS

are in some way more perfect than the sensory information which suggest them. In Reid's terms, the mathematical concepts are "accurate and elegant forms which the senses never did nor can exhibit." 4 1 Neither Campbell, Reid's colleague, nor Stewart, his follower, was completely satisified with Reid's interpretation of abstraction in connection with mathematics because it smacked too much of the conceptualist doctrine which allowed the mind an almost unlimited power to mold and combine its ideas. Nonetheless, in order to avoid the Humian charge which could be leveled at an empiricist mathematics, they had to acknowledge that the concepts of mathematics provided by abstraction really were separated from physical existence. Thus, while Stewart claimed that the notion of superposition depended on our knowledge of material triangles, he adopted a peculiar definition of material: "The material triangle itself, as conceived by the mathematician, is the object, not of sense, but of intellect. It is not an actual measure, liable to expansion or contraction, from the influence of heat or cold; nor does it require, in the ideal use of it which is made by the student, the slightest address of hand or nicety of eye." 4 2

T H E SPECIAL NATURE O F MATHEMATICAL E N T I T I E S

To explain precisely how men could develop perfect, immutable mathematical concepts on the basis of their sensory experience of an imperfect, changing material world, without allowing such scope to the intellect as Reid had implied, Stewart was forced to assert that the particular qualities of sensible objects which mathematicians chose to study were metaphysically distinct and distinguishable from all other qualities of matter. 41

lbid., p. 419.

«Stewart, Works, in, p. 151.

77

GROWTH OF COMMON SENSE PHILOSOPHY

The other qualities—those studied by the natural philosopher, for example—could never be separated by abstraction from the physical existence of bodies. But those qualities considered by the mathematician not only could but inevitably had to be dissociated from material­ ity. "Of these mathematical affections (magnitude and figure)," Stewart wrote: Our first notions are no doubt derived (as well as of hardness, softness, roughness, and smoothness) from the exercise of our external senses: but it is equally certain, that when the notions of magnitude and figure have once been acquired, the mind is immediately led to consider them as attributes of space no less than of body; and (abstracting them entirely from the other sensible qualities perceived in conjunction with them) becomes impressed with an irresistible conviction, that their existence is necessary and eternal, and that it would remain unchanged if all bodies in the universe were annihilated. 43 Stewart could not say why men believed in the immuta­ bility of mathematical affections and in their separable existence. Like Newton speaking of gravity, he simply had to say: "It is with the fact alone that we are concerned at present: and this I conceive to be one of the most obviously incontrovertible which the circle of our knowledge embraces." 44 Just as one peculiarity of the mathematical properties of bodies insured that those properties could not be tainted with the uncertainties associated with sensations, an­ other insured that sensed facts of nature could be rein­ tegrated with mathematical statements. The special properties of mathematical qualities not only allow the derivation of purely intellectual notions from experience but they also guarantee that the results of reasoning 43 Ibid.,

p. 145.

44 Ibid.

CONCERN WITH THE NATURE OF MATHEMATICS

done upon these mental entities will conform to the do­ main of reality from which its initial concepts come. Again in Stewart's words: This remarkable and indeed singular coincidence of propositions purely hypothetical, with facts which fall under the examination of our senses is owing .. . to the peculiar nature of the objects about which mathematics is conversant and to the opportunity which we have (in consequence of that measurability which belongs to them) of approximating nearly to the truth, the data from which we are to reason in our practical operations, to those which are assumed in our theory. 45 The notion of measurability presented here brings us back to Reid's earlier discussions of mathematics. Though Reid was not driven to it by the same logic as his protege was, he too argued that the qualities of material bodies considered by mathematicians were radically different from those considered by non-mathematical natural philosophers. In fact, in his first published work, "An Essay on Quantity: Occasioned by Reading a Treatise in which Simple and Compound Ratios are Applied to Vir­ tue and Merit," (1748), Reid argued that measurability is the distinguishing characteristic of mathematical entities and that by analyzing what can and cannot be measured we can determine the proper range of applicability of mathematical arguments and avoid some of the absur­ dities which arise out of trying to reason mathematically about inappropriate objects. "Mathematics," Reid stated, "deals with quantity, defined as what may be measured." 46 Some quantities are unique in the sense that they are measured by their own kind. Such quantities, called proper quantities, may all be reduced to three kinds, extension, duration, and number. 47 45 Ibid.,

p. 155.

46 Reid, Works,

p. 715.

«Ibid., p. 716.

GROWTH OF COMMON SENSE PHILOSOPHY

In the "Essay on Quantity," Reid did not satisfactorily explain why these self-measuring qualities should provide grounds for more certain knowledge than any other set would. He merely argued that all quantities which can be dealt with through mathematics are proper quantities or may be measured by proper quantities—as velocity is measured by extension and duration—and asserted that the clearness and certainty of mathematics raises from the nature of these fundamental proper quantities. 4 8 But in his major books, An Inquiry into the Human Mind on the Principles of Common Sense (1764) and Essays on the Intellectual Powers of Man (1785), Reid greatly expanded his consideration of both the origin and the special nature of mathematical entities by analyzing the sources of the notion of extension in touch. Basically, Reid appealed to the old distinction, revived by Locke, between primary and secondary qualities. Most sensory knowledge is of secondary qualities like color, smell, sound, etc. These qualities do not belong to the objects of sense themselves but are produced in the perceiving subject through some kind of process about which we can have only probable knowledge. There are other qualities—called primary qualities—which do belong to the objects of perception themselves; according to Reid, the primary qualities admit of intuitive and certain knowledge. F u r t h e r m o r e , mathematics deals with primary qualities: There are no different opinions about the nature of extension, figure, or motion, or the nature of any primary quality. Their nature is manifest to our senses and cannot be unknown to any man. . . . The primary qualities are the objects of the mathematical sciences, and the distinctness of our notions of them enables us to reason demonstrably about them . . . their various modifications are thereby capa48

Ibid., pp. 716-717.

80

CONCERN WITH THE NATURE OF MATHEMATICS

ble of being compared, and their relations determined with precision and certainty. 49 Reid was fully aware of Hume's and Berkeley's attacks on the distinction between primary and secondary qual­ ities. And in order to justify his contention that such a distinction does truly hold, he provided a long discussion of extension in which he ultimately had to appeal to com­ mon sense against the teaching of philosophers. Exten­ sion, like the other primary qualities, is suggested to us by sensations in a rationally inexplicable way but with such force and clarity that its nature simply cannot be doubted by a sane man. The primary qualities, he admitted, "do not at all tally with any system of the human faculties that have been advanced. They have no resemblance to any sensation or to any operation of our minds; and therefore, they cannot be ideas either of sensation or reflection. The very conception of them is irreconcilable to the principles of all our philosophic systems of the understanding." But, "the belief of them is no less so." 50 The only way to understand how we get the notions of primary quantities associated with touch is to realize that "the feelings of touch, which suggest the primary qual­ ities, have no names, nor are they ever reflected upon. They pass through the mind instantaneously, and serve only to introduce the notion and belief of external things, which, by our constitution are connected with them. They are natural signs, and the mind immediately passes to the thing signified, without making the least reflection upon the sign, or observing that there has been any such thing." 51 Whether one agrees with either Reid's analysis of the nature of mathematical qualities or with Stewart's modifi­ cation that further distinguished extension, number, and 49Ibid., 51Ibid.,

p. 315. p. 126-127.

50Ibid.,

p. 126. Emphasis mine.

GROWTH OF COMMON SENSE PHILOSOPHY

figure from the traditional primary qualities of hardness and roughness, it is very clear that their considerations had several important implications with respect to the proper domain of mathematical reasoning and for the study of mathematics, per se, in Scotland. The most important implication for the non-mathema­ tician arose from the fact that only subjects which could be clearly tied to extension, number, and duration were proper concerns for mathematical reasoning. This restric­ tion caused little problem for natural philosophers, since such concepts as velocity, momentum, density, tempera­ ture, elasticity, and force could all be easily related to counting operations or measurements of length and time. But it did provide a major critique of those who hoped to develop quantitative methods for moral considerations. This was true not only for Continental rationalists in the Cartesian or Leibnizean traditions but also for British empiricists like Francis Hutcheson, whose Inquiry Into Our Ideas of Beauty and Virtue had provided the occa­ sion for Reid's initial "Essay on Quantity," and James Gregory, who had tried to put anti-necessitarian moral philosophy on a firm scientific foundation in his Essay on the Difference between the Relation of Motive and Action and that of Cause and Effect in Physics; on Physical and Mathematical Principles (1792). Reid and Stewart condemned such attempts to apply mathematics to moral philosophy. They pointed out that such notions as taste, smell, beauty, pleasure, wisdom, folly, etc. may well admit of degrees but that none of them has been reduced to measure and properly associated with extension, duration, or number. Until such time as "our affections and appetites shall be themselves reduced to quantity, and exact measures of their various degrees be assigned, in vain shall we essay to measure virtue and merit by them. This is only to ring changes on words and to make a show of mathematical reasoning without ad­ vancing one step in real knowledge." 52 52 Ibid.,

p. 24.

CONCERN WITH THE NATURE OF MATHEMATICS Perhaps even more important than the argument pro­ hibiting the application of mathematics directly to mental and moral phenomena was the extension of this argument to deny the propriety of using physical arguments in the moral sphere. The fact that the physical relations between forces and motions could be properly dealt with mathe­ matically because of the measurable nature of the proper­ ties involved, conjoined with the fact that mental and spiritual phenomena could not be assigned measures, provided a compelling argument against employing phys­ ical analogies in connection with moral concerns. This line was taken by Reid in criticizing James Gregory's attempt to compare the willful acts of a human being subject to conflicting motives with the motion of a body subject to conflicting forces. Gregory had discussed the case of a man offered varying sums by two people to carry a letter in two different directions and had concluded (arguing from the parallelogram of force law) that he would walk along the diagonal between the two direc­ tions weighted by the rewards offered. Reid pointed out the absurdity of this argument—since the man would then reach neither destination and would be paid nothing. Because such quantitative arguments lead to palpably absurd conclusions, the supposition that motives are like the physical causes of action must be false. 53

IMPLICATIONS OF THE REID AND STEWART VIEWS FOR MATHEMATICS PER SE Reid, as we have seen, associated mathematical ideas with the primary qualities of bodies and insisted that those primary qualities were all suggested by touch rather than by any of the other senses. It would seem, then, that all mathematics must be based on and relate to tactile experience. But Reid knew that geometers frequently use visible figures in the course of developing their demon53Ibid.,

p. 85.

GROWTH OF COMMON SENSE PHILOSOPHY

strations, and he knew that mathematics is applied to problems in natural science in which visual rather than tactile data provide the basis for reasoning (all mathemati­ cal astronomy, for example, depends on reasoning about magnitudes interpreted by the eye rather than by the sense of touch). George Berkeley's interpretation of these circumstances led Reid to a fascinating discussion of the relationships between "visible" extension and tangible or real extension, or, in his terms, between the "geometry of visibles" and real magnitude. Reid's discussion of these relationships apparently had little or no direct influence upon students of mathematics, but it is worth considering in some detail for two reasons. First, it contains a curious discussion of one of the earliest forms of non-Euclidean geometry; one in which straight lines intersect in two points. Secondly, it provides a spe­ cial and limited illustration of a question which was raised in a much more important general form by Dugald Stewart. This is the question of how mathematical reasoning can be justified when its objects are not obviously and im­ mediately connected with those special mathematical quantities, extension, duration, and number, suggested through tactile experience. In Stewart's hands this ques­ tion formed the basis of a strong and influential critique of analytic mathematics—that science in which mathemati­ cal symbols were used and manipulated with little or no consideration for their meaning or referents. Reid's goal was a much more limited one of refuting Berkeley's claim that tangible and visible extension are quite different things, related to one another only by the mind which perceives both. Reid praised Berkeley for being the first to recognize that visible and tangible extension were not identical, saying, He made the distinction between that extension which we perceive by sight only, and that which we perceive by touch; calling the first visible, the second, tangible

CONCERN WITH THE NATURE OF MATHEMATICS

extension and figure. He showed, likewise, that tangible extension and not visible is the object of geometry, although mathematicians commonly use visible diagrams in their demonstrations. 5 4 But Reid could not agree with Berkeley that the two forms of extension became associated only through human experience. If Berkeley's contentions were accepted, then objects seen and objects touched would be fundamentally different objects connected to one another only through the simultaneity of their presence in the mind of the perceiver. This possibility directly contradicted the common-sense belief in an external reality whose visible and tangible manifestations are necessarily connected through objects themselves. Reid's major argument against the independent and equivalent status of visible and tangible extension and figure arose out of the fact that while our visual experience leads us automatically to think about tangible magnitude, our tactile experience almost never leads in the opposite direction. Thus, Reid argued: "While that figure and that extension which are objects of touch have been tortured ten thousand ways for twenty centuries, and a very noble system of science [Euclidean Geometry] has been drawn out of them, not a single proposition do we find with regard to the figure and extension which are the immediate objects of sight." 55 The only way to explain this drastic asymmetry between visual and tactile experience, Reid believed, was to accept that tactile experience and tangible figure and extension are more fundamental—as his consideration of primary qualities had already established—and that visible figure and extension are derivative. In fact, he argued, visible figure was intended by nature to serve merely as a sign of the tangible figure of bodies. And nature, "hath taught us, by a kind of instinct, to put it always to this use. 54

Ibid., p. 282.

55

Ibid., p. 147.

85

GROWTH OF COMMON SENSE PHILOSOPHY

. . . It is as unnatural to the mind to stop at the visible figure, and attend to it, as it is to a spherical body to stop upon an inclined plane. There is an inward principle, which constantly carries it forward, and which cannot be overcome but by a contrary force." 56 To illustrate just how completely men have passed over visible extension in their rush to consider the tangible extension which it signifies, Reid pointed out that even mathematicians had remained unaware of the fact that the visible figures which they have before them when they demonstrate geometrical theorems have radically different properties from those of the tangible figures to which the proofs truly apply. In the geometry of visible extension, Reid assumed that the basic definitions of point, line, angle, and circle were the same as in ordinary Euclidean geometry. Next he supposed the eye placed at the center of a sphere. Every great circle of the sphere would then appear to the eye as a straight line, for the eye cannot perceive curvature in the plane formed by the rays of light moving from the circle to the eye. In turn, every visible right-line segment would correspond to a portion of a great circle of a sphere centered on the eye. Among the consequences of these circumstances, Reid noted some propositions with regard to visible figure and space which, he said "are not less true nor less evident than the propositions of Euclid, with regard to tangible figure." For example, "Any two right lines being produced, will meet in two points, and mutually bisect each other." And, "If two lines be parallel, that is, everywhere equally distant from each other, they cannot be straight." 57 These two statements, of course, contradict Definition 23 and Postulate 1 of Euclid's Elements, which establish respectively the existence of straight parallel lines and that two straight lines may not enclose a space. Thus, Reid claimed to have shown that a geometry based on visible extension alone would differ fundamentally from the ac56

Ibid., p. 146.

"Ibid., p. 148.

86

CONCERN WITH THE NATURE OF MATHEMATICS

cepted geometry. That men had not developed such an alternative offered presumptive evidence that visible ex­ tension does not have the ability to command human concern in the same degree as does tangible extension. In the course of his argument Reid produced one of the first suggestions that a non-Euclidean geometry might be pos­ sible. Buthe withdrew from this suggestion because of his belief in the primacy of tangible experience; and it seems that no student of mathematics chose to exploit this possi­ bility as a result of Reid's comments. Not even the editor of Reid's Collected Works, Sir Wil­ liam Hamilton, really recognized the significance of Reid's presentation. Hamilton saw thatthe visual implica­ tions of a "geometry of visibles" were directly derivable from Euclidean geometry and corresponded to the socalled "doctrine of perspective" which had been well developed since the late Renaissance. What Hamilton missed was the fact that the correspondence between the visual consequences of Reid's geometry of visibles and the Euclidean doctrine of perspective did not invalidate Reid's argument. In fact, Reid would have been in serious trouble if they had not corresponeded, for one of the things he wanted to show was that visible and tangible extension were not independent as Berkeley had claimed. Fundamentally, Reid wanted to show that if we base our arguments on visual experience only, we will logi­ cally be led to develop a non-Euclidean geometry; a geometry from which proper inferences about tangible experience could not be made. Furthermore, he simply wanted to point out that mathematicians had not bothered to develop such a geometry. On the other hand, he in­ sisted that if we reason from concepts abstracted out of tangible experience, we can develop a geometry which accounts not only for the properties of tangible experience but also for those of visual experience. He wrote: Supposing external objects to exist, and to have the tangible extension and figure which we perceive, it

GROWTH OF COMMON SENSE PHILOSOPHY

follows demonstrably, from the principle now mentioned, that their visible extension and figure must be just what we see it to be. The rules of perspective, and of the projection of the sphere, which is a branch of perspective, are demonstrable. They suppose the existence of external objects, which have a tangible extension and figure; and, upon that supposition, they demonstrate what must be the visible extension and figure of such objects, when placed in such a position and at such a distance. Hence, it is evident that the visible figure and extension of objects is so far from being incompatible with the tangible, that the first is a necessary consequence from the last in beings that see as we do. 58 That visible magnitude can b e derived from tangible magnitude not only destroys Berkeley's argument for their logical independence (which was Reid's major aim). It also has a more important implication for our present purposes. It guarantees the legitimacy of mathematical reasoning about visible entities by establishing a one-toone correspondence between visible quantities and the more fundamental proper quantities, tangible figure and extension. Thus, for one case, Reid has shown that mathematical reasoning may be used in a domain which considers something other than proper quantities. It is this latter demonstration which is particularly important in light of Dugald Stewart's subsequent discussions of the applications of mathematical reasoning. STEWART'S ATTACK ON ANALYSIS

Because the certainty of mathematical knowledge arises in large measure out of its connection with the primary (for Stewart, the mathematical) qualities of matter 58

Ibid., p. 326.

88

CONCERN WITH THE NATURE OF MATHEMATICS

rather than out of the hypothetical-deductive nature of the demonstrations alone, it is crucial that some power of the mind other than mere mechanical and logical reasoning be applied to insure that mathematical reasoning does not stray from its appropriate objects or extend beyond those circumstances to which it may be suitable. This is particu­ larly true because mathematical concepts are both ab­ stract and uncommonly general—i.e., they are applied to a vast variety of specific entities—and because, according to a long-accepted Common Sense doctrine, abstract and general terms are peculiarly susceptible to misinterpreta­ tion. George Campbell had developed this doctrine in his Philosophy of Rhetoric. He argued that since general terms must encompass great numbers of individuals, they demand extensive knowledge for their correct interpreta­ tion. Furthermore, since abstract terms are assigned to qualities which are never really perceived independently or by themselves, they are particularly difficult to inter­ pret. "It is no wonder," he says, "that misapplication of such words, whether general or abstract, should fre­ quently escape our notice. The more general any word is in its signification, it is the more liable to be abused by any improper or unmeaning application.... When the rightful applications of a word are extremely numerous, they can­ not all be so strongly fixed by habit, but that, for greater security, we must perpetually recur in our minds from the sign to the notion of the thing signified." 59 Stewart took Campbell's doctrine and applied it di­ rectly to the concepts of mathematics. The geometrical terms "line," "plane," and "surface," interpreted as signs, could easily be referred to the things which they signified. But the terms or symbols of algebraic or analytic mathe­ matics provided a much greater problem. Some of them, like the square root of minus 1, were virtually impossible 59 George

Campbell, Philosophy of Rhetoric, p. 270.

GROWTH OF COMMON SENSE PHILOSOPHY

to interpret, for they seemed related to no external objects or attributes of space and certainly not to the primary (mathematical) qualities which were the true and proper objects of mathematical concern. Unlike Reid's "geome­ try of visibles," algebra and analysis seemed riddled with philosophically unjustifiable arguments. Stewart wrote: In algebraical investigations, it is well known that the practical application of a general expression, is fre­ quently limited by the conditions which the hypothesis involves, and that in consequence of a want of attention to this circumstance, some mathematicians of the first eminence have b e e n led to adapt the most paradoxical and absurd conclusions. Without th[e] most cautious excercise of the judgment, in the interpretation of the algebraical language, no dexterity in the use of the cal­ culus will be sufficient to preserve us from error. 6 0 As an example of the problems which can arise in analysis because the domain of its applicability is not constantly checked, Stewart cited Laplace's discussion of the apparent paradox which arises in summing the series expansion of 1/(1 +x) when χ becomes 1. The fraction obviously becomes V2, b u t the series becomes 1 — χ + χ 2 — jc3 . . ., etc. By taking the terms two by two, the series is transformed into another, each term of which is zero; so one arrives at the paradox that 1/2 = O. 6 1 Geometry, unlike algebraic analysis, is protected against such problems through its constant reference to the things signified by its terms. Thus, " I n geometry we are not liable to adopt the same paradoxical conclusions as in algebra, because the diagrams to which our attention is directed serve as a continual check on our reasoning powers. These diagrams exhibit to our very senses a variety of relations among the quantities under consideration, which the language of algebra is too general to express." 6 2 ei

""Stewart, Works, π, p. 178. Stewart, Works, II, p. 178.

e2

90

Stewart, Works, iv, p. 204.

CONCERN WITH THE NATURE OF MATHEMATICS

Stewart's argument that the excessive generality of algebraic symbols cast doubt upon the results of algebraic mathematics formed the basis for at least one major Scottish mathematician's emphasis upon geometrical rather than analytic mathematics, as we shall see in Chapter 7. Together with the general pedagogical argument in favor of geometry expressed by all the Common Sense philosophers it goes a long way toward explaining the continuing predilection for geometrical arguments among mathematical physicists like James Clerk Maxwell and William M. Rankine who received their early scientific training in the Scottish University system or from its graduates before being introduced to analysis.

T H E FRENCH COUNTERVIEW

If Common Sense ideas about the foundations of mathematics in fact played a significant role in maintaining the Scottish emphasis on geometry rather than analytic mathematics, we should expect to find much different attitudes toward the nature of mathematics among those who contributed substantially to the development of analysis. Two obvious cases show this to be true. The first systematic texts introducing Leibnizian calculus into France and emphasizing the algebraic treatment of problems which had traditionally been presented in Euclidean form were written by a group of scholars gathered around Nicholas Malbranche, 6 3 the famous Cartesian metaphysician. Out of this group, for example, came Ie Marquis de l'Hopitai's L'analyse des infiniment petits in 1694, N. Guisnee's Application de Valgebre a la geometrie, ou Methode de demontrer par Valgebre, les theorems de geometrie et d'en resoudre et construire tous les problems in 1705, the Abbe Reyneau's Analyse 63 See Andre Robinet, "Le Groupe malbranchiste, introducteur du calcul infinitesimal en France," Revue d'histoire des Sciences, 13(1960), 287-308.

91

GROWTH OF COMMON SENSE PHILOSOPHY

demontree in 1714, and the Elemens de mathematiques de Monsieur Varignon in 1731. These were the principal textbooks of analysis during the first half of the eighteenth century, and all were written by men who followed Malbranche in believing that the laws of mathematics consti­ tuted the intelligible aspects of God revealed by Him to the minds of men. For these Continental scholars, mathematics was thus, in a very important degree, super­ natural and totally independent of the sensory world; 64 and there was no need to puzzle over the possible sensory referents of analytic symbols. Much more interesting, both from our point of view and for the subsequent development of the exact sciences, are the attitudes toward the foundations of mathematics held by Jean D'Alembert and his pupil, Joseph Louis La­ grange. Like Reid and Stewart, D'Alembert and Lagrange were influenced by the sensationalist philosophy of John Locke and believed that mathematical concepts were ac­ quired by a process of abstraction from experience. But the French analysts split radically from the Scots with regard to the consequences of this process of abstraction. The Scots, as we have seen, believed that the more gen­ eral and abstract a notion was, the more susceptible of misinterpretation and obscurity. Therefore, for them, geometry was more rigorous than algebra because the diagrams of geometry provided a check on the misin­ terpretation of geometrical concepts. D'Alembert, on the other hand, argued for the greater value and certainty of the more abstract concepts: Indeed, there is a sort of gradation and shading, so to speak, to be observed in the enlightenment which these sciences [algebra, geometry, and mechanics—which 64See Leon Brunshvieg, Les Stapes de la philosophie mathematique (Paris; F. Alcan, 1912), pp. 130-138. I am indebted to Thomas L. Hankins, Jean D'Alembert: Science and the Enlightenment (Oxford; The Clarendon Press, 1970), pp. 19-21 and 126-127, for my introduction to the Malbranchiste school's concern with analysis.

CONCERN WITH THE NATURE OF MATHEMATICS

D'Alembert placed among the mathematical sciences] bestow upon our minds. The broader the object they embrace and the more it is considered in a general and abstract manner, the more also their principles are exempt from obscurities. It is for this reason that geometry is simpler than mechanics and both are less simple than Algebra. 65 The immense impact which this philosophical pre­ dilection for the simplicity of algebraic in contrast to geometrical arguments had on Continental physics is most clearly illustrated by Lagrange's boast at the begin­ ning of his Mechanique Analytique, one of the most in­ fluential books in the history of mechanics. Mirroring D'Alembert's sentiments, Lagrange prided himself on the fact that "One will find no figure in this work, the methods I set forth demand neither constructions nox geometrical or mechanical reasonings, but only algebraic operations subject to a regular and uniform series of steps. 66 It is inconceivable that such a boast would have been made by a man trained in the Scottish tradition. 65 Jean D'Alembert, Preliminary Discourse to the Encyclopedia of Diderot, translated and edited by Richard N, Schwab (Indianapolis; Bobbs-Merrill, 1963), from the 1751 original, pp. 26-27. Emphasis mine. 86 Joseph Louis Lagrange, Mechanique Analytique in Oeuvres de Lagrange (Paris; Gouthier-Villars, 1867-92), Vol. 11, p. 3. Emphasis mine.

CHAPTER 4

A Change in Mood: Dugald Stewart, Thomas Brown, and the Acceptance of Hypothetical and Analogical Methods in Science ALTHOUGH Common Sense philosophers differed in their interpretations of the nature of mathematics, there was no steady temporal growth within their philosophy of mathematics. When we turn to analyze Common Sense attitudes toward the proper methods of natural science, however, we find not only differences but also development. Certainly, many of the central canons of scientific method articulated by Reid were openly and enthusiastically embraced by second- and third-generation Common Sense philosophers. Both Dugald Stewart and Thomas Brown, 1 for example, continued to laud the inductive method of Bacon and of Newton. 2 Both followed Reid in adopting the Humian definition of causation as the only intelligible meaning of the word in natural science. 3 Thus, they decried as fruitless the search to understand 1

MoSt students of Common Sense Philosophy have emphasized the differences between Stewart's and Brown's systems of thought, in part because Brown's Lectures on the Philosophy of the Mind were often formulated explicitly as critiques of Stewart's opinions. I acknowledge that great differences exist and will return to discuss some of them later, but, for now, I wish to emphasize shared characteristics and attitudes. 2 See Stewart, Elements of the Philosophy of the Human Mind, in Works, III, pp. 230-250, especially p. 249 where Bacon and Newton are paired just as in Reid's works; and Brown, Lectures on the Philosophy of theHumanMind, 19th ed. (Edinburgh: Adams and Charles Black, 1851), I, pp. 107-109. 3 Stewart wrote, "In natural philosophy, however, when we speak of one thing being the cause of another, all we mean is that the two are

94

D U G A L D STEWART AND THOMAS BROWN

the "essential" nature of objects or the "efficient" causes connecting events. Instead, they saw the primary aim of science as the formulation of descriptive laws rather than explanatory principles. Stewart summarized this issue most succinctly when he wrote: . . . natural philosophers have, in modern times, wisely abandoned to metaphysicians all speculations concern­ ing the nature of that substance of which it [the material world] is composed; concerning the possibility or im­ possibility of its being created; concerning the efficient causes of the changes which take place in it; and even concerning the reality of its existence, i n d e p e n d e n t of that of percipient beings: and have confined them­ selves to the humbler province of observing the phenomena it exhibits, and of ascertaining their general l a w s . . . . Whether (for example) the cause of gravitation be material or immaterial is a point about which two Newtonians may differ, while they agree perfectly in their physical opinions. It is sufficient if both admit to the general fact that bodies tend to approach each other, with a force varying with their mutual distance accord­ ing to a certain law. 4 Finally, Stewart and Brown continued to warn philos­ ophers against the reckless use of analogies and hypoth­ eses in natural science. In Brown's words, " T o reason from analogy is, in most cases, to mislead, rather than to guide the understanding," 5 and, "to form a [conjectural] system is to incapacitate ourselves for just observation." 6 constantly conjoined; so that when we see the one we may expect the other," Works, II, p. 97; Brown wrote " T o express shortly, what appears to m e to be the only intelligible meaning of the three most important words in physics, immediate invariable antecedent in any sequence is a cause; the immediate invariable consequent is the correlative effect.", Lectures on the Philosophy of the Human Mind, I, p. 201. 4 Stewart, Works, π, pp. 48-49. 5 Thomas Brown, Observations on the Zoonomia of Erasmus Darwin, 6 M. D. (Edinburgh, Mundell and Son, 1789), p. viii. Ibid., p. ix.

95

GROWTH OF COMMON SENSE PHILOSOPHY

In spite of these fundamental areas of agreement with Reid, Stewart and Brown demonstrate a major change in emphasis and tone. Their critiques of analogical and hypothetical arguments, in particular, lack the stridency and sting of Reid's. In fact, both begin to see important and creative roles for well-controlled analogies and hy­ potheses. Brown even followed his comment on the evils of conjectural systems by stating that those evils are often "more than counterbalanced by [their] advantages." 7 His justification of this statement provides an excellent guide to the reasons for the change in emphasis among Common Sense philosophers at the end of the eighteenth and beginning of the nineteenth centuries: If phenomena were connected in our mind merely by the order of time, in which they occurred, few would be remembered nor, though memory were tenacious, could much aid be derived from it; as the advantages of experience consists, not in suggesting indifferently a multitude of circumstances, but in suggesting those par­ ticular circumstances, which we have found, at differ­ ent times, to produce effects, similar to those we desire. We cannot observe the various appearances of nature, without remarking certain circumstances in which they agree; and to remark these circumstances is to arrange the similar appearances. It is thus impossible not to systematize; and hence, the question should be not whether systems be useful, but to what extent, and in what mode, they can be most usefully formed. 8 Brown's comment on systems contains several differ­ ences in emphasis from the notions of Reid. Perhaps most important, it implies a renewed commitment to the utilitarian aspect of Bacon's writings not stressed by Reid. His contention that memory should "aid," that experience should provide "advantages" in attaining what we "de­ sire," and that systems should be "useful," all point to7 Ibid.,

p. ix.

8 Ibid.,

pp. ix-x.

DUGALD STEWART AND THOMAS BROWN

ward the fundamental Baconian assertion that knowledge is power. This is in complete conformity with the attitude of Stewart, who introduced his Outlines of Moral Philosophy (1793) with the contention that: The ultimate object of philosophical inquiry is the same which every man of plain understanding proposes to himself, when he remarks the events which fall under his observation with a view to the future regulation of his conduct. The more knowledge of this kind we acquire, the better can we accommodate our plans to the established order of things, and avail ourselves of natural Powers and Agents for accomplishing our purposes. 9 Since Stewart and Brown were interested in the exploitation of knowledge, they began to turn attention to those attributes of science which make it useful as well as true. They were far more impressed than had been their predecessors, for example, by men's need to organize information in order to remember the vast number of facts being accumulated. So they were far more sympathetic to the development of provisional scientific systems which invite empirical testing but which may transcend (though they may never violate) the results of prior inductions. They also realized that, in the absence of complete inductive information, analogies or metaphors and strategic devices like a principle of simplicity may be the only guides available to gain valuable insights into nature. They were, of course, always vigilant against the dangers of conjecture, and they constantly emphasized the need to maintain the possibility for empirical control over speculations; but their writings are more concerned with the active role played by scientists in formulating scientific knowledge than those of their mentors had been. Reid, like most of his empirically minded predecessors, was convinced that natural phenomena speak for themselves (at least when coaxed through experiment) and that 9

Stewart, Works, n, p. 6.

97

GROWTH OF COMMON SENSE PHILOSOPHY

the investigator's role is merely to record nature's laws. Stewart and Brown, on the other hand, recognized that science involves an interpretive and creative role for the scientist, not merely a receptive and passive one. It would be difficult and perhaps impossible to isolate all the factors which urged Common Sense philosophers toward a modification of Reid's rigorous construction of proper scientific method. We have already pointed out in chapter 2 for example, that Reid's own writings contain strong arguments for the psychological appeal of analogical arguments and the principle of simplicity—arguments which naturally began to take on increasing importance as the specter of Hume and his skeptical criticisms took a smaller place in concerns of Common Sense Philosophy and as the generation of a positive philosophy of mind began to dominate. Furthermore, the late eighteenth century saw the growth of a more positive attitude toward hypotheses among continental methodologists. Among this group was the Serbian Jesuit, Roger Joseph Boscovich, whose works seem particularly important in light of the attention they received from Stewart and his students. D U G A L D STEWART AND T H E W R I T I N G S O F R O G E R J O S E P H BOSCOVICH

It might seem at first glance that the writings of Roger Boscovich should have had little appeal to Common Sense philosophers, for Boscovich acknowledged a great intellectual debt to Leibniz, whose rationalistic philosophy had almost nothing in common with the Scot's empiricism. Boscovich's writings were, moreover, probably introduced to the Scottish moral philosophers through the work of another open enemy, Joseph Priestley. But once they were brought to Stewart's attention, he found that Boscovich's attitudes reinforced basic Common Sense doctrines. In order to understand in what way Boscovich's ideas 98

DUGALD STEWART AND THOMAS BROWN

were relevant to the problems of concern to Stewart, one must have some idea of his point-atomist theory of matter and of its relationship to the problem of the communication of motion by the impact of bodies. Throughout the later seventeenth and early eighteenth centuries it was widely agreed that all phenomena of the material world must ultimately be explicable in terms of the impact of hard, solid bodies. This assumption, the foundation of the so-called mechanical or corpuscular philosophy, in turn rested on an implicit assumption which was at least as old as Aristotle: i.e., that no body may act where it is not, or that action at a distance is impossible. What Boscovich did was to analyze the impact of solid bodies in such a way that the traditional assumptions about the nature of "impacts" and of "matter" itself needed modification. He de-emphasized the old denial of action at a distance and accepted quite a different principle as fundamental. Following Leibniz, he called his basic principle the law of continuity. He wrote: " T h e law of continuity as we here deal with it consists in the idea that . . . any quantity in passing from one magnitude to another, must pass through all intermediate magnitudes of the same class." 10 This law was of fundamental importance in his theory and could be established a priori from metaphysical principles or by induction from phenomena. 1 1 10 Boscovich, A Theory of Natural Philosophy (Cambridge, Mass., M.I.T. Press, 1966), translated by J. M. Child, p. 27. 11 TlIe status of the law of continuity for Boscovich is most fully discussed by D. Nedelcovich, La philosophie naturelle et relativiste de R.J. Boscovich (Paris, Editions de la Vie Universitaire, 1923), pp. 105-113, 126-129. We might well argue that Boscovich's theory of matter was motivated by a Newtonian tradition which supposed that particles of matter were very small indeed and acted as centers of force (see Arnold Thackray, " 'Matter in a Nut Shell,' " Newton's "Opticks and Eighteenth-Century Chemistry," Ambix, 1968, 15:29-53, for a discussion of this tradition and Boscovich's place in it). But the unique element of Boscovich's theory was its total denial of extension to atoms, and this denial d e p e n d e d on the consequences of the law of continuity.

99

GROWTH OF COMMON SENSE PHILOSOPHY

As a second fundamental principle, Boscovich accepted the proposition that the ultimate particles of matter must be totally impenetrable. Assuming the continuity of motion and the impenetrability of matter. Boscovich considered the case of two objects moving along the same straight line. Suppose one object has velocity six and a second object is catching up to it with velocity twelve. At the instant of impact, if no penetration can take place, the two bodies must be moving with equal speed. Hence, the second body will have both velocities twelve and nine at the same time, and the first body will have velocities six and nine. This, however, contradicts the law of continuity which demands that the initial velocities change progressively through the intermediate degrees of velocity. It can be argued that macroscopic bodies are composed of aggregations of small impenetrable bodies and that large bodies might thus penetrate one another and distort one another while they continually transfer motion. But if this argument is used, the problem faced by Boscovish is just pushed a step further to come up again when one considers the contact interaction of the small hard particles within each macro-body. Boscovich's criticism still holds on the microscopic level, and one must then conclude that impulsive action as usually conceived cannot take place in nature. If one agrees with Boscovich's premises, the changes of velocity which occur when motion is transferred between two bodies must be acknowledged to begin before the bodies actually touch. Using the law of continuity, the principle of impenetrability, and the realization that bodies attract one another nearly according to Newton's inverse square law at large distances, Boscovich established a theory by which all natural phenomena could, in principle, be explained as interactions among point-atoms, each of which exists solely as the center of a force which depends only on the distance from the central point: "The primary elements of matter are . . . perfectly indivisible and nonextended points; they are so scattered in an immense vacuum that every two of them are separated from one another by a 100

DUGALD STEWART AND THOMAS BROWN

Attractive

>

Repulsive

3

O

3 ο 1-1 B

Figure 1. definite interval; this interval can be indefinitely in­ creased or diminished but can never vanish altogether." 12 The basic elements of Boscovich's theory are com­ pleted by considering the law of forces (see Figure 1) which describe the attractions and repulsions between 12 Boscovich,

Theory of Natural Philosophy, p. 20.

GROWTH O F COMMON SENSE PHILOSOPHY

any two points. The forces are repulsive near the origin, oscillate between repulsive and attractive through an interval small with respect to ordinary distances, and approach an inverse square law of attractive force as they reach ordinary macroscopic distances. Thus, there exists a continuous and simple law of forces. Boscovich acknowledged that there could be no way of finding out why such force configurations might be associated with mere points in space, but he felt that if one assumed the existence of such force centers, then many physical phenomena could be explained. Priestley's first printed discussion of Boscovich's work appeared in The History and Present State of Discoveries Relating to Vision, Light, and Colours, where it was used to support a corpuscularian theory of light against Leonhard Euler's criticisms. 13 This work might have been seen by Stewart and it probably did spark the interest of John Robinson, Stewart's colleague in the chair of natural philosophy at Edinburgh, in Boscovich's optical writings; but during the next few years Priestley used Boscovichian arguments in two tracts devoted to central problems of Common Sense Philosophy, and these almost certainly claimed Stewart's attention. In Hartley's Theory of the Human Mind of 1755 and again in his anti-Common Sense Disquisitions Relating to matter and Spirit of 1777, Priestley appealed to the Jesuit's theory of matter to attack the Common Sense distinction between mind and matter. Since Boscovichian matter, like mind, seemed to exist only as force and not as material extension, Priestley could deny the traditional distinctions. It is clear that Boscovich did not see in his theory those implications which Priestley had drawn, for he wrote a series of letters heartily condemning Priestley's interpretation. 1 4 And when Stewart approached Bos13 Joseph Priestley, The History and lating to Vision, Light, and Colours 390-394. 14 See, for example, the letter from October, 1778, and printed in Robert

102

Present State of Discoveries Re(London; J. Johnson, 1772), pp. Boscovich to Priestley dated 17 Schofield, A Scientific Autobiog-

DUGALD STEWART AND THOMAS BROWN

covich's theory, he too saw dramatically different impli­ cations—implications which not only coincided more nearly with those drawn by Boscovich but also rein­ forced the long-standing Common Sense attacks on both the "ideal theory" of perception and necessitarian materialism. Stewart, like Reid before him, argued that the "ideal theory," as expressed by Locke, for example, was inspired by mechanical analogies which demanded a principle of cognitive contact in order to conform to the assumption that bodies cannot act where they are not and hence, that all communication must be by impact. Since the ideal theory drew upon the mechanistic analogy, Stewart saw that it could be discredited by demonstrating that the traditional mechanism of contact action was itself not only problematic but completely unsupportable. Boscovich's critique of impact theory provided him an ideal means for accomplishing this end. Stewart wrote: Some of the ablest philosophers in Europe [Boscovich is singled out by name a few lines later] are now satis­ fied that there is no evidence of motion in any case produced by the actual contact of two bodies, but that very strong proofs may be given of the absolute impos­ sibility of such suppositions. . . . It must appear a very curious circumstance in the history of science, that philosophers have been so long occupied in attempting to trace all of the phenomena of matter and even some of the phenomena of mind, to a general fact, which upon accurate examination, is found to have no existence. 15 Not only did Boscovich's theory of matter provide pow­ erful support for the Common Sense cause in this particu­ lar argument against idealism, but Boscovich's fully developed attitude toward the distinctions between mat­ erial and physical entities also correspond, almost in toto, raphy of Joseph Priestley, 1733-1804 (Cambridge, Mass., M.I.T., 1966), pp. 168-171. 15Stewart, Works, π, p. 107.

GROWTH OF COMMON SENSE PHILOSOPHY

with Common Sense beliefs. Here, for example, is a segment of Boscovich's supplement to Stay's De Systemate Mundi quoted at length in Stewart's "Philosophical Essays": By the power of Reflection, we are able to distinguish two different classes of ideas excited in our minds. To some of these we are impelled, by a very powerful instinct, common to all men, to ascribe an origin foreign to the mind itself, and depending on certain external objects. Others we believe with the utmost conviction to have their origin in the mind itself, and to depend upon the mind for their existence. The instruments or organs by which we receive the first kind of ideas are called the senses: their external cause, or , as it is commonly called, the object, is denoted by the words, matter and body. The source of the second class of our ideas (which we discover by reflecting on the subjects of our own consciousness) is called mind or soul. In this manner we become acquainted with two different kinds ofsubstances (the only substances of which we possess any knowledge); the one, a sensible or perceptible substance; the other, a substance endowed with the powers of thought and volition. Of the existence of neither is it possible for us to doubt (such is the force of those intimations w e receive from nature), not even in those cases when, offering violence to ourselves, we listen to the suggestions of the Pyrrhonists and the Egoists, and other sophistical perverters of the truth. 16 In writing this, said Stewart, Boscovich coincides "so exactly with Reid in the very phraseology he uses, as to afford a presumption that it approaches nearly to a correct and simple enunciation of the truth." 1 7 Boscovich also fully supported the Scots in their assertion of the existence of free will against such neces16

Stewart, Works, v, pp. 95-96.

"Ibid., p. 96.

104

DUGALD STEWART AND THOMAS BROWN

sitarians as Priestley. He denied the Leibnizian notion of sufficient reason precisely because it undermined the concept of free will and led to determinism in philosophy. Thus he wrote: "Moreover, I consider that the principle of sufficient reason is altogether false, and one that is calcu­ lated to take away all idea of true freewill. . . . Once this idea is accepted, it is truly wonderful how it tends to point the way finally to fatalistic necessity." 18 Finally, Boscovich agreed with the Scots on one of the most important aspects of their interpretation of physical knowledge. He emphasized the notion that physical laws can be fruitfully considered as mere descriptions of phenomena and that such laws are independent of any assumptions one might make about underlying causes. Discussing the propensity which his point-atoms have to remain in a state of rest or of uniform motion in a straight line—a "propensity" which merely summarizes the in­ ductive evidence derived from observing bodies—he wrote: Whether this is dependent on an arbitrary law of the Supreme Architect, or on the nature of points itself, or on some attribute of them, whatever it may be, I do not seek to know; even if I did wish to do so, I see no hope of finding an answer; and I truly think that this also applies to the law of forces, to which I now pass on. 19 The close correspondence between Boscovichian and Common Sense ideas regarding such important topics as the fundamental nature of scientific statements as well as the critiques of necessitarian-materialist and idealist metaphysics led Stewart to a deep appreciation of many aspects of Boscovich's work. In fact, Stewart was so taken with the Jesuit that he praised him as the most influential, sound, original, and talented metaphysician south of the Alps and as a man who demonstrated the "rare balance of 18 Roger 19 Ibid.,

J. Boscovieh, Theory of Natural Philosophy, p. 47. p. 21.

GROWTH OF COMMON SENSE PHILOSOPHY

imagination, and of the reasoning powers [in which] the perfection of the human intellect will be allowed to consist." 20 Stewart even followed Boscovich on issues where he departed from traditional Common Sense doctrine. Some of the most important of these dealt with the use of hypotheses, analogies, and the principle of simplicity in natural science. A NEW ROLE FOR HYPOTHESES

In order to understand why Stewart should have been willing to allow an increased role to hypotheses in physi­ cal science in spite of the fact that he shared the Common Sense belief that science was basically descriptive rather than explanatory, we must keep in mind the Humian element in Common Sense attitudes toward natural sci­ ence. Before Hume, most scientists who abandoned the search for causes in natural philosophy seemed to do so largely as an admission of temporary defeat, although they retained a belief that it might at some future time be possible to discern the efficient causes of observable phenomena. Galileo's famous description of accelerated motion in Two New Sciences is, for example, preceded by a statement that although that was not the time to investi­ gate the causes of accelerated motion they might nonethe­ less bear study. 21 And Newton's acknowledgment that he was unable to discover the causes of gravity did not inhibit him from making an attempt, which was published in a 20 Dugald Stewart, et al. Dissertations, Historical and Philosophical Exhibiting a General View of the Progress of the Metaphysical, Ethical and of Mathematical and Physical Science (Edinburgh: Adam and Charles Black, 1835), pp. 202-203. 21 SeeDialogues ConcemingTwoNew Sciences; ed., HenryCrewand Alfonso de Salvio (New York: The Macmillan Company, 1914), pp. 166-167.

DUGALD STEWART AND THOMAS BROWN

letter to Robert Boyle dated 1678. 22 Both Galileo and Newton abandoned their search for natural causes be­ cause they were, at least temporarily, unable to find a satisfactory way of removing causes from the realm of the hypothetical, and both sought more certainty in science than hypotheses would allow. Buthypotheses were worse than merely uncertain. These unsupported conjectures about the fundamental functioning of the universe re­ tained an ontological as well as an epistemological con­ tent; to persist in using an incorrect hypothesis would thus be to maintain an absolutely false view of nature. With the Common Sense followers of Hume, the search for causes was dropped from science completely; but the aim of science remained twofold. Science still aimed to establish the manner in which nature acted, but instead of searching for some kind of underlying reason for this activity, it took on the less ambitious task of trying to systematize and generalize the laws which were estab­ lished, so that the finite human mind could more easily encompass and exploit the huge amount of available knowledge. When knowledge is generalized, said Stewart, "the mind dwells habitually, not on detailed facts, but on a small number of general principles; and by means of these, it can summon up, as occasion may re­ quire, an infinite number of particulars associated with them, each of which, considered as a solitary truth, would have been as burdensome to the memory as the general principle with which it is connected." 23 Thus, Stewart adumbrated the emphasis on economy of thought as a prime end of science which became an important element of Ernst Mach's positivistic philosophy of science. 24 22 See I. B. Cohen and Robert Schofield, eds., Isaac Newton's Papers and Letters on Natural Philosophy (Cambridge, Mass.: Harvard Univer­ sity Press, 1958), p. 253. 23 Stewart, Works, v, p. 395. 24 Stewart also discussed the way organization aids memory inWorks, ri, pp. 388, 394-398.

GROWTH OF COMMON SENSE PHILOSOPHY

In line with this emphasis on systematization, hypoth­ eses were looked on more as a means for suggesting new relationships between ever greater numbers of disparate facts than as assertions about the true makeup of the world. Hypotheses had not yet entirely lost their residue of ontological meaning for Stewart and Brown. Yet both argued that it was more important to judge the value of hypotheses in suggesting extensions of accepted general­ izations or in suggesting new directions for research than to judge their truth. In interpreting the role of hypothetical arguments in natural science from this point of view, Stewart appealed directly to the methodological writings of R. J. Boscovich. Boscovich clearly was not driven by the same motives as was Stewart (his justification of the use of hypothetical reasoning involved no pragmatic considerations). None­ theless, his concern with hypotheses led to a set of methodological precepts which were admirably adapted to the Scot's needs. So Stewart was quite willing to state his opinion about the role of hypotheses in science in the very words of Boscovich: The argument in favor of hypothesis might be pushed much further by considering the tentative hypothetical steps by which the most cautious philosophers are often under the necessity of proceeding . . . these cannot be better described than in the words of Boscovich, the slightest of whose logical hints are entitled to peculiar attention. In some instances, observations and experiments at once reveal to us all that we wish to know. In other cases, we avail ourselves of the aid of hypotheses—by which word, however, it is to be understood, not fic­ tions altogether arbitrary, but suppositions conforma­ ble to experience or to analogy. By means of these, we are enabled to conjecture or divine the path of truth; always ready to abandon our hypotheses, when found to involve consequences inconsistent with fact. And, in-

DUGALD STEWART AND THOMAS BROWN

deed, in most cases, I conceive this to be the method best adapted to physics, a science in which the proce­ dure of the inquirer may be compared with that of a person attempting to decipher a letter written in a secret character; and in which legitimate theories are gener­ ally the slow result of disappointed essays and of errors which have led the way to their own detection. 25 Stewart's attitude toward hypotheses involved a con­ scious break with Reid who, he said, "has been led to carry, farther than was necessary or reasonable, an indis­ criminate zeal against every speculation to which the epithet hypothetical can in any degree be applied." 26 The extent of this divergence was truly great; Stewart not only approved the use of certain kinds of hypotheses but he even wrote: "Indeed it has probably been this way [through the use of hypotheses] that most discoveries have been made; for although a knowledge of facts must be prior to the formation of a legitimate theory, yet a hypothetical theory is generally the best guide to the knowledge of connected and of useful facts." 27 In spite of this change in emphasis, however, Stewart was not turning his back on the fundamental Baconian tradition, for which Reid appeared as a spokesman, nor on many of Reid's specific criticisms of the use of hypoth­ eses. One of his main concerns, for example, was to be quite sure that hypotheses were not confused with theories. Like Reid, he was not convinced by Hartley's implication from the cipher analogy that any hypothesis which explained the phenomena under consideration thereby derived indirect evidence for its truth, just as any key to a code derived through guesses and hypotheses had to be accepted as true if it allowed one to make sense of the 25 Stewart, Works, I I I , p. 305. The Boscovich statement is quoted from De Solis a Lunae Defectibus (London: 1760, pp. 211-212). Emphasis Stewart's. 26 Stewart, Works, h i , p. 314. 27 Ibid., p. 301.

GROWTH OF COMMON SENSE PHILOSOPHY

coded message. Reid had been unable to provide a good counter to Hartley, but Stewart pointed out that "there are few if any physical hypotheses which afford the only way of explaining the phenomena to which they are applied; and, therefore, admitting them to be perfectly consistent with all the known facts, they leave us in the same state of uncertainty in which the decypherer would find himself, if he should discover a variety of keys to the same cypher." 2 8 Thus, "In what I have hitherto said in defense of hypothesis, I have confined myself entirely to its utility as an organ of investigation; taking all along for granted, that, till the principle assumed has been fairly inferred as a law of nature, from undoubted facts, none of the explanations which it affords are to be admitted as legitimate theories." 2 9 On this score he was in full agreement with Reid and John Gregory, appealing to Gregory's works to support his own position: The prejudice against hypotheses which some people entertain, says the late Dr. Gregory, is founded on the equivocal signification of a word. It is commonly confounded with theory—but a hypothesis properly means the supposition of a principle of whose existence there is no proof from experience, but which may be rendered more or less probable by facts which are neither numerous enough, nor adequate to infer its existence. When such hypotheses are proposed in the modest and diffident manner that becomes mere suppositions or conjectures, they are not only not harmless, but even necessary for establishing a just theory. . . . Hypotheses then only become dangerous and censurable, when they are imposed upon us for just principles; because in that case they put a stop to further inquiry, by leading the mind to acquiesce in principles which may as probably be ill as well founded. 30 28 29

Ibid., pp. 313-314. Emphasis Stewart's. 30 IbId., p. 307. Ibid., p. 302.

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DUGALD STEWART AND THOMAS BROWN

For Stewart, as for Reid, the greatest danger came from those like Hartley and Priestley, who argued that any hypotheses which sufficed to explain the phenomena in question deserved credence as truths even though no direct evidence confirmed them. Such an attitude could lead not only to acquiescence in a false doctrine, but, more importantly for Stewart, it led to a cessation of further investigation and discovery. To him the value of hypotheses did not depend so much on their accordance with "truth" as on their capacity to suggest further associations and/or experiments. In fact, he explicitly stated that the value of a hypothesis may be equally great whether it leads to experiments which confirm it, demand its modification, or demand its abandonment. It will bring a new range of facts immediately under the domain of justified theories (if it be confirmed), it will lead to its own correction by pointing out what modifications are necessary to bring it into conformity with experience, or it will at least eliminate one false conjecture from consideration. More importantly, a properly selected hypothesis will suggest new associations which may lead to new knowledge. 3 1 Stewart did not continue this argument as far as Hamilton later did in arguing that the process of investigation was inherently more important than the results, but he did set the stage for such an extension.

BROWN AND T H E P R O B L E M S O F V E R I F I C A T I O N AND F A L S I F I C A T I O N

For both Reid and Stewart, a hypothesis which met both the sufficiency and existence criteria could presumably be verified (i.e., given a degree of probability verging on moral certainty) if it adequately predicted hitherto unknown phenomena and if any substances supposed to act in the changes intervening between previously observed changes could, in fact, be discovered. Stewart, though not 31

IbJd., pp. 301-302.

Ill

GROWTH OF COMMON SENSE PHILOSOPHY

perfectly consistent in his terminology, called such a ver­ ified hypothesis a theory; at least by implication he al­ lowed such theories a status very similar to pure inductive generalizations or laws of nature with respect to further scientific investigation. Brown, on the other hand, inter­ jected a more skeptical note into Common Sense attitudes toward science by denying that the traditional distinction between hypotheses and theories was valid and by argu­ ing that no hypothesis could ever be "confirmed" in the strong sense assumed by his predecessors. For Brown, the distinction between hypotheses and theories reduced itself to the following: We commonly give the name of hypothesis to cases, in which we suppose the intervention of some substance, of the existence of which, as present in the phenomena, we have no direct proof, or of some additional quality of a substance before unobserved; and the name of theory to cases, which do not suppose the existence of any substance that is not actually observed, or of any quality that has not been actually observed, but merely the continuance, in certain new circumstances, of tenden­ cies observed in other circumstances. 32 The theory of gravitation, for example, warrants our sup­ position that any newly discovered planet will be subject to the same inverse-square-law forces and allows us (once we have determined the body's position and velocity) to predict its future motions. And it takes for granted no new quality nor the existence of any new substance. If we ascribe the tendencies which keep the body moving in its orbit to the operations of an ether, however, we have introduced a hypothesis; for the existence of such an ether has never been directly established. 33 Theories for Brown were certainly not subject to all the errors of hypotheses; for "ifwe were to imagine falsely the 32 Brown, 33 Ibid.,

Lectures on the Philosophy of the Human Mind, p. 239. p. 240.

DUGALD STEWART AND THOMAS BROWN

presence of some third substance, our supposition might involve as many errors as that substance has qualities; since we should be led to suppose, and expect, some or all of the other consequences, which usually attend it when really present." 34 According to Brown, however, theories, like hypotheses, can be wrong and must be tested every time they venture to predict any event beyond the limits of former observation. Even such a theory as that of gravi­ tation, which (at least as presented by Newton) arose directly as an inductive generalization, could not carry absolute certainty. Its applicability to any situation not previously observed is problematic and depends on the correctness of the Brownian equivalent of Reid's princi­ ple of induction—a principle which, at least for Brown, did not carry proof of its own truth. Thus, Brown con­ cluded his discussion of scientific method by arguing that no scientific theory—and every scientific law of nature is a theory insofar as it is assumed to apply in circumstances which have not yet been observed—can ever be capable of complete confirmation or verification. We can be sure when it is wrong because it fails to correspond to some observed event; but we can never have absolute certainty about its complete generality. Nevertheless we must, for practical purposes, suppose the validity of scientific laws until they are shown to be false, and we are psychologically incapable of doing otherwise. In this sense, Brown previews the attitudes later developed by William Hamilton (who argued that certain theories which we believe to be true must be assumed to be true until they can be demonstrated to be either self-contradictory or inconsistent with observed phenomena) and by Karl Popper, who urges falsifiability rather than verifiability as a proper criterion for scientific theories. 35 34 Ibid.,

p. 241. Karl Popper, Conjectures and Refutations (London, Rouledge and Kegan Paul Ltd., 1962), passim. 35 See

GROWTH O F COMMON SENSE PHILOSOPHY T H E VALUE O F ANALOGICAL R E A S O N I N G

Though Stewart was confident that even the least welljustified conjectures about nature would utlimately lead toward valuable knowledge, 3 6 he by no means advocated arbitrary speculation as an acceptable source of scientific hypotheses. With a whole world to understand and a virtually infinite number of possible hypotheses to account for even a small class of phenomena, we must have a way of selecting those hypotheses which hold out the greatest prospect of being fruitful. The clearest and surest guides in this selection are, Boscovich suggested, experience and analogy. Reid had written against the case of hypotheses: If a thousand of the greatest wits that ever the world produced were, without any previous knowledge in anatomy, to sit down and contrive how, and by what internal organs, the various functions of the human body are carried on—how the blood is made to circulate, and the limbs to move—they would not, in a thousand years, hit upon anything like the truth. 37 Stewart replied: Nothing could be juster than this remark; but does it authorize the conclusion that, to an experienced and skillful anatomist, conjectures founded on analogy, and on the consideration of uses, are of no avail as media of discovery? The logical inference, indeed, from Dr. Reid's own statement, is not against anatomical conjectures in general, but against the anatomical conjectures of those who are ignorant of anatomy. 38 3e See "Dissertation First: Progress of Metaphysical and Ethical and of Mathematical and Physical Science" by Dugald Stewart, Sir James Mackintosh, John Playfair and Sir John Leslie (Edinburgh: Adam and Charles Black, 1835), p. 138 or Works, I, p. 286. 37 Quote by Stewart in Works, in, p. 309. 38 Ibid., p. 309.

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In a separate subsection of his Elements of the Philosophy of the Human Mind Stewart discussed just how experience and analogy offer grounds for scientific inferences and conjectures and what limiting conditions must be considered. Here he stated that arguments from experience and analogy differ only in degree and not in kind. Analogic arguments depend merely on an extension of Reid's principle of induction beyond the notion that the "same" kind of effects have the "same" causes to suggest that "similar" effects must have "similar" causes. As Stewart put it, arguments from experience and analogy both assume a "Unity of Design in the universe." 3 9 Such an extension of the inductive principle, of course, cannot claim certainty; it only provides a plausible and useful guide for speculation—a guide which is the more powerful as the "similarity" between the causes and effects under consideration is greater. When the things under consideration resemble one another so closely as to be considered individuals of the same species (in the logical, not biological sense), then our arguments from one to the other are properly said to depend upon experience and to have a high degree of probability. But when the things are sufficiently different to be distinguished as different species, or when the things have no obvious resemblance to one another but the relations they have with other things are similar, then our arguments from one situation to the other are said to depend on analogies or metaphors, and their power to persuade must be less as the disparities between things or relationships are more obvious and more numerous. 4 0 Analogical arguments are far more problematic than those drawn from the more tightly controlled domain of direct experience (as defined by Stewart) and tend to be at once more fruitful and more dangerous. They are more fruitful because they may give rise to a broader principle 39

IbId., p. 289.

40

IbId., pp. 286-287.

115

GROWTH OF COMMON SENSE PHILOSOPHY of arrangement and a greater number of associations than experience (which is limited to considering members of the same species). On the other hand, they are more dangerous because, as Stewart says, "mankind are much more disposed to confound things which ought to be dis­ tinguished, than to distinguish things which are exactly or nearly similar." 41 Men are thus easily led to receive mere analogies as direct evidence rather than as guides to further investigation. 42 This is what happened, for exam­ ple, when pre-Vesalian anatomists accepted the results of dissections of other animals as evidence for the structure of the human body. 43 STRICTURES ON THE USE OF ANALOGY Stewart nowhere developed a careful list of strictures upon the use of analogical reasonings, but he did agree with Reid on one improper use of analogy and he did make a major contribution to the discussion of analogic thought which subsequently became very important, especially in the writings of James Clerk Maxwell. Stewart argued that there was a "general analogy" be­ tween the material and moral worlds and between the laws which regulate the phenomena in each. 44 It was this general analogy, in fact, which justified applying the same inductive rules of inquiry to both fields and which legitimized the whole process of trying to establish a "philosophy of mind" similar to natural philosophy. But Stewart also agreed with Reid and with Boscovich that specific analogies between physical and mental phe­ nomena were to be rejected. It is from the principles of inductive philosophy which apply to both material and mental worlds, he said, "that we infer the necessity of resting our conclusions in each upon its own appropriate phenomena." 45 41Ibid., 44Ibid.,

p. 286. p. 295.

42Ibid., 45Ibid.,

p. 290. p. 296.

43Ibid.,

p. 289-290, note.

DUGALD STEWART AND THOMAS BROWN

When we develop hypotheses about the mental world based on physical analogies, we are misled into the ideal theory or into deterministic materialism, both of which contradict Common Sense principles. "If the science of mind admit of any illustration from the aid of hypotheses, it must be from such hypotheses alone as are consonant to the analogy of its own phenomena. To assume, as a fact, the existence of analogies between these phenomena and those of matter, is to sanction that very prejudice which it is the great object of the inductive science of mind to eradicate." 46 There is a clear contradiction in Stewart's argument. The very analogy which justifies applying inductive philosophy to mental phenomena is rejected in develop­ ing specific arguments. Reid had avoided this contradic­ tion by denying that the analogy between methods in physical and mental sciences depended in any way upon an analogy between subject matters. Stewart's successors, Brown and Hamilton, avoided the contradiction by giving credence to properly controlled analogies between phys­ ical and mental events. But Stewart provided a transition between the near-total rejection of and the near-total de­ pendence on analogical reasoning, and he was not always consistent. Stewart's acknowledgment of the general importance of analogical reasoning, along with his distrust of the pos­ sible misleading effects of specific analogies, led him to an important suggestion which was mentioned in his Elements of the Human Mind and expanded in his later Philosophical Essays. In order to understand this sugges­ tion, we must recall Reid and Campbell's analysis of lan­ guage as the medium of science and their discussion of the role of metaphor and analogy in providing the vocabulary for scientific discussion. Both these men had argued that we have no choice but to speak of newly discovered phenomena in terms of familiar ones and that this bor46 Ibid.,

p. 315. Emphasis Stewart's.

GROWTH OF COMMON SENSE PHILOSOPHY

rowed language in some sense imposes upon our philo­ sophical discussions an analogical character which we must struggle to transcend. Stewart was struck by the cogency of this argument and sought to find a way to avoid the pitfalls inherent in the use of metaphorical and analog­ ical terminology. In his discussion of this problem he first raised the suggestion made by the French philosopher and encyclopedist, Du Marsais, that one should eliminate all figurative words from philosophical discussions. But he agreed with D'Alembert that such a project would require the construction of a new language which no one could understand. He went on to provide his own sugges­ tion. "No one has hit on the only effectual remedy against this inconvenience—to vary, from time to time, the metaphors we employ, so as to prevent any one of them from acquiring an undue ascendant over the others, either in our own minds or in those of our readers. It is by the exclusive use of some favorite figure, that careless think­ ers are gradually led to mistake a simile or distant analogy for a legitimate theory." 47 The extension of this analysis from the linguistic use to the conscious use of analogy is obvious. Since it is the function of analogy to suggest and stimulate rather than to explain, there is no special virtue in using analogies con­ sistently; in fact, one gains the greatest benefits and avoids the greatest liabilities of analogical thinking by changing analogs occasionally. This attitude of Stewart's was in marked contrast to that taken by Reid and proved to be a very fruitful one among British natural scientists. We need only look at the early papers of James C. Maxwell on electrodynamics to see that it was exploited with great success during the nineteenth century. Of course, it is not immediately obvi­ ous that Stewart's writings played any role—either direct or indirect—in forming Maxwell's attitude toward the use of analogy; but they did provide a major key to the 47 Stewart, Works,

v, p. 173; see also ill, pp. 315-316.

DUGALD STEWART AND THOMAS BROWN

methodological writings of William Hamilton, who, as we shall see, was a principal source of Maxwell's explicit pronouncements on the use of analogies in physical science. T H E P R I N C I P L E O F SIMPLICITY

When Reid attacked h y p o t h e t i c a l and analogical reasoning in science, he also provided a warning against the evils of accepting the "principle of simplicity" as a guide. And just as Stewart provided a new emphasis with regard to the first two issues, he also tended to acknowledge a greater role for the third. Once again, Stewart's ideas paralleled those of Roger Boscovich. In the first section of his Theory of Natural Philosophy, Boscovich claimed the virtue of simplicity both for his theory as a whole and for the point-atoms it involved, arguing that experience and analogy drawn from nature justify the belief that the most fundamental natural laws must be simple. Thus, he wrote of the homogeneity and simplicity of his point-atoms, saying: Nature herself provides us with the analogy, chemical operations especially do so; for since the result of the analysis of compound substance leads to classes of elementary substances that are so few in number, and still less different from one another in nature; it strongly suggests that the further analysis can be pushed, the greater the simplicity and homogeneity, that ought to be attained; thus, at length, we should have, as a result of a final decomposition, homogeneity and simplicity of the highest degree. 4 8 As with other analogies, the simplicity of established natural laws can only suggest the value of hypotheses which are simple, and these hypotheses must in turn be subjected to proper empirical and critical testing. But 48

R. J. Boscovich, Theory of Natural Philosophy, p. 19.

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simplicity in and of itself lends strong credence to a hypothesis and may justify its entertainment in the ab­ sence of any other motive. Thus, Stewart argued that "the probability of an hypothesis increases in proportion to the number of phenomena for which it accounts, and to the simplicity of the theory by which it explains them." 49 In speaking of the Copernican hypothesis in particular, Stewart made his point clearly: The only evidence which the author was able to offer in its favor, was the advantage which it possessed over every other hypothesis in explaining with simplicity and beauty all the phenomena of the heavens. In the mind of Copernicus, therefore, this system was nothing more than an hypothesis—but it was an hypothesis con­ formable to the universal analogy of nature, always accomplishing her ends by the simplest means. 50 Similarly, he applauded atomic or corpuscular theory be­ cause of "its conformity to that luminous simplicity which everywhere characterizes the operations of nature," and congratulated Bacon and Gassendi for having "perceived so clearly the strong analogical presumption which this conformity afforded in its favour, prior to the unexpected lustre thrown upon it by the researches of the Newtonian school." 51 Once more, Stewart did not carry his belief in the prin­ ciple of simplicity as far as did Hamilton, who asserted that the love of unity or simplicity is both the efficient cause and guiding principle of all philosophical dis­ covery. 52 On the contrary, Stewart continued to empha­ size the basis for our expectation of simplicity in nature, arguing that "simplicity is not essentially a principle or axiom. It is the result of work . . . the greatest of truths 49 Stewart, Works,

ill, p. 311. Emphasis Stewart's. p. 300. 51 Stewart, Works, I (Dissertation First), p. 143. 52 See Hamilton Lectures on Metaphysics and Logic, I (Boston: Gould Lincoln, 1859), p. 49. 50 Ibid.,

DUGALD STEWART AND THOMAS BROWN

arrived at by observation of effects." 53 But Stewart's em­ phasis on the fruitfulness of this principle—whatever its source—was far different from the earlier position of Reid who saw its application as basically pernicious; it does represent a major step in the direction of Hamilton's posi­ tion.

STEWART AND ADAM SMITH'S "HISTORY OF ASTRONOMY"

In 1795, between the appearance of the first and second volumes of Stewart's Elements of the Human Mind, an important alternative to his interpretation of the aims and methods of natural philosophy was published in Edin­ burgh. This work, Adam Smith's "Principles which Lead and Direct Philosophical Enquiries: Illustrated by the History of Astronomy," 54 is worth careful consideration in a study of Common Sense attitudes toward science for two reasons. First, it gave rise to some specific criticisms by Stewart—criticisms which emphasize his continuity with the methodological concerns of Reid. Second, Smith's analysis of the scientific enterprise prefigures a great many of the subsequent modifications of Common Sense doctrines made by William Hamilton. This point is sig­ nificant not because any direct connection between Smith and Hamilton can be made (in fact, Smith is one of the few eighteenth-century Scottish authors whom Hamilton sel­ dom cited in his philosophical discussions, if he ever does). It is significant rather because Smith's work, writ­ ten before 1758 and long before the development of Kant's critical philosophy, derives most of its analysis from classical Aristotelian and Epicurean traditions and demonstrates the extent to which many of the supposedly 53 Stewart, Works, in, p. 300, note 1, quoted from J. Bailie Histoire de VAstronomie Modern. 54 Adam Smith, Philosophical Essays, edited by Joseph Black and James Hutton (London; Τ. CadeII, Jr., and W. Davies, 1795).

GROWTH OF COMMON SENSE PHILOSOPHY

Kantian aspects of Hamilton's writings might be strongly reinforced if not motivated by Hamilton's appreciation of Aristotle and classical philosophy. Smith's "History of Astronomy" places the source of all scientific and philosophical investigations in a human psychological need rather than in any practical material need or any disinterested or religiously motivated desire to know the "truth" about God's world. Philosophy is the science of the connecting principles of nature. Nature, after the largest experience that common observation can acquire, seems to abound with events which appear solitary and incoherent with all that go before them, which therefore disturb the easy movement of the imagination, which makes its ideas succeed each other, if one might say so, by irregular starts and sallies; and which thus tend, in some mea­ sure, to introduce those confusions and distractions we formerly mentioned. Philosophy, by representing the invisible chains which bind together all these dis­ jointed objects, endeavours to introduce order into this chaos of jarring and discordant appearance, to allay this tumult of the imagination, and to restore it, when it surveys the great revolutions of the universe, to that tone of tranquility and composure, which is both most agreeable in itself, and most suitable to its nature. 55 Since it is the primary purpose of philosophy to satisfy man's need for coherence, philosophical systems need not be judged principally with respect to their truth or falsity; hence, Smith explicitly stated that he was going to study them, "without regarding their absurdity or proba­ bility" or "their agreement or inconsistency with truth and reality." 36 Smith does not deny that there is some connected reality independent of man to be studied. He 55 Adam Smith "History of Astronomy" in J. R. Lindgren, ed., The Early Writings of Adam Smith, (New York: Augustus M. Kelley, 1967), p. 45. 56 Ibid., p. 45.

DUGALD STEWART AND THOMAS BROWN

implicitly assumed that such a reality does exist, and he even seemed to think that the philosophical "truth" may have been attained in the Newtonian system. He admitted with respect to Newtonian science that "even we, while we have been endeavouring to represent all philosophical systems as mere inventions of the imagination, to connect together the otherwise disjointed and discordant phe­ nomena of nature, have insensibly been drawn in to make use of language expressing the connecting principles of this one, as if they were the real chains which nature makes use of to bind together her several operations." 57 Smith never made an unambiguous claim for the truth of the Newtonian system, however. Nor did it seem to him necessary or even possible to establish that some particu­ lar coherent system is "true." The great significance of Smith's doctrine is that since it measures the value of philosophical systems solely in relation to their satisfaction of the human craving for order, it sets up a human rather than an absolute or natural standard for science, and it leaves all science essentially hypothetical. Furthermore, Smith implied that unceasing change rather than permanence must be the characteristic of philosophy. On both the issues of the relativity of sci­ ence to human psychological characteristics and the ceaselessness of the scientific quest, Smith's doctrines are very similar to those articulated later by William Hamil­ ton, but on both issues they directly subvert the essential Common Sense distinction which Stewart tried to retain between hypothetical and legitimate theories. In response to Smith's analysis Stewart admitted that one of the objects of philosophy is to satisfy our desire for coherence and organization. But Stewart also demanded that philosophical theories predict new testable "facts" as well as accord with established ones, and that they meet a criterion of permanence based on the nature of their con­ firmatory evidence. He wrote: 57 Ibid., p.

108. Also quoted in Stewart, Works,

III, p.

252.

GROWTH OF COMMON SENSE PHILOSOPHY

Of all philosophical systems, indeed, hypothetical or legitimate, it must be allowed that, to a certain degree, they both please the imagination and assist the memory, by introducing order and arrangement among facts, which had the appearance before of being altogether unconnected and isolated. But it is the peculiar and exclusive prerogative of a system fairly obtained by the method of induction [which may include a proper hypothetical theory brought to the test of experiment] that, while it enables us to arrange facts already known, it furnishes the means of ascertaining, by synthetic reasoning, those which we have had no access to deter­ mine by direct observation. The difference, besides, among hypothetical theories, is merely a difference of degrees, arising from the greater or less ingenuity of their authors; whereas legitimate theories are distin­ guished from all others, radically and essentially; and, accordingly, while the former are liable to perpetual vicissitudes, the latter are as permanent as the laws which regulate the order of the universe. 58 Ultimately, then, in spite of his important support for the use of hypotheses based on analogical arguments and the principle of simplicity, such hypotheses could for Stewart form only the first stage of the scientific process, a process which had to test these candidates for legitimate theoretical status not only for their conformity to the phenomena to be accounted for but also for independent observational evidence of the existence of the causes which they implied and for their ability to generate new knowledge. 58 Stewart, Works, III,

p. 251. Emphasis Stewart's.

CHAPTER 5

Thomas Brown and William Hamilton: The Relativity of Scientific Knowledge and the Triumph of Simplicity and Analogy ONE OF THE most complete and concise treatments of scientific method to come from the Common Sense School appears in the first part of Thomas Brown's Lectures on the Philosophy of the Mind, written during 1808 and 1809. 1 Brown spent most of his literary and scholarly effort throughout his life in writing poetry, but his abilities and interests ranged widely. H e trained at Edinburgh University in medicine and was for a short time a practicing physician in partnership with James Gregory. As a student he was a member of the "Academy of Physics" with Henry Brougham, Jeffery Horner, and George Birkbeck; when several members of that group established the Edinburgh Review, he wrote a number of articles for them, including the first published British analysis of Kantian critical philosophy. 2 In 1805, he further established his claim as a metaphysician by writing an Inquiry into the Relations of Cause and Effect which defended Hume's analysis of causation against the claims that it led to a rejection of morality and religion. In 1808, Stewart chose his former

T h o m a s Brown, Lectures on the Philosophy of the Mind, 2 vols. (Edinburgh: Adam and Charles Black, 1820). The lectures were written largely in 1808-1809 but were published posthumously by Brown's successor in the chair of moral philosophy, John Stewart. 2 Review of Viller s Philosophie de Kant, Edinburgh Review (January, 1803), i, pp. 253-280.

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student to substitute for him, and shortly thereafter Brown was appointed to the chair of moral philosophy. Just as Stewart had varied Reid's methodological em­ phasis, Brown varied Stewart's, placing a much greater stress on the role of the human mind in forming scientific knowledge than had any of his Common Sense predeces­ sors. In fact, Brown first developed the extreme emphasis on the relativity of scientific knowledge which is often ascribed to William Hamilton. 3 Brown's general interest in methodology and his stress on relativism, moreover, seem to have arisen directly out of the fact that he took David Hume more seriously than had any of his Common Sense predecessors. THE RELATIVITY OF SCIENTIFIC KNOWLEDGE As we have seen, Hume asserted that all science—all knowledge, in fact—depends upon the human mind. This assertion, moreover, had formed the implicit justification for much of the Scottish emphasis on the centrality of moral philosophy to education. But none of the Scottish moral philosophers before Brown had been so forceful about keeping this idea constantly before their students; nor did any of them see the radical implications that Brown enunciated. Brown's reasonings on this topic are admirably sum­ marized in his second lecture of 1808, "The Relation of the Philosophy of the Mind to the Sciences": To the philosophy of mind, then, every speculation, in every science, may be said to have relation as to a common centre. The knowledge of any quality of mat­ ter, in the whole wide range of physics, is not itself a phenomenon of matter, more than the knowledge of any 3 See,

for example, S. A. Grave, The Scottish Philosophy of Common Sense (Oxford: Oxford University Press, 1960), pp. 126-129, for the impression that Hamilton introduced the relativistic position into Com­ mon Sense Philosophy.

THOMAS BROWN AND WILLIAM HAMILTON

of our intellectual or moral affections; it is truly in all its stages of conjecture, comparison, doubt, belief, a phenomenon of mind; or, in other words, it is only the mind itself existing in a certain s t a t e . . . . It would surely be absurd to suppose that the mixture of acids and alkalies constitutes chemistry or that astronomy is formed by the revolution of planets round a sun. Such phenomena, the mere objects of science, are only the occasions on which astronomy and chemistry arise in the mind of the inquirer, Man It is the object indeed, which affects the mind when sentient; but it is the original susceptibility of the mind itself which determines and modifies the particular affection, very nearly . . . as the impression which a seal leaves on melted wax depends not on the qualities of the wax alone, or of the seal alone, but on the softness of the one and the form of the other. Change the external object which affects the mind in any case, and we all know that the affection of the mind will be different. It would not be less so, if, without any change of object, there could be a change in the mere feeling, whatever it might be, which would result from that different susceptibility, becoming instantly as different, as if not the mind had been altered, but the object which it perceived. There is no physical science, therefore, in which the laws of mind are not to be considered together with the laws of matter; and a change in either set of laws would equally produce a change in the nature of the science itself.4 The philosophy of mind is a prerequisite for scientific knowledge, then, because scientific knowledge can only be relative to (or dependent upon) our special capabilities for knowing. At first, Brown's insistence that scientific knowledge depends on the laws of thought as well as on the laws of matter may seem merely to be a reiteration of the basic 4

Brown, Lectures, pp. 102-104.

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Common Sense principle that there are certain things that we believe simply from the constitution of our nature. But Brown's arguments contain an important additional implication. For him, the limitations of the human senses and mentality did not serve merely as a sieve to screen out certain absolute truths which we cannot know and to allow us access to other truths which exist independently. He spoke of the mind as an intellectual medium for transmitting knowledge: The medium in this case, as truly as in the transmission of light, communicates something of its own to that which it conveys; and it is as impossible for us to perceive objects long or often together, without that comparison which invests them with certain relations, as it would be for us to perceive objects, for a single moment, free from the tint of the coloured glass through which we view them. 5 To understand what Brown means by this statement, let us consider his example of the way man is inevitably and justifiably led to ascribe a unity to objects merely because of his sensory limitations. Brown speaks of a piece of glass which appears to us a single, homogeneous, transparent body. If our senses were sufficiently acute, he said, we would be unable to recognize the unity of the glass. We would see an aggregation of dissimilar, opaque particles separated from one another by space, but because our eyes cannot resolve the spaces between the particles of silica and alkaline material within the aggregation, we are led to formulate scientific statements about "glass," a kind of unity, "derived from the mind of the observer only, and not from its constituent bodies, which are truly separate and independent of each other, and must always be independent, whatever changes they may seem to undergo, in the various processes of composition and decomposition. 5

Ibid., p. 171.

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THOMAS BROWN AND WILLIAM HAMILTON 6

.. ." For Brown, then, even the nature offactual information might be directly dependent upon the observer. We may well question the grounds upon which Brown assigned reality to particles of matter presumed to underlie our sensory experience, but his corpuscularian assumption was almost universally shared by his contemporaries in Scotland. If the atomist view is accepted, Brown's example provides an interesting illustration of how perceptual limitations could have positive as well as negative implications with respect to the "objects" of scientific study. Since the limited abilities of our perceptual processes often lead us to define as unitary objects which seem on other bases to be complex, we are almost forced to create a science to resolve the apparent paradox: To dissipate this imaginary aggregate of our own creation, and to show us those separate bodies which occupy its space, and are all that nature created, is the great office of the analytic art of chemistry, which does for us only what the microscope does, that enables us to see the small objects, which are before us at all times, without our being able to distinguish them. When a chemist tells us, that glass, which appears to us as one uniform substance, is composed of different substances, he tells us what, with livelier perceptive organs, we might have known, without a single experiment; since the siliceous matter and the alkali were present to us in every piece of glass, as much before he told us of their presence, as after it. The art of analysis, therefore, has its origin in the mere imperfection of our senses. 7 The very necessity of the existence of some sciences depends upon the nature of our perceptual processes. The sciences of the spatial composition of matter not only exemplify one way in which scientific knowledge is «Ibid., p. 169.

'Ibid., p. 172.

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relative (dependent not only on the supposed intrinsic nature of natural objects but also upon the characteristics of their human observers) but they also present illustrations of two additional senses in which scientific knowledge might be said to be relative and, perhaps more importantly, relational. Brown was quite aware that chemists were to some extent ignorant of the nature of the supposed elementary bodies which constitute the aggregates that we perceive. But, he argued, "though the co-existing bodies be separately unknown, the effect, which they produce when co-existing in the circumstances observed by us, is not the less certain and definite." 8 That is, while we may be unable to know the elements in themselves, we are nonetheless able to know by observation the effects of their relations with one another. Furthermore, since we do not know the nature of those entities which immediately underlie the aggregates accessible to our senses, we cannot be certain that they are not in turn composed of more elementary substances. In fact, Brown was inclined to believe that matter may be successively decomposed in a "never-ending analysis." Thus, our scientific knowledge is relative in a further sense insofar as what appears elementary at any given time may be further analyzed in the future. This notion is important because it makes even a descriptive science open-ended in a way which fit nicely with the arguments of Adam Smith and which could satisfy objections like those raised by Lord Kames against Reid's restrictive Humian interpretation of causation. Brown's analysis of the critical role of man's limitations in generating scientific facts and questions turned Common Sense philosophy of science in a radically new direction, one which was further developed at the hands of his successor and avowed enemy, Sir William Hamilton. 8

Ibid., p. 179.

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THOMAS BROWN AND WILLIAM HAMILTON W I L L I A M H A M I L T O N AND A N E W E C L E C T I C I S M

Hamilton (1788-1856) presents a number of difficult problems in interpretation not shared with his predecessors. Like Reid, Stewart, and Brown he had a Scottish university education with some scientific emphasis. He attended Glasgow University and then the University of Edinburgh, where he began preparation for a career in medicine. But Hamilton also studied at Oxford, where he became an expert on Aristotle and his commentators. And he traveled in Germany, where he became a serious student of German language and philosphy, including the critical philosophy of Kant and its extensions and modifications at the hands of Fichte and Schelling. Thus, when Hamilton began to publish his philosophical opinions in 1829, they contained a complicated and often apparently inconsistent mixture of Scottish Common Sense, classical Greek, and contemporary Continental ideas. Though Brown had greatly modified certain aspects of traditional Common Sense Philosophy, interjecting a relativistic and Humian skeptical element into a tradition which had sought an absolute understanding of nature not subject to skeptical attacks, even the neophyte reader can recognize the kinship of Brown to Reid and Stewart. His language and style of reasoning are the same. He was slightly more prone to abstract arguments than Stewart and more willing to cite the witty and eloquent Frenchmen, Fontenelle and Voltaire; but there is a common simplicity of prose and thought which ties him to Reid and Stewart, and there is no mistaking his agreement with them on our ultimate dependence on an intuitively justified principle of induction for all of our scientific knowledge. When we come to study the writings of Sir William Hamilton, doctrinal and stylistic continuities are much harder to recognize. His prose is almost consciously complex and esoteric, and his language tends to obfuscate his 131

GROWTH O F COMMON SENSE PHILOSOPHY

doctrinal agreements with his predecessors. Furthermore, for Hamilton the very aims and purposes of philosophy were—explicitly, at least—vastly different from those of his Scottish predecessors. Though he clearly felt that philosophical knowledge would lead to a more or less traditional Christian religious faith, he denouced attempts (like those made by Reid, Beattie, and Campbell) to develop philosophy in order to justify particular religious beliefs. Similarly, though he was aware that philosophical knowledge might be exploited for material advantage, his philosophy was not consciously pragmatic, as was that of Stewart and Brown. For Hamilton, the act of philosophizing was an end in itself. With Aristotle he believed that "We are created with the faculty of Knowledge, and, consequently, created with the tendency to exert it," 9 and that "speculative truth is only held of value, for the sake of intellectual activity." Every philosopher and scientist is willfully ignorant of a thousand established facts—of a thousand which he might make his own more easily than he could attempt the discovery of even one. But it is not knowledge—it is not truth—that he principally seeks; he seeks the exercise of his faculties and feelings; and, as in following the one he exerts a greater amount of pleasurable energy than in taking formal possession of the thousand, he disdains the certainty of the many, and prefers the chances of the one. Accordingly, the sciences always studied with the keenest interest are those in a state of progress and uncertainty; absolute certainty and absolute completion would be paralysis of any study; and the last worst calamity that 9 William Hamilton, Lectures on Metaphysics and Logic, ed. by Henry Mansel and John Veitch, (Boston: Gould and Lincoln, 1859), I, p. 46. Speculative knowledge is only one kind of knowledge, and Hamilton did point out that some important philosophizing is practical in a variety of ways leading to both material and spiritual well being. But the main focus in all of his work is on what he calls speculative knowledge.

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THOMAS BROWN AND WILLIAM HAMILTON

could befall man as he is at present constituted would be that full and final possession of speculative truth, which he now vainly anticipates as the consummation of his intellectual happiness. 1 0 In particular, Hamilton argued that there is an essential twofold psychological source for all philosophy. We feel a necessity to connect causes with effects, and we desire to discover a unity in nature. 1 1 Oddly enough, though Hamilton explicitly objected to almost every statement made by Thomas Brown, he borrowed an important technique from Brown in explaining the drives for causal knowledge and unity in philosophy: he attributed both to human limitations. Because the human mind cannot conceive that anything which begins is anything more than a new modification of pre-existent elements, we are unable to think of any object or event except as a link in a chain involving other objects or events, and we must seek to discover the supposed connections. "It is thus," Hamilton said, "that we are unable to rest satisfied with a mere historical knowledge of existence; and that even our happiness is interested in discovering causes, hypothetical at least, if not real, for the various phenomena of the existence of which our experience informs us." 1 2 Similarly, we desire unity in our philosophy because of our mental limitations. "We are lost in the multitude of the objects presented to our observation, and it is only by assorting them in classes that we can reduce the infinity of nature to the finitude of mind." 1 3 But we cannot rest content with such a partial unification, "Reason, Intellect, vous in fine, concatenating thoughts and objects into system, and tending always upwards from particular facts to general laws, from general laws to universal principles, is never satisfied in its ascent till it comprehends (what, however, it can never do) all 10

Hamilton, Lectures, I, p. 47. 13 Ibid., p. 47. Ibid., p. 47.

12

133

"Ibid., p. 46.

GROWTH OF COMMON SENSE PHILOSOPHY

laws in single formula." 14 Our love of unity is, in fact, so strong that it leads us to anticipate that nature must demonstrate a corresponding unity, and since this assumption has been confirmed by experience, Hamilton raised the search for unity to the fundamental principle of science and philosophy: "It not only affords the efficient cause of philosophy, but the guiding principle to its discoveries." 1 5 It is important here to understand that Hamilton's search for unity in nature corresponds directly with what his predecessors called the principle of simplicity and that he was very consciously making a virtue out of what his predecessors thought to be a weakness. Reid had condemned the attempt to reduce the number and form of natural laws beyond what he considered legitimate, and both Stewart and Brown had echoed his warning. But Hamilton cited what is obviously the same psychological drive as the guiding principle for all discovery. In fact, Hamilton even made this psychological drive underlie the process of induction—the most fundamental mode of scientific reasoning. Both Reid and Stewart, of course, had acknowledged that the inductive process depends upon our assumption of the uniformity of nature. But their interpretation did not emphasize the creative aspect of this principle. For them, the principle merely allowed the recognition of a natural and inherent connection between past enumerated instances and an indeterminate number of future ones. For Hamilton, on the other hand, it was the human mind guided by its drive for unity which "binds up the separate substances observed and collected into a whole, and converts what is only the observation of many particulars into a universal law." 1 6 Universal laws are not discovered; they are made. And they are made only because the human mentality must seek generality and unity in phenomena. "Ibid., p. 48.

15

Ibid., p. 49.

134

16

Ibid., p. 73.

THOMAS BROWN AND WILLIAM HAMILTON

Hamilton's emphasis on the act of philosophizing as an end in itself and on our drive for unitary understanding seems to place him quite outside the Common Sense tradition, and many commentators on him have argued that they clearly identify him with the Kantian critical philosophy in which both emphases also play central roles. It is my contention, however, that in spite of his obvious use of terms borrowed from German philosophy and his interest in certain problems raised by Kant, Hamilton's most fundamental epistemological and methodological views are very closely tied to those of his Common Sense predecessors and that where he apparently diverged most from Common Sense notions— particularly with respect to the psychological sources of t h e d r i v e s for c a u s a l a n d u n i t a r y e x p l a n a t i o n s in philosophy—these divergencies are less radical than most commentators have asserted; where they do exist, they depend as centrally on his classical philosophical background as on his reading of contemporary Continental philosophy. His discussion of unity as a goal in philosophy, for example, involves citations from Anaxagoras, Plato, Priscianus, Lydus, Plotinus, and St. Augustine and only the barest reference to Kant. 17 Furthermore, he saw unity not in accordance with Fichte and Schelling, as an absolute and ultimately divine principle imposed upon man, but as a human psychological principle imposed by man upon phenomena. In spite of the fact that Hamilton gave the principle of simplicity or search for unity a much greater positive role than did his Scottish predecessors, he did accept certain elements of the Common Sense view. He acknowledged that simplicity or unity is primarily a human demand rather than an a priori law of nature and that, as such, it must constantly be tested against experience. "To this love of unity—to this desire of reducing the objects of our knowledge to harmony and system—a source of truth and 17

Ibid., pp. 46-47.

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GROWTH OF COMMON SENSE PHILOSOPHY

discovery if subservient to observation, but of error and delusion if allowed to dictate to observation, what phenomena are to be perceived; to this principle, I say, we may refer the influence which preconceived opinions exercise upon our perceptions and our judgements, by inclining us to see and require only what is in unison with them." 1 8 Unity may be our primary guiding principle, but it is not to be implicitly trusted. It will guide well only if we constantly guard against its deceptions. Hamilton's analysis of the notion of causality also differs fundamentally from both German and traditional Common Sense views, but it shares major elements with the revisionist views of Brown. According to Hamilton: Our judgement of causality simply is: we necessarily deny, or rather, are unable to affirm in thought, that the object which we apprehend as beginning to be, really so begins; but, on the contrary, affirm, as we must, the identity of its present sum of being, with the sum of its past existence. And here, it is not requisite for us to know, or even to be able to conceive under what form or under what combination this quantum previously existed, in other words, it is unnecessary for us to recognize the particular causes of this particular effect. A discovery of the determinate antecedents into which a determinate consequent may b e refunded, is merely contingent—merely the result of experience; but the judgement, that every event should have its causes, is necessary, and imposed upon us as a condition of our human intelligence itself. This necessity of so thinking is the only phenomenon to be explained. The question of philosophy is not concerning the cause but concerning a cause. 1 9 Certain aspects of this causal principle clearly coincide 18

IbId., p. 52. William Hamilton, Discussions on Philosophy (London: Longman, Brown, Green and Longmans, 2nd ed., 1853), pp. 610-611. Emphasis Hamilton's. 19

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THOMAS BROWN AND WILLIAM HAMILTON

with both Common Sense and Kantian positions. Although we must discover individual causes through experience, our belief in the necessity of causality is dependent upon our mental makeup and is prior to experience. Furthermore, causality is reduced, as for Brown, to a relationship of immediate antecedence. But Hamilton disagreed with his predecessors about the reason for our thinking causally. For Reid, Stewart, Brown, and Kant the need to think causally was a fundamental, positive, and irreducible component of our mental structure; for Hamilton, it was only a derivative of a more fundamental principle—the Law of the Conditioned. Hamilton's doctrine of the Conditioned is a complex theory relating to the conditions under which men may claim to have knowledge. Its full explication lies beyond the aims of this work, but the basic premises underlying the Law of the Conditioned and its application to the notion of causality are simple and of great importance to an understanding of Hamilton's methodological precepts. Basically, although Hamilton did not acknowledge the fact, his doctrine of the Conditioned bears very close affinities to Brown's doctrine of the relativity of all knowledge; it claims that the form of all our knowledge is det e r m i n e d by h u m a n limitations and that paramount among those limitations is an inability to think about things except relationally. When we think of some object or event, we cannot avoid thinking of it in terms relative to other things or events; because we simply lack the ability to think without making comparisons, much as we lack the ability to see things smaller than a certain size or to hold in our memories more than a limited number of apparently unconnected "facts." In Hamilton's words, "the mind is restricted to think in certain forms, and, under these, thought is possible only in the conditioned interval between two unconditioned, contradictory extremes or poles, each of which is inconceivable. . . ." 20 The causal principle arises as a corollary of this general principle 20

Ibid., p. 618.

137

GROWTH OF COMMON SENSE PHILOSOPHY when we think of existence in time. When we think of something existing in time we must think of it as relative to other objects, i.e., as having something else before it and after it. Thus, "we cannot know or think a thing to exist in time and think it absolutely to commence or terminate." 21 Absolute commencement and termination are, after all, precisely those kinds of unconditioned ex­ tremes which the general principle of the conditioned denies to our knowledge (though not to external reality). "Unable positively to think an absolute commencement, our impotence to this drives us backwards on the notion of cause; unable positively to think an absolute termination, our impotence to this drives us forwards on the notion of effect." 22 Hamilton differed from all his Common Sense pred­ ecessors and German contemporaries in this analysis of causality principally by denying that the causal principle is an independent, positive belief and by referring it to a more general, negative source. His justification for taking this course provides an important insight both into the scholastic element in his thought and into a methodologi­ cal principle which played a central role in his philosophy of science. THE LAW OF PARSIMONY In order to understand Hamilton's opposition to his predecessors on the status of causality, we must recognize that he believed that all explanations of the necessity of our causal judgment (including his own) are hypothetical in a fundamental sense. Since all explanations of the causal principle are hypothetical, we must apply to them the general standards of criticism which justify choices among competing hypotheses. And in Hamilton's opin­ ion, after the elementary maxims that a hypothesis should be sufficient to account for the phenomenon in question 21 Ibid.,

p. 618. Emphasis Hamilton's.

22 Ibid.,

p. 619.

THOMAS BROWN AND WILLIAM HAMILTON

and should be self-consistent, the law of parsimony pro­ vides "the most important maxim in regulation of philosophical procedure where it is necessary to resort to an hypothesis." 23 This law, of course, corresponds in most respects to Newton's first rule of philosophizing made central by both Reid and Stewart. But for Hamilton its primary source lay in the writings of Aristotle and William of Occam; no one had previously formulated it in its proper and most general form: "Neither more nor more onerous causes are to be assumed than are necessary to account for the phenomena." 24 The law of parsimony as enunciated by Hamilton has two distinct parts. First, no more causes are to be posited than are necessary to account for phenomena. Virtually all accounts of the law of parsimony include this assertion, and it alone would be sufficient to justify Hamilton's analysis of the source of causality, for Hamilton had al­ ready established that our inability to think about any­ thing except as relative accounts for the principle of cau­ sality. This part of the Law of Parsimony is adverse to the doctrine which assumes, as a separate intellectual reg­ ulative, what is called the "Principle of Causality," that every event must have its cause. . . . For while the separate "Principle of Causality" is excogitated to explain— why it is that we must prefix in thought a cause to every charge which we think—it cannot be denied, however marvelously overlooked, that this same mental necessity is involved in the general inabil­ ity which we find of construing positively to thought anything irrelative, and specially, of thinking anything absolutely to commence. This general inability ex­ plains, among sundry other mental phenomena, the causal judgment; and it must be left at work, howbeit a new principle is called in to perform this part of its multiform operations. As new and expressed, this prin23 Ibid.,

p. 628.

24 Ibid.,

p. 628.

GROWTH OF COMMON SENSE PHILOSOPHY

ciple is therefore pleonastic, otiose, useless, and its assumption, so soon as the old is signalized, becomes philosophically absurd. 25 The second and more original part of Hamilton's formu­ lation of the law of parsimony—that no more onerous causes be admitted—provided additional justification for choosing Hamilton's over the traditional explanation of causation. His explanation involves a less onerous cause because it depends upon a negative impotence rather than the assumption of a positive power. All our analyses of knowledge lead us to acknowledge that our mentality is finite and limited; we need postulate nothing new to base causation on our limitations. On the other hand, we must postulate a new and "unknown inspiration of knowledge" in order to agree with Reid. "The one hypothesis is thus, again, comparatively cheap, the other comparatively dear." 26 In addition to the fact that principles of impotence seem somehow less dear than positive assertions of power, Hamilton's principle is less onerous because it is not hypothetical in the sense described by Brown. That is, the doctrine of the conditioned is already a proven reality before it is adopted to explain causation. "All is different in the counter theory," writes Hamilton, "here the 'Prin­ ciple of Causality' is itself hypothetical. It is not other­ wise known to exist, and to exist independently of what it is only created—only called into being in order to explain." 27 Like the damnable ether of Hartley, only the fact which it is called on to explain justifies its existence, and it does not satisfy the Newtonian demand for inde­ pendent support. Finally, Hamilton's version of the causal principle is less onerous because it does not have the same neces­ sitarian implications that can be drawn from Reid's expla­ nation, which makes causality a fact of objective existence as well as a subjective human need. Hamilton's explana25Ibid.,

p. 629.

26Ibid.,

p. 636.

"Ibid., pp. 630-631.

THOMAS BROWN AND WILLIAM HAMILTON

tion alone accounts in a non-contradictory way for the fact that even though all our understanding of phenomena, spiritual as well as material, must be causal, there may nonetheless be a Liberty of the Will which is directly intuited and simply incapable of explanation. If Reid were correct, then our reason would necessarily be deceitful. Reid claimed that our belief in the principle of causality is, in fact, a God-given awareness of a real causal necessity at the same time that he claimed an immediate God-given awareness of freedom. He was thus driven to state that God gives us an absolute knowledge which is contradictory. This fact raises grave problems; once we know that God deceives us, we can no longer trust any of our intuitive knowledge, and the whole structure of Common Sense Philosophy is undermined. By basing our causal belief on human limitations, however, Hamilton was able to retain a trust in both reason and intuition as long as they are confined to their proper spheres. The problem of developing a philosophical system which does not undermine its own basis is a key one for understanding other aspects of Hamilton's philosophy of science. It is raised even more blatantly in connection with Hamilton's most traditional Common Sense belief—that of natural realism (the doctrine that we have immediate, rather than mediate, knowledge of external reality). C O H E R E N C E AND C O R R E S P O N D E N C E AS C R I T E R I A FOR S C I E N T I F I C SYSTEMS

In his second major philosophical essay, "The Philosophy of Perception," published in the Edinburgh Review in 1830, 28 Hamilton fully justified his firm placement within the Common Sense tradition. He sided with Reid against all opposition in asserting that the ultimate 28 Hamilton, "Philosophy of Perception" Edinburgh Review (October, 1830) 52, pp. 158-207.

141

GROWTH OF COMMON SENSE PHILOSOPHY

bases of our knowledge are "certain facts of conscious­ ness, which, as primitive and consequently incom­ prehensible, are given less in the form of cognitions than of beliefs." 29 Foremost among these facts of conscious­ ness is a belief that a material world exists and that it is this external reality itself which is the object of our conscious­ ness in perception. 30 It is in defending these basic propositions of Common Sense Philosophy against skeptical attack and against the alternative theories of idealists, materialists, and hypothetical realists (those like Kant and Brown who be­ lieved in a reality underlying experience but who denied our direct access to it through perception) that Hamilton developed an epistemological doctrine which provides important methodological directives: If it is true that our primary experience be a faith, the reality of our knowledge turns on the veracity of our constitutive beliefs. As ultimate, the quality of these beliefs cannot be inferred; their truth, however, is in the first instance to be presumed. As given and possessed, they must stand good until refuted; "neganti incumhit probatio"? It is not to be presumed, that Intelligence gratuitously annihilates itself—that the Author of na­ ture creates only to deceive. . . . But though the truth of our instinctive faiths mustin the first instance be admit­ ted, their falsehood may subsequently be established: this, however, only through themselves—only on the ground of their reciprocal contradiction. 31 This argument, which is made here only for the viability of fundamental Common Sense beliefs, has two elements which are transferable to an analysis of scientific systems or theories in general. The first transferable element re­ lates to the statement that the principles of Common Sense must initially be assumed true because they are 29 Hamilton, 31 Ibid.,

Discussions, p. 86. p. 86.

30 Ibid.,

p. 89.

THOMAS BROWN AND WILLIAM HAMILTON

incapable of rational verification and that we can then do no more to test them than to try to establish their false­ hood. The basic principles underlying such natural sci­ ences as physics and chemistry are not all primary experi­ ences, so it is not clear that they must be assumed true and only subsequently be tested or falsified. In fact, Hamilton did establish other criteria—some of which, as we have seen, are based on the laws of parsimony—to preselect assertions which we are to accept as legitimate hypotheses on which to base scientific systems. But it is clear that the selection of legitimate hypotheses does not guarantee their truth; once selected, a legitimate hypothesis must play the role in its theory that a primary datum of consciousness would. It cannot be more certain than such a fact of consciousness; nor can it be indepen­ dently verified. It can only be assumed true and subse­ quently be falsified if it is incorrect. Thus, Hamilton was led to an interpretation of science in which no theory can be verified in a strong sense but in which theories made plausible by their dependence on legitimate hypotheses (chosen according to certain criteria) must constantly be tested in order to attempt to falsify them. The second transferable element derives from the as­ sertion that the principles of Common Sense can be fal­ sified only by establishing that they are inconsistent with one another. In Hamilton's words, "The argument from Common Sense, therefore, postulates, and founds on the assumption that our original beliefs be not proved, self-contradictory." 32 Since coherence thus becomes the central criterion for the viability of the most fundamental epistemological doctrine, we might expect that it should be applied as a critical test for the viability of scientific theories as well. And so it is, but with one stipulation. A scientific system may not only be falsified by establishing a self-contradiction, but it may also be falsified if it can be shown to be inconsistent with an independent datum of 32 Ibid.,

p. 86.

GROWTH OF COMMON SENSE PHILOSOPHY consciousness (for example, with an independent and well-established observation). "Are the principles which a particular system involves convicted of contradiction; or, are these principles proved repugnant to others, which, as facts of consciousness, every positive philos­ ophy must admit; there is established a relative skepti­ cism, or the conclusion, that philosophy, insofar as it is realized in this system, is groundless." 33 For scientific theories, then, coherence is not enough; they must also correspond in their implications with direct experience and with all fundamental dictates of Common Sense. THE CRITERIA FOR LEGITIMATE HYPOTHESES Hamilton's discussion of natural realism provides the occasion for presenting one further set of demands upon the basic principles which underly scientific theorizing. Some scientific arguments may be founded upon princi­ ples which cannot be reduced to primary facts of con­ sciousness, and for these arguments, coherence and con­ formity with a limited range of experience are insufficient to command our assent. The principles underlying such arguments must also meet what Hamilton called the re­ quirements of legitimate hypotheses. Some requirements for legitimate hypotheses—those arising out of the law of parsimony—had already been analyzed in his earlier dis­ cussion of causation. But Hamilton completed his discus­ sion of the criteria for utilizing hypotheses in connection with his analysis of the hypothetical realist, or representationist, alternative to the doctrine of natural realism. According to Hamilton, a hypothesis must be necessary to be legitimate; i.e., that which is to be explained must not be a primitive fact of consciousness, for such facts neither need nor admit of explanation. The hypothesis of representationism advanced by Kant purports to explain how it is that we come to infer the real existence of some33Ibid.,

p. 87.

THOMAS BROWN AND WILLIAM HAMILTON

thing underlying phenomena. But, said Hamilton, our belief in the external existence of bodies is an integral part of our primitive experience, and, as such, it needs no explanation. 34 The second requirement listed by Hamilton, is in fact merely a reiteration of the demand for self-consistency applied to individual principles rather than to a system of propositions as a whole. By denying the testimony of consciousness with regard to our immediate perception of an outer world, the doctrine of representative realism undermines the principle of the veracity of consciousness which is, in turn, a s s u m e d true by the r e p r e s e n t a tionalists. Thus "the doctrine of representative perception annihilates itself," 35 and is not, therefore, a legitimate hypothesis. The third condition of a legitimate hypothesis is that the fact or facts for which it is to account must not themselves be hypothetical. Since the representationists do not acknowledge that external reality is known through a fact of consciousness, they must, according to Hamilton, hypothesize its existence and then account for the relationships between it and our phenomenal knowledge. But in this case the very facts to be explained are only hypothesized. Consequently, hypothetical or representational realism is not a legitimate hypothesis. 3 6 In the fourth place, "a legitimate hypothesis must account for the phenomenon, about which it is conversant, adequately and without violence in all its dependencies, relations, and peculiarities." 3 7 That is, a legitimate hypothesis must not be selective with regard to the facts of experience for which it is designed to account. It must leave them all on the same observational footing and not choose some to be taken as more fundamental than others. Furthermore, it must account not only for the general characteristics of the phenomenon but also for its detailed 34

Ibid., pp. 63-64. Ibid., p. 65.

35

Ibid., p. 64.

37

145

36

Ibid., pp. 64-65.

GROWTH OF COMMON SENSE PHILOSOPHY

interrelationships. Hypothetical realism fails to qualify under this requirement because it takes the fact of our immediate intuition of external existence and accepts only the intuition without accepting that the intuition itself is the only justification for accepting the external reality. Reality becomes a hypothesis while the intuition of its existence remains a fact; thus the hypothetical realist selects only part of the evidence of primitive consciousness as basic and relegates other aspects to hypothetical status. This separation of the elements of our perception of external reality into two logically distinct categories leads to the violation of a fifth requirement of legitimate hypotheses—that all facts which a legitimate hypothesis is devised to explain must lie within the sphere of experience.38 For the hypothetical realist or representationist, however, the factual reality which is assumed to be represented through experience, is itself asserted to transcend all experience. Hamilton's sixth and final requirement of a legitimate hypothesis is closely related to his third and fifth requirements. Not only must the facts, which a hypothesis is developed to explain, be within the sphere of experience and be well established by direct perception, but the hypothesis itself must also be independent of subsidiary hypotheses and elements which are transcendent, occult, or supernatural. In Hamilton's terms, it must work simply and naturally;39 i.e., we may not posit intermediate variables for which there is no direct evidence. Thus he restated Reid's, Stewart's, and Brown's demand for true causes. H A M I L T O N ON ANALOGY

So far, there is one topic related to most Common Sense discussions of science which we have not seen touched on 38

Ibid., p. 66.

39

Ibid., p. 66.

146

THOMAS BROWN AND WILLIAM HAMILTON

by Hamilton, and that is the role of analogical thinking. Hamilton intended to write an explicit discussion of the Law of Analogy as a portion of his notes to Reid's Works. But he did not complete his discussion, and his notes on this topic w e r e n e v e r found by his l i t e r a r y executors. 40 There are several places in his writings, however, which provide good evidence that his attitude toward analogy was very similar to that of Dugald Stewart. Analogies are the primary source of strongly suggestive arguments, but like the principle of simplicity or drive for unity, analogy could mislead as well as guide; so analogical arguments had to be tested where possible. The critical role played by analogical thinking was most clearly discussed by Hamilton in connection with the attributes of God. In this case, analogy provides the only key to understanding and one which he clearly accepted as adequate for the foundation of our theological beliefs. As far as Hamilton was concerned, "the Deity is not an object of immediate contemplation; as existing in and of himself, he is beyond our reach; we can know him only mediately through his works, and are only warranted in assuming his existence as a certain kind of cause necessary to account for a state of things, of whose reality our faculties are supposed to inform us." 4 1 This being the case, we can infer the properties of the Deity only from those of the known world. One traditionally accepted aspect of the Deity is that it involves a free and independent intelligence; Hamilton raised the question of how this belief is to be warranted: We can affirm naught of intelligence and its conditions, except what we may discover from the observation of our own minds, it is evident that we can only analogically carry out into the order of the universe the relation in which we find intelligence to stand in the order of the human constitution. . . . If, then, the original indepen40

See Reid's Works, II, p. 915. Note. ""Hamilton, Lectures, I, pp. 18-19.

147

GROWTH OF COMMON SENSE PHILOSOPHY

dence of intelligence on matter in the human constitu­ tion, in other words, if the spirituality of mind in man, be supposed as a datum of experience [as for Hamilton it was], in this datum is also given both the condition and the proof of a God. For we have only to infer, what analogy entitles us to do, that intelligence holds the same relative supremacy in the universe which it holds in us, and the first positive condition of a Deity is estab­ lished, in the establishment of the absolute priority of a free intelligence. 42 Thus, for Hamilton, analogy played the central role in theological arguments of the greatest moment. The centrality of analogy is not, moreover, limited to the transcendent domain of theology; it also plays a key role in the physical and mental sciences, where observation pro­ vides a critical check on its use. Hamilton made this par­ ticularly clear in his discussion of William Cullen in "On the Revolutions of Medicine in Reference to Cullen," 43 where he intemperately praised the philosophical scien­ tist over the mere experimenter: In physical science the discovery of new facts is open to every blockhead with patience, manual dexterity, and acute senses; it is less effectually promoted by genius than by cooperation, and more frequently the result of accident than of design. But what Cullen did, it re­ quired individual ability to do. It required, in its highest intensity, the highest faculty of mind—that of tracing the analogy of unconnected observations, of evolving from the multitude of particular facts a common princi­ ple, the detection of which might recall them from con­ fusion to system, from incomprehensibility to science. 44 Earlier Common Sense philosophers (Reid, for exam­ ple) might have argued that the exercise of man's highest 42Ibid.,

p. 22.

43 Edinburgh 44Hamilton,

Review, (July, 1932), 55, pp. 461-479. Discussions, p. 243.

THOMAS BROWN AND WILLIAM HAMILTON powers does not necessarily lead to the highest attain­ ments iii science. But such an argument was completely foreign to Hamilton's thought. His praise of Cullen must be read as an assertion that the systematization of observa­ tions based on analogical relations is among the most laudable and important of scientific activities. Hamilton's advocacy of analogical reasoning was not, however, uncritical. Like both Stewart and Brown he saw it as an extremely useful guide and stimulus to theorizing—a first step in scientific work—rather than the end of investigation. Thus, in arguing against Whewell's "Demonstration that all Matter is Heavy," Hamilton wrote that Whewell's argument "supposes, as a logical canon, that a presumption from analogy affords a criterion of truth, subjectively necessary, and objectively certain." 45 But, Hamilton said, it is not subjectively neces­ sary; "for however inclined, we are never necessitated, a posteriori, to think that because some are, therefore all the constituents of a class must be, the subjects of a predi­ cate a priori contingent." 46 And it is not objectively cer­ tain; "for though a useful stimulus and guide to investiga­ tion, analogy is, by itself, a very doubtful guarantee of truth." 47

THE APPLICATION OF HAMILTON'S METHODOLOGICAL PRECEPTS TO THE SCIENCE OF PHRENOLOGY Because Hamilton's major interests were in metaphysi­ cal and epistemological topics, almost all his methodolog­ ical ideas were developed in the course of arguments not primarily related to discussions of traditional natural sci­ ence. But it is clear that he intended them to be applied to the physical sciences as well as to metaphysics and the philosophy of the mind (psychology) both because he occasionally used illustrative materials from physics, as45 Hamilton 46 Ibid.,

(ed.), Reid's Works, II, p. 854, note D. 47 Ibid., p. 854. p. 854.

GROWTH OF COMMON SENSE PHILOSOPHY

tronomy, biology, and matter theory and because he, like his Scottish predecessors since Hume, felt that there was but one proper method of philosophizing applicable to all subject matters. Hamilton, moreover, wrote directly about at least one contemporary physiological theory—phre­ nology—and we can see several of his methodological principles applied in his analysis and critique of this science. The phrenological theory or hypothesis, developed most fully by Franz Joseph Gall, is that there is a corres­ pondence between the volume of certain parts of the brain, called developments (measured externally), and the intensity of certain qualities of mind and character, called manifestations. Hamilton became interested in this doctrine in about 1819, when George Combe was popularizing the new "science" in Edinburgh. Hamilton did a series of experiments to test its validity, rapidly concluded that it was false, and began to prepare a work entitled "The Fictions of Phrenology and the Facts of Nature." 48 But he decided that the doctrine did not war­ rant such serious treatment, and most of his results were published later as short articles, "On the Frontal Sinuses" 49 and "On the Weight and Relative Proportions of the Brain and Cerebellum," 50 or included in his lec­ tures on consciousness. Hamilton's discussions played little role in the arguments about phrenology, but they do provide interesting insights into use use of explicity de­ veloped methodological guidelines. In the analysis of phrenology appended to his Lectures on Metaphysics, Hamilton began by writing: This doctrine professes to have discovered new princi­ ples, and to arrive at new conclusions; and the truth or 48 See

Appendix II in Hamilton's Lectures, I , p. 662, note 1. Times (May, 1845) 12: 159, (June, 1845) 12: 177, and (Au­ gust, 1945) 12: 371. 50 Hamilton cites Dr. Alexander Munro, Anatomy of the Brain, which I have been unable to identify. 49 Medical

THOMAS BROWN AND WILLIAM HAMILTON

falsehood of these cannot, therefore, be estimated merely by their conformity or disconformity with those old results which the new professedly refute. . . . Such an opinion must be taken on its own ground. We must join issue with it upon the facts and inferences which it embraces. 5 1 That is, Hamilton used his criteria of internal consistency and correspondence with fact and denied that the theory can be judged against any other theory-dependent assertions, no matter how well established they may seem to be. "To do so," he said "would be mere prejudice, a mere assumption of the point at issue." 5 2 Next, he undertook an investigation of the "fundamental facts" upon which the phrenological hypothesis is based. In order to be a legitimate hypothesis it must connect facts which are themselves well established by observation, and it must do so in such a way that it (1) is capable of falsification, (2) does not depend on subsidiary hypotheses, and (3) accounts for both the general and the detailed phenomena within its compass. On all counts phrenological doctrine must be rejected. In the first place, since the phrenologists offer no standard by which cerebral development could be accurately and precisely measured and because their definitions of mental manifestations are usually so vague and indeterminate, "individual cases could prove little against it. . . ,"S3 Thus phrenology should be discarded because in many cases there is simply no way of unambiguously falsifying the doctrine by reference to experience. Secondly, Hamilton argued, the phrenologists introduce numerous subsidiary hypotheses in the course of defining manifestations. They assert the independent existence of such qualities as temperament and activity as well as of such mental manifestations as causality, comparison, and a representative faculty—manifestations posited by ear51

S2

Hamilton, Lectures, I, p. 650. Ibid., p. 651.

53

151

Ibid., p. 650.

GROWTH OF COMMON SENSE PHILOSOPHY

lier German philosophical theories but never established as factual in any way. 54 Therefore their main hypothesis fails to meet the requirement that the facts about which it is conversant are themselves non-hypothetical. Finally, in the few cases where the developments and manifestations are both well established facts and unambiguously defined, the phrenological doctrine is based on presumed correlations which are contrary to fact. For example, phrenologists assert that the size of the cerebellum provides an accurate measure of sexual appetite. This assertion is testable; Hamilton set out to check its validity. In the course of measuring over 1,000 brains of fifty different species of animals, Hamilton discovered that in all animals the ratio of cerebellum to total brain size is greater in females than in males and that in humans the female cerebellum is, on the average, absolutely larger than the male. This was in direct opposition to Galls' contention. 5 5 In all animals, moreover, the cerebellum reaches its maximum size long before puberty and the ratio of cerebellum to brain size declines thereafter, again in contrast to Galls' assertion. 56 Hamilton's experiments on the cerebellum, therefore, established the falsity of one of the central "facts" of phrenology and condemned it as an illegitimate scientific hypothesis. Hamilton organized his writing in a manner vastly different from that of his Common Sense predecessors, seldom if ever making scientific methodology the explicit concern of his writings. Yet his metaphysical, epistemological, and critical works all imply a clear theory of scientific method which agrees in remarkable detail with the notions of both Stewart and Brown. Hamilton placed far greater initial emphasis on the psychological elements in science and gave a new primacy to the drive for unity and to the hypothetical method based on analogy. Furthermore, he seemed to give much more emphasis to internal coherence in a theory as presumptive evidence for its 54

Ibid., pp. 651, 656-657.

55

Ibid., p. 652.

152

56

Ibid., p. 652.

THOMAS BROWN AND WILLIAM HAMILTON

value. But by the time he qualified these emphases—urging empirical control over our desire for unity, de­ veloping an extensive series of criteria for judging the acceptability of hypotheses, and requiring that a theory correspond with a wide range of experience as well as exhibit internal consistency—Hamilton offered an almost traditional Common Sense theory of scientific method.

PART II

The Influence of Common Sense Ideas on the Exact Sciences in Britain

CHAPTER 6

Common Sense Reflections in the Natural Philosophy of John Robison and John Playfair doubt that Scottish natural philosophers were strongly influenced by metaphysical and epistemological considerations throughout the second half of the eighteenth century. But for many cases during the period between 1770 and 1815, it is difficult to deter­ mine whether natural philosophers were adopting ideas initially presented by their colleagues in moral philoso­ phy or whether moral philosophers like Reid, Stewart, and Brown were merely formalizing and systematiz­ ing methodological rules and epistemological doctrines already implicit in the work of the natural philos­ ophers. 1 The problem of sorting out the order in which methodological ideas developed is particularly diffi­ cult because the natural and moral philosophers were in close daily contact within the universities and within local literary and philosophical societies. At Edinburgh in the late eighteenth century, for example, not only were Dugald Stewart, Joseph Black, John Robison, and John Playfair all members of the same small university faculty, but they were also all members of the Royal Society of Edinburgh and of the "Oyster Club," an intimate social club which met weekly for food and conversation. As a result, their interchange of ideas often depended less on formal writings than on informal discussions of which no clear record remains.

THERE IS NO

1 See G. Cantor, "Henry Brougham and the Scottish Methodological Tradition," Studies in the History and Philosophy of Science 2 (1971), pp. 78-79.

COMMON SENSE AND THE EXACT SCIENCES

When we look at the writings of natural philosophers who attended Scottish universities—especially at Edinburgh—after the ascent of Dugald Stewart to the chair of moral philosophy in 1785, we see that regardless of how methodological and metaphysical ideas were introduced into the Scottish tradition, they were developed and propagated most clearly and effectively by the moral philosophers and subsequently applied in natural philosophy. Thus, most of my attention in discussing the Common Sense component of Scottish science will center on the writings of men who formally studied Common Sense Philosophy before they began their careers as scientific authors. However, there is enough evidence for a movement of ideas from Common Sense moral philosophy into the scientific works of earlier writers that some comment seems worthwhile. So, it is useful to begin by looking quickly at the writings of John Robison (1739-1804) and John Playfair (1748-1819), successive holders of the prestigious chair of natural philosophy at the University of Edinburgh from 1774 to 1805 and from 1805 to 1819, and two of the most influential of eighteenth-century Scottish natural philosophers. Both of these men made frequent and explicit references to the general philosophical underpinnings of their scientific beliefs and espoused methodological principles which correspond very closely to those enunciated by their contemporaries in moral philosophy. From the early 1780s, for example, Robison opened his natual philosophy course with a discussion of the epistemological problems facing the scientist who attempts to account for natural phenomena: When philosophers began to turn their attention to this subject [natural philosophy], they were convinced that the very existence of the external object, nay the very nature of its being external, rendered it impossible for it to be the imagined object of thought or perception. It 158

JOHN ROBISON AND JOHN PLAYFAIR

was an established principle that nothing could act where it was not, and therefore the external object could not act on the mind, nor be an immediate object of its contemplation. Some media was therefore necessary for us to hold an intercourse with external bodies, and different views of this subject led to different contrivances. 2 Thus, Robison set the fundamental problem of the epistemological basis of natural philosophy in terms almost identical to those laid down by Reid in his earlier and more general work. Furthermore, his response to the problem was very similar to Reid's and to Stewart's: he rejected the old mechanistic and etherial theories associated with Priestley and eventually embraced most aspects of the Roscovichian system when it became known to him later in the 1780s. It appears that Robison's interest in Roscovich predates Stewart's by at least three or four years, but it is very likely that Robison's basic epistemological attitudes and his response to Priestley's ideas in particular did derive from Thomas Reid. 3 I know of no explicit reference to Reid by Robison; but when Robison returned to Glasgow in 1764 to work closely with Joseph Rlack for two years, Reid had just become professor of moral philosophy there and not only attended Rlack's lectures but also became a close personal friend of the man who sponsored Robison. Thus E d i n b u r g h University Library, Dc. 729, "Lectures of John Robison before his Natural Philosophy Class," p. 30 of second numbered sequence. This is the 29th of 40 volumes of handwritten lectures by Robison. Unfortunately the lectures were bound topically rather than chronologically, and we can only guess, on the basis of the handwriting, at the date of this lecture. I would place it late in the 1770s or early in the 1780s. 3 See R. Olson, "The Reception of Boscovich's Ideas in Scotland," I sis 60(1969), pp. 94-95, and J. B. Morrell, "Professors Robison and Playfair and the Theophobia-Gallica: Natural Philosophy, Religion, and Politics in Edinburgh, 1789-1815," Notes and Records of the Royal Society of London, 26 (1971), pp. 43-60.

159

COMMON SENSE AND T H E EXACT SCIENCES

Robison and Reid must have met. When Robison attacked Priestley's philosophy for its necessitarian and atheistical tendencies in his Proofs of a conspiracy against all the religions and governments of Europe, carried on in the secret meetings of Freemasons, illuminati, and reading societies of 1797, his attack exactly paralleled Reid's earlier works in content. It condemned etherial fluids both because they failed to explain phenomena, and because they encouraged atheism "by blandly reducing God to nothing but the most extensive and refined undulation, and his own mental processes to 'the quiverings of some fiery marsh miasma.' " 4 If Robison's critique of Priestley did come from Reid, then it is clear that Common Sense Philosophy had a major impact on his scientific work. It led him to reject Euler's theory of ether vibrations in his "On the Motion of Light as Affected by Refracting and Reflecting Substances which are also in Motion." 5 The same arguments made him suspend belief with respect to all fluid theories of electricity, 6 even though he felt that Aepinus' hypothesis "not only seems to explain the phenomena, but is practically useful for directing us to the procedures which are likely to produce the effect we wish." 7 Robison's attitudes toward the relative virtues of geometrical and analytic mathematics were also clearly attuned to Common Sense pedagogical arguments. His appreciation of the writings of French theoretical astronomers like Lagrange and Jean D'Alembert convinced him that advanced topics in mechanics and theoretical astronomy called for using algebraic as well as geometrical 4

J. B. Morrell, op. cit., p. 48. transactions of the Royal Society of Edinburgh 2 (1788), pp. 97-98. My attention was called to this paper by G. N. Cantor's "Henry Brougham and the Scottish Methodological Tradition," Studies in the History and Philosophy of Science, 2 (1971), see pp. 77 and 80-81. 6 See John Robison, A System of Mechanical Philosophy, edited D. Brewster (Edinburgh: John Murray, 1822), iv, pp. 177-198. 'Ibid., iv, p. 176.

160

JOHN ROBISON AND JOHN PLAYFAIR 8

analysis. But he chose to write his Elements of Mechani­ cal Philosophy in geometrical form because he believed that geometrical techniques were more valuable for elementary instruction. They exhibited greater logical purity, and they helped to concentrate a student's atten­ tion on the problem at hand rather than allowing him to have recourse, to algebraic manipulations in which he could "proceed without ideas of any kind and obtain a result without meaning and without being conscious of any process of reasoning."9 The sources of John Playfair's basic epistemological and methodological commitments are even less clear than are Robison's. But once again there is at least some indica­ tion that his knowledge of Reid played a role in his at­ titudes toward natural philosophy and mathematics. Playfair was a student at St. Andrew's from 1762 to 1769, studying both natural philosophy and theology. After sev­ eral years of private study at Edinburgh, where h e came to know Principal Robertson, Adam Smith, James Hutton, Joseph Black, and Mathew and Dugald Stewart, Playfair became Minister at Liff in Forfarshire. It is from his cor­ respondence at this time that we can gather something of his early explicit philosophical background and his appli­ cation of Common Sense notions to questions in natural philosophy. In 1773, Playfair wrote several letters to his former student, William Robertson, discussing the rela­ tive opinions and merits of the philosophers Reid, Beattie, 10 Bacon, Priestley, and Hartley. Among these letters, one, preserved in the Robertson papers at the National Library 8

John Robison, Elements of Mechanical Philosophy (Edinburgh: Ar­ chibald Constable and Company, 1804), pp. 272-273. 9 Quoted by Sir William Hamilton in Discussions, p. 317, from Robi­ son's Encyclopedia Britannica article on his teacher Robert Simson. Emphasis is Robison's. 10 See the "Biographical Account of the Late Professor Playfair," by James Playfair prefaced to Volume ι ofThe Works ofJohn Playfair, Esq. (Edinburgh: Archibald Constable and Co., 1822), p. xv, for mention of these letters. 161

COMMON SENSE AND T H E EXACT SCIENCES

of Scotland, provides a good example of his use of metaphysical arguments suggested by Reid to discredit etherial media: As you ask my opinion of the aetherial fluid, I shall give you the arguments which, however, induced me to doubt of its existence. The difficulty with which the hypothesis of gravity is attended as supposing bodies to act where they are not is thought to be a strong presumption in favor of this fluid.... But let it be considered that the action of one body on another by contact is equally inexplicable. That one body should put another in motion is a fact we know, but the cause of it we cannot pretend to assign. Mr. H u m e reasons well on this subject in his essay on necessary connection. If you consider the theory metaphysically, you will easily be convinced, that there is no reason why a body should compel another when near, anymore than it should tend to at a distance. 1 1 Although Hume is the only philosopher named in this statement, the argument used is not compatible with his demand for physical continuity in causal sequences. 1 2 It is, on the other hand, precisely that developed by Reid as an extension of Hume's reasoning. Even if one could admit that, in principle, contact action is more understandable than actions at a distance and that a mechanistic-ether explanation of gravity would be desirable, no etherial hypothesis yet devised was acceptable. In Playfair's words, "the great objection to this fluid is that it is by no means adequate to the purposes for which it is supposed." 1 3 Every etherial theory seemed to raise as many problems as it solved. If the ether were so subtle u J o h n Playfair to William Robertson, Liff, June 28 (1773), National Library of Scotland, Ms. 3942. 12 See G. Buchdahl, Metaphysics and the Philosophy of Science, (Cambridge, Mass.: M.I.T. Press, 1969), ch. VI, for a discussion of Hume's continuity requirement. 13 Playfair to Robertson, National Library of Scotland, Ms. 3942.

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JOHN ROBISON AND JOHN PLAYFAIR

that it could freely pervade all bodies (and how else could one account for the unimpeded orbital motions of the planets?) then it certainly would be incapable of impres­ sing the motions classed as gravitational. And if it were capable of moving bodies, then how could one account for the apparently unimpeded orbital motions of the planets? Certainly no hypothesis which raised such serious prob­ lems could possibly be correct. Between 1772 and 1808, when Playfair returned in print to an analysis of etherial explanations of gravity, he became aware of at least one gravitational ether which he thought was not subject to this argument from in­ adequacy—George Louis Le Sage's hypothesis of a mech­ anistic gravic fluid. But at the same time he also learned of an alternative theory of gravity—Boscovich's— which seemed as effective as Le Sage's theory in accounting for gravitational and phenomena but which re­ duced impulsive actions to attractions and repulsions rather than vice versa. Thus, Playfair found himself very much in the quandary of Stewart's decipherer with two effective but contradictory keys. "The result of all this is to throw considerable uncer­ tainty over all of our speculations concerning the cause of gravitation, and, what is more, concerning the es­ sence of body, and the substratum in which its proper­ ties are conceived to be united. To know the laws of the phenomena of body, is all that science has yet attained with certainty—perhaps all that it is ever destined to attain. What lies beyond that point, may exercise the ingenuity, and amuse the fancy of speculative men; but whether it will lead to more substantial acquisitions, must be left for futurity to determine. 14 The only proper course for a scientist in this case was to withhold assent from any hypothesis while remaining 14 Review of Vince's "Observations on the Hypotheses which have been assumed to account for the Causes of Gravitation from Mechanical Principles," Edinburgh Review, 23 (1808), pp. 115-116.

COMMON SENSE AND THE EXACT SCIENCES

open to the unlikely possibility that one might eventually be shown to b e uniquely true. Playfair disagreed with the argument (emphasized by Thomas Brown in lectures which Playfair attended during 1808) that no universal property like gravitation could receive further explanation and that the search for a cause of gravity was therefore an inherently illegitimate enterprise. But in doing so, he d e p e n d e d upon Common Sense arguments about the simplifying, generalizing, and unifying function of scientific theory: If indeed gravitation were not only known to be universal among material substances, but if all other causes of motion could be reduced to it, and shown to be modifications of one and the same law, there would be little reason to expect that we could ever carry our inquiries much further. . . . But our knowledge of gravitation has by no means reached this perfection. We are not sure that it is quite universal—that heat and light, for example, are subject of its power—and what is of more importance in the present question, we are sure that all the causes of motion have not yet been reduced to one; so that gravitation is neither known to depend on impulse or impulse upon gravitation. Two laws, very different from one another, direct the motions of the material world; and, till these two can be reduced to one, or be shown to depend on the same cause, or till they be demonstrated to arise from different causes, our knowledge of them is incomplete. 1 5 Just as his attitudes toward the nature and limitations of natural philosophy mirrored the concerns of Common Sense philosophers, Playfair's first published mathematical paper shows an attitude toward the foundations of mathematics identical with that of Reid and Stewart. The whole paper, " O n the Arithmetic of Impossible 15

Ibid., p. 104.

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JOHN ROBISON AND JOHN PLAYFAIR

Quantities," 1 6 is, in fact, an attempt to justify the usefulness of operations with imaginary or "impossible" quantities in spite of their philosophical unintelligibility. In an introductory statement, which was fully in accordance with the doctrines of Reid and which was probably later paraphrased by Steward, Playfair wrote: In geometry every magnitude is represented by a line and angles by an angle. The genus is always signified by the individual, and a general idea by one of the particulars which fall under it. By this means, all contradiction is avoided, and the geometer is never permitted to reason about the relation of things which do not exist, or cannot be exhibited. In algebra again every magnitude being denoted by an artificial symbol, to which it has no resemblance, is liable, on some occasions, to be neglected while the symbol may become the sole object of attention. It is not perhaps observed where the convection between them ceases to exist, and the analyst continues to reason about the characters after nothing is left which they can possible express: if, then, in the end, the conclusions which hold only of the characters be transferred to the quantities themselves, obscurity and paradox must necessarily ensue. 1 7 He went on to show that this potential for abuse in algebra is actualized in many important instances, although the predictions about real physical phenomena which arise out of utilizing what are literally impossible quantities do invariably hold true. The crucial question then becomes: "If the operations of this imaginary arithmetic are unintelligible, why are they not also useless?" 1 8 The traditional explanation—that when we apply imie

Philosophical Transactions of the Royal Society of London, 68 (1778), reprinted in The Works of John Playfair, Esq. (Edinburgh: Archibald Constable and Co., 1822), in, pp. 3-29. Subsequent citations are from Playfair's Works. 17 Playfair's Works, ill, p. 3-4. Emphasis mine. 18 Ibid., p. 6.

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aginary analysis to real problems, the imaginary terms compensate or destroy each other—was unsatisfactory to Playfair because he could not conceive one impossibility destroying another. "Is not this to bring impossibility under the predicament of quality, and to make it a subject of arithmetical computation? And are we not thus brought back to the very difficulty to be removed?" 19 His answer to the problem lay in looking at the circumstances in which imaginary expressions most often arise in practical problems. Imaginary quantities arise in considering a variety of properties of the circle because the trigonometric func­ tions may be represented by series which in turn may be given the following easily manipulated form: sin a =

e as/~i

.g-ov'-i τ=

Iyfl

and cos a =

e a \/ -1 +e~ a 2

,

where a is the arc of a circle of unit radius and e is the number whose hyperbolic logarithm is unity. Playfair showed that if we consider the hyperbolic functions sinh a and cosh a rather than the analogous circular functions, then all the relations which can be proved for the one, using imaginary quantities, can be proved for the other simply by replacing V-T by VT, and that this suggests the significance of imaginary quantities: The operations, therefore, performed with the imagi­ nary characters, though destitute of meaning them­ selves, are yet notes of reference to others which are significant. They point out, indirectly, a method of de­ monstrating a certain property of the hyperbola, and then leave us to conclude, from analogy, that the same property belongs also to the circle.... The investigation therefore, revolves itself ultimately into an argument from analogy; and, after the strictest examination, will be found without any other claim to the evidence of 19 Ibid.,

p. 7.

JOHN ROBISON AND JOHN PLAYFAIR

demonstration. Had the foregoing proposition been proved of the hyperbola only, and afterwards concluded to hold of the circle, merely from the affinity of the curves, its certainty would have been precisely the same as when a proof is made out by the intervention of imaginary symbols. 20 Such an interpretation of the nature of mathematical reasoning clearly must have been unwelcome to those for whom the demonstrative certainty of geometry provided the prime characteristic of mathematics, and it must have been unacceptable to any who believed in the absolute distinction between physical and mathematical entities. Even for those who accepted the argument, it left complex analysis with a justification vastly inferior to that enjoyed by geometry. But in spite of the traditional standards of mathematical certainty, Playfair was willing to accept the analogical relationship as sufficient to justify confidence in the utility, if not the certainty, of complex analysis. After an extended analysis of the limits of the relationship between circular and hyperbolic functions, he argued that "supported on so sure a foundation, the arithmetic of impossible quantities will always remain a useful instrument in the discovery of truth, and may be of service when a more rigid analysis can hardly be applied." 2 1 This confidence in the value and importance of analogical reasoning certainly went beyond the methodological ideas of Reid, but it is very similar in tone to the emphasis on the value of analogical arguments—which are often all we have—in the writings of Dugald Stewart. There are innumerable other examples of Playfair's use of methodological contentions discussed by Common Sense philosophers after he became professor of mathematics and later of natural philosophy at Edinburgh (1785-1819). In his Outlines of Natural Philosophy of 1814, for example, Playfair emphasized the use of analogy as a prime source of physical hypotheses and expressed 20

IbId., pp. 11-12.

2I

Ibid., p. 28.

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the unusual definitional distinction between hypotheses and theories which Thomas Brown had presented in his Lectures on the Philosophy of Mind—that hypotheses are explanations which have no evidence independent of their ability to account for the phenomena in question, while theories are founded on facts known independently of the phenomena to be accounted for.22 We cannot be certain of whether Brown learned from Playfair or vice versa. We do know that Brown expressed this distinction in lectures presented in 1808 and 1809 and that Playfair attended these lectures, 2 3 however, and I know of no indication in Playfair's writings or from student notes taken in Playfair's classes before 1811 that he made the distinction earlier. Although it is virtually impossible to prove that Playfair borrowed from the methodological precepts of Reid or of his colleagues Stewart and Brown, the fact that he expressed many of the same ideas, read Reid's works, spoke with Stewart frequently, and attended Brown's lectures—and that where parallel sentiments appear they frequently occur first in the works of the moral philosophers—makes it plausible to believe that Common Sense methodological precepts were not always drawn from contemporary natural philosophy but were frequently developed first among moral philosophers and subsequently adopted by contemporary natural philosophers. 22 John Playfair, Outlines of Natural Philosophy (Edinburgh: Archibald Constable and Co., 1814), pp. 3-4. 23 See David Welsh, Account of the Life and Writings of Thomas Brown, M.D. (Edinburgh: W. and C. Tait, 1825), p. 174.

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CHAPTER 7

Common Sense Elements in Scientific Reviews: 1790-1840 IT IS OFTEN difficult to infer much about the Scottish scientists' general philosophical attitudes from their technical papers, even though unstated assumptions may have played an important role in guiding their work. This is so because in the early nineteenth century, as today, the metaphysical and methodological presuppositions which underlay scientific work were usually implicit rather than overtly expressed in the research reports written by scientists. In their critical assessments of colleagues' work, however, the Scots were frequently more explicit about epistemological and methodological issues, so it makes sense to seek evidence for a Common Sense element within the exact sciences through an analysis of contemporary reviews. Two circumstances make it particularly appropriate to use review literature to study the characteristics of Scottish science in the early nineteenth century. First, almost all the most significant Scottish scientists wrote articles for one or more of the widely read literary reviews; 1 and second, the anti-etherial arguments of the early Common Sense scientists had one of their most obvious manifestations in Henry Brougham's unfavorable review of Thomas Young's Bakerian lecture of 1801. There is some danger in this approach; scientists, like !Playfair, for example, wrote more than twenty-five scientific reviews for the Edinburgh Review; John Leslie wrote for the Monthly Review; and David Brewster contributed to the Quarterly Review, North British Review, and Edinburgh Review.

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any other men, are capable of self-delusion—of believing that they adhere to stated principles which, in fact, play little or no role in their work. If we follow u p an investigation of explicit methodological and metaphysical statements by showing that the original researches of the men in question conform to their avowed statements of principle however, then any objections to the method should be minimal. OPPOSITION TO ETHERIAL HYPOTHESES IN T H E S C O T S ' R E V I E W S

One of the most important sets of arguments drawn from Common Sense Philosophy in terms of its implications for early nineteenth-century physics was that urged against admitting the existence of etherial media because 1) they were subject to no proof of existence independent of that inferred from their explanatory power, 2) in many cases a careful consideration of the proper notion of cause obviated any logical n e e d to introduce intermediate entities to connect events, and 3) the modes of action of etherial media were themselves quite inexplicable, either because they involved an assumption about the primacy of impacts which had been cogently criticized by Boscovich or because they involved the assumption of equally inexplicable mutual attractions and/or repulsions among etherial particles. The basic opposition to ethers among the moral philosophers, of course, arose out of their desire to maintain a radical distinction between mental and physical phenomena and thus to do away with the medullary ether posited by Hartley and defended by Joseph Priestley. But the arguments developed in connection with their enforced disjunction between mind and matter were widely adopted by natural philosophers to reject etherial explanations of physical as well as psychical events. In most cases the physical scientists showed no explicit awareness of the original context of these anti-etherial 170

SCIENTIFIC REVIEWS

arguments, ignoring Reid's and Stewart's analysis of the misleading psychological appeal that etherial arguments had because of their origins in metaphorical language and analogical thinking. In a few cases, however, we can see a direct link between Reid's antagonism to medullary ether and the natural scientists' opposition to these subtle fluids. The clearest such case appears in a review of G. C. Morgan's Lectures on Electricity written by John Leslie in 1794 for the Monthly Review. In this review, Leslie, who had been a student of Dugald Stewart in 1786. and who was to become one of the most outstanding Scottish scientists of the early nineteenth century, took issue with all fluid theories of electricity by offering the three major criticisms of subtle fluids usually presented by natural philosophers: The existence of an electric fluid has generally been taken for granted. This fundamental principle Mr. Morgan attempts to demonstrate, and he conceives that the striking effects exhibited on bodies under the electric influence afford indubitable evidence of the presence of some corporeal agent. We cannot admit the legitimacy of this argument [i.e., Morgan can offer no more than inference from the phenomena to be explained in proof of the fluid's existence, and this is not enough]. As well might we conclude that the phenomena of gravitation and magnetism are produced by certain subtile intermedia; nay, that the communication of motion from one body to another is performed by the operation of a peculiar aetherial aura [i.e., no intermediate mechanism is really needed to explain electrical attractions and repulsions because those attractions are somehow primary phenomena in the same way that gravity is, and they must be causally understood only in Hume's sense]:—but how much soever we refine on the senses, the agent is still material; and the real difficulty, we should say impossibility, of accounting for the origin or continuance of motion subsists in its full force [i.e., 171

COMMON SENSE AND THE EXACT SCIENCES

even granted an ether, the interactions between aether particles are no more explicable than those between the larger particles whose behavior is to be explained]. Once he had made these observations, Leslie went on to show the direct connection between his critique of elec­ trical theories and the Common Sense critique of material theories of the mind: It is curious to observe the efforts made in different periods of society to emerge from sensible objects in order to attain an adequate idea of mind. The concep­ tions were usually borrowed from those material, but almost invisible and intangible, substances, which we recognize principally from their effects. In the ancient languages, the terms which denote mind primarily sig­ nified a wind or breathing. The same prejudice, the same darkness of apprehension, has directed the views of modern electricians. 2 Though Leslie presented the most explicit connection between the rejection of subtle mediums in natural philosophy and in moral philosophy, he was by no means alone in using the moral philosophers' criteria to turn away from etherial media. Robison's and Playfair's oppos­ ition to etherial explanations for gravity and electrical phenomena had preceeded Leslie's critique of electrical theories, and Henry Brougham used similar arguments in his notorious opposition to the luminiferous ether as­ sumed by nearly all early proponents of the undulatory or wave theory of light. Brougham, who became one of the most popular and powerful liberal politicians of the early century, studied at the University of Edinburgh under Robison, Playfair, and Stewart; published ten scientific papers—largely on the nature of light and on higher mathematics—betwen 1796 and 1858; wrote several popular scientific books; and was 2 John Leslie, "Lectures on Electricity by G. C. Morgan," Monthly Review 16 (1794), p. 30. Emphasis on last sentence mine.

SCIENTIFIC REVIEWS

one of the principal early contributors to the Edinburgh Review on scientific and political topics. In his first scien­ tific review, written for the Edinburgh Review in 1802, Brougham indicated his opposition to any luminiferous ether by singling out for criticism some comments on Newton's conjectures about the vibratory nature of light made by James Wood in his Elements of Optics. Wood had written that Newton concluded from the phenomena of reflection and refraction that these effects were pro­ duced by a medium diffused over the surface of bodies which reflect or bend light.3 Brougham took violent ex­ ception to this remark, arguing that Newton's writings on this topic had been "generally perverted by ignorant theorists, who, on the supposed authority of his name, have built the most extravagant hypotheses." "Newton," he goes on to say, does not conclude, from the phenomena of reflection and refraction that these effects are produced by some power or medium, diffused over their surface: he only says, with the modesty peculiar to himself that the prob­ lem is scarce to be solved, otherwise than by supposing some power of the body evenly diffused over all of its surface, and by which it acts on the ray without im­ mediate contact. Optics, B.2, part 3, prop. 8. He then goes on to illustrate this idea, by the analogy of gravita­ tion, inflection, etc., but never once, in this whole prop­ osition, does he hint at any medium. On the contrary, he refers all to those powers of attraction and repulsion; to explain which, the hypothesis of a medium is called in.4 All the emphases in this statement make it clear that Brougham's objection was to Wood's inference that a spe3 See

James Wood, The Elements of Optics, 2nd ed., (Cambridge: J. Deighton, 1801), p. 13. 4 Henry Brougham, review of "The Elements of Optics, designed for the use of Students in the University by James Wood," Edinburgh Review 1 (1802), p. 162. All emphases Brougham's.

COMMON SENSE AND THE EXACT SCIENCES

cial medium must be assumed to account for attractions or repulsions which occur at some finite distance. Brougham was forced to admit that Newton did offer an etherial hypothesis to explain the refraction and reflection of light. But this hypothesis, Brougham rightly pointed out, was kept to itself in queries 18-24 (of the third edition of the Optics), where it was offered only as a conjecture unsupported by strict induction; 5 and Brougham, like his mentors Reid, Stewart, and Playfair, was insistent that such speculations not be confused with properly established scientific laws. The fullness of Brougham's opposition to etherial media was made manifest in his famous review of Thomas Young's "Bakerian Lecture on the Theory of Light and Colours" which appeared in the Edinburgh Review in early 1803. 6 Both the vindictive tone and the content of this review have traditionally been seen as the result of a personal feud between Brougham and Young. But, as Geoffrey Cantor has recently shown, there is little evidence that such a feud existed. 7 The content is much more easily accounted for by Brougham's adherence to Scottish methodological principles, and the tone—though perhaps inexcusably bitter—was typical of that assumed by Brougham for rhetorical effect in many of his writings and speeches, even when his barbs were likely to hit friends as well as foes. Young's Bakerian Lecture of 1801, which Brougham chose to use as his target, introduced the undulatory theory of light to a large audience. Basically, it argued that light is really nothing other than a vibratory or undulatory motion in an etherial medium and that such phenomena as the colors seen in thin and thick plates and in 5

Ibid., p. 163. The Edinburgh Review 1 (1803), pp. 450-456. 1 G. N. Cantor, "Henry Brougham and the Scottish Methodological Tradition," Studies in the History and Philosophy of Science, 2 (1971), pp. 69-89. e

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"Newton's Rings" are produced by the interference of light "waves." 8 Brougham opened his attack on the paper by chiding the Royal Society for publishing a paper which "contains nothing which deserves the name, either of experiment or of discovery." 9 Then he turned his pen against the kind of theorizing ostensibly indulged in by Young: An hypothesis which is assumed from a fanciful anal­ ogy, or adopted from its apparent capacity of explaining certain appearances, must always be varied as new facts occur, and must be kept alive by a repetition of the same process of touching and retouching, of successive ac­ commodation and adaptation, to which it originally owed its puny and contemptible existence. But the making of an hypothesis is not the discovery of a truth. . . . A mere theory is in truth destitute of all pre­ tentions to merit of every kind except that of a warm and misguided imagination. It demonstrates neither pa­ tience of investigation, nor rich resources of skill, nor vigorous habits of attention, nor powers of abstracting and comparing, nor extensive acquaintance with nature. It is the unmanly and unfruitful pleasure of a boyish and prurient imagination, or the gratification of a cor­ rupted and depraved appetite. 10 Such a throughgoing rejection of hypotheses, if it places Brougham in any philosophical tradition, seems to ally him firmly with Thomas Reid; but care should be taken to observe that his attack is really centered on such hypoth­ eses as are drawn solely from analogy or invented solely to account for one given set of phenomena. That Brougham 8 Thomas Young, "The Bakerian Lecture on the Theory of Light and Colours," Philosophical Transactions, 92 (1802), pp. 12-48, 9 Henry Brougham, review of Tfoe Bakerian Lecture on the Theory of Light and Colours by Thomas Young. Edinburgh Review, 1 (1801-3), p. 450. 10 Ibid., p. 452.

COMMON SENSE AND THE EXACT SCIENCES

did in fact acknowledge a value to some hypotheses, we can see by his comparison between what he believed to be Newton's true hypothesis—i.e., that particles of light might interact with and set up vibrations in an etherial medium—and Young's hypothesis (borrowed from Euler and attributed in error to Newton) that vibrations in an etherial medium actually constitute light. After establishing certain optical phenomena, Brough­ am wrote, Newton "amuses himself by conjecturing how the rays of light would act upon, and be affected by, an aetherial, subtile medium, were the existence of such a medium ascertained. That the concession of such an exis­ tence would enable us to resolve a variety of facts, appar­ ently anomalous, into one general, and uniform, and suffi­ ciently simple law, no one can entertain any doubt, who has read the passages in which this fanciful supposition is pursued by that great genius. . . Z' 11 Newton's hypothesis can still be accepted as only a "fanciful supposition," but if the ether could be shown to meet the criterion of inde­ pendent existence propounded by both Reid and Stewart, then it would have to be taken seriously. It would involve no more than known laws of nature accounting for the interaction of independently existing entities (this, of course, ignores the obvious problem of how the existence of light particles is established. Brougham believed, as had Newton, that the particulate nature of light followed from Newton's optical experiments). The undulatory theory of Young, however, in which undulations in the ether constitute light, was subject to further insuperable problems, for even if an ether were shown to exist, one would still be faced with determining by what mechanisms the phenomena of optics were to be explained. In Brougham's words: "From such a dull in­ vention, nothing can be expected. It only removes all the difficulties under which the theory of light laboured, to the theory of this new medium, which assumes its place. It 11 Ibid.,

p. 455. Emphasis mine.

SCIENTIFIC REVIEWS

is a change of name; it teaches no truth, reconciles no contradictions, arranges no anomalous facts, suggests no new experiments, and leads to no new inquiries." 12 Wrong though Brougham might have been about some of these charges—as he clearly was with respect to the last two—there was an element of justice in his critique. As long as the wave theory maintained its 1802 form (assum­ ing longitudinal rather than transverse undulations) it could not account for very important phenomena as­ sociated with double refraction and polarization. Nor did it offer anything significant regarding the absorption of light until much later, when physical optics and electro­ magnetic theory were joined by Maxwell and Hertz. Totally aside from the question of its justice, however, Brougham's critique of Young's theory raises precisely those criteria for good theories which had been taught by his philosophy teacher, Stewart. If an intermediate medium were to be assumed, its existence would first have to be established; it would be valuable as an hypothetical entity only if its properties or laws of be­ havior were better known than were the phenomena to be explained. Furthermore, no hypothesis could stand in the face of contradictions or anomalies, and every worthwhile hypothesis was obligated to suggest new experiments and lines of investigation. DAVID BREWSTER'S EXPOSITION OF THE SCOTTISH POSITION ON HYPOTHESES

Brougham never abandoned his opposition to the wave theory of light, and he continued to do optical research based on a particulate theory until 1858. But after the first decade of the nineteenth century, the explanatory succes­ ses of a transverse wave theory made it increasingly dif­ ficult to ignore or oppose. Thus, most nineteenth-century Scots adopted the wave theory, although their opposition 12Ibid.,

p. 456.

COMMON SENSE AND THE EXACT SCIENCES

to etherial media certainly conditioned this acceptance and led them to insist upon the provisional, hypothetical, and, to a certain extent, ultimately unsatisfactory nature of the etherial hypothesis. Such a conditioned acceptance of Young's theory is nicely displayed in the scientific reviews of David Brewster and in his "Report on the Recent Progress of Optics," written for presentation at the second meeting of the British Association for the Ad­ vancement of Science held in 1832. 13 Brewster, like Leslie and Brougham, attended the Uni­ versity of Edinburgh during the last decade of the eigh­ teenth century. Apparently at Brougham's suggestion, Brewster took up optical studies and he was launched on a scientific career which eventually resulted in over 300 scientific papers, almost all concerning physical optics. It is not known whether or not Brewster formally attended Stewart's moral philosophy class at Edinburgh, but dur­ ing the academic year of 1796-1797 he was reading inten­ sively from the Common Sense philosophers, including Reid and Beattie as well as Stewart, 14 so it seems likely that he at least audited the class. In either case, he was thoroughly acquainted with the writings of the members of the Common Sense tradition and sympathetic to many, if not all, of the principal tenets of Common Sense methodology as expressed by Dugald Stewart. Brewster's attitude toward the etherial undulatory theory of light is particularly interesting because of its constant emphasis on the great utility and value which may accrue to the hypothesis even if it is incorrect in some absolute sense—so long as one recognizes that it is merely a 13 David Brewster, "Report on the Recent Progress of Optics," Report of the First and Second Meetings of the British Association for the Advancement of Science, at York in 1831, and at Oxford in 1832. Lon­ don, 1835, pp. 308-322. 14 See Edinburgh University Library, Da. 2.26, StudentReceipt Book, for a record of Brewster's borrowing, which included "Reid's Active Powers," in December of1796 and "Beattie's Essay s," in March of 1797.

SCIENTIFIC REVIEWS

hypothesis. In this vein he clearly developed and ex­ tended the arguments made by Stewart. In his "Report on the Recent Progress of Optics," Brewster committed himself to neither an emission nor an undulatory theory of light. He did devote more attention to the undulatory theory, but he was careful to point out that even a series of subsidiary hypotheses about the na­ ture of the ether had left the undulatory theory incapable of explaining the dependence of refraction on color or the selective absorption which Wollaston and Fraunhofer had established as a property of gaseous media. Each new supposition about the nature of the ether seemed only "to remove the difficulties a step further." 15 In 1834, Brews­ ter stated more positively a leaning toward the undulatory theory, but once again he insisted that it must be consi­ dered not as an established fact, but as a provisional hypothesis. 16 Finally, in two reviews devoted to Auguste Comte's Cours de Philosophie Positive and William Whewell's Philosophy of the Inductive Sciences, written in 1838 and 1842, respectively, Brewster provided de­ tailed discussions of the value and cognitive status of the undulatory theory of light which clearly distinguished the nineteenth-century Scottish attitude toward such hypoth­ eses both from positions which had been adopted by Comte and from the new modified idealist position de­ veloped by Whewell. Although Comte acknowledged that "the introduction of hypotheses into natural philosophy is strictly indis­ pensable," he insisted that only such hypotheses could be allowed as "bear exclusively on the laws of phenomena, and never on their modes of production." 17 The undulat­ ory theory, with its supposition of an etherial medium to 15 Report of the First and Second Meetings of the British Association for the Advancement of Science, London, 1835, pp. 321-322. 16See David Brewster, review of "On the Connexion of the Physical Sciences by Mary Somerville," Edinburgh Review, 59 (1834), p. 163.

COMMON SENSE AND THE EXACT SCIENCES

explain the mechanism by which optical phenomena were produced, obviously violated this requirement and thus had to be dropped from science. In some ways this argument was completely consistent with the Common Sense emphasis on Humian notions of causation, and it closely paralleled one of Stewart's and Brown's argu­ ments against positing an etherial medium to explain gravity. But the Scots could not accept quite such a restric­ tive rule because it closed off an important potential source of valuable insights—after all, even Brougham had acknowledged that the etherial medium posited by New­ ton could lead to important understanding if its existence could be established. Brewster provided an eloquent ex­ pression of the position which had been emphasized by Stewart: There can be no doubt that, to a certain extent, M. Comte is right. If the mind rests on any hypothesis as disclosing the real cause of the phenomena which it explains, and thus paralyses all our efforts in searching for any other, and perhaps the true cause; then science has not in this case performed her proper functions. But if the undulatory, or any other hypothesis, is adopted, and used only as a temporary auxiliary—as a bond of cement which unites a number of insulated facts, or even as a fertile principle which may indicate new phenomena—science cannot be considered as having overstepped its limits. 18 Certainly, Brewster overstepped the limits maintained by his Scottish predecessors in suggesting that even an hypothesis which gratuitously supposes the existence of an invisible, intangible, and imponderable ether is "worthy of our adoption as a valuable instrument of dis17 Quoted by Brewster in his review of Cours de Philosophie Positive par Auguste Comte, Edinburgh Review, 67 (1838), p. 305. 18 David Brewster, review of "The Philosophy of the Inductive Sci­ ences, Founded on Their History, by the Rev. William Whewell." Edinburgh Review, 74 (1842), p. 304.

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covery, and of our admiration as an ingenious and fertile philosophical conception." 19 But none of his predeces­ sors had been faced with a theory so powerful in its ability to suggest new discoveries and to account in great detail for such odd and diverse phenomena as the undulatory theory could in Brewster's chosen field of optics by the 1830s. Brewster, moreover, remained in the fold by ob­ jecting as much to Whewell's acceptance of the undula­ tory theory as established fact as to Comte's outright re­ jection of it. It was unquestionable, Brewster asserted, that Whewell and others had violated proper canons of scientific method "by maintaining that the luminiferous ether really exists, filling universal space, and occupying the pores of all bodies whatsoever; and this on the false and ridiculous assumption that the theory is perfect, and has been demonstrated." 20 So far was it from being demon­ strated, in fact, that Brewster felt certain that its ultimate demise as a "physical theory"—i.e., a theory whose ele­ ments were established as truly existing—was imminent. In his earlier review of Whewell's History of the Induc­ tive Sciences, Brewster had presented a whole series of detailed failures of the theory 21 to counter Whewell's dogmatic assertion of its truth. And he concluded his re­ view of the Philosophy of Inductive Sciences with a fas­ cinating condemnation, not of the undulatory theory, but of the cognitive status that it had been assigned by men like Airy and Whewell: Whatever be the value of the undulatory theory, it has been pursued in England, since the death of Dr. Young, in a spirit, and with a temper most injurious to the interests of knowledge. . . . It has usurped the 19 Brewster review of Comte's Cours de Philosophie Positive, p. 306. 5 20 Brewster, "Whewell's Philosophy of the Inductive Sciences," p. 305. 21 David Brewster, "History of the Inductive Sciences, from the Ear­ liest to Present Times, by the Rev. William Whewell," Edinburgh Review, 66 (1837), pp. 143-144.

COMMON SENSE AND THE EXACT SCIENCES

judgment-seat of science; and its abettors have not scrupled to condemn as correct all optical researches which do not confirm its anticipations, and all results as worthless which it cannot explain One hypothesis of vibration drives out its predecessor, and every new discovery either saddles it with a fresh incubus which threatens its vitality, or draws from its overflowing treasury a duality of explanations. It utters predictions and contrives to fulfill them; and not content with the dignity of a prophet, it wields the sceptre of a king in attempting to crush the spirit of experimental philosophy. . . . Thus armed with inquisitional powers, it has enjoyed a temporary triumph. But its doom, as a physical theory, is sealed, and when it has lingered for another century as a mathematical hypothesis, the true cause of the phenomena of light will reward the dili­ gence and genius of those who, in the spirit of genuine induction [this includes the use of provisional hypoth­ eses], have advanced in the straight and narrow way that leads to the Temple of Truth. 22 The fact that Brewster could take this attitude toward the undulatory theory and still continue to teach and to use the theory to guide his research points up the radical difference between the nineteenth-century Scots' as­ sessment of the role of scientific hypotheses and the as­ sessment of Positivists and Idealists alike. Positive scientific knowledge, for Comte, was true and certain knowledge and could under no circumstances be derived from causal hypotheses whose validities were not only unproven but incapable of being proved. This clearly accounts for the very restricted use of hypotheses among Positivist scientists, but it is slightly harder to understand the Idealist position of Whewell. In contrast to both the Positivists and Common Sense philosophers, Whewell denied Hume's assertion that we can know nothing of 22 Brewster,

"Whewell's Philosophy . . .," p. 306.

SCIENTIFIC REVIEWS

essential causal connections.23In fact, he believed that true scientific knowledge is causal knowledge. This being the case, a false causal hypothesis could not provide an element of scientific knowledge, even though it might account for those spatio-temporal relations which constitute true scientific knowledge for the Scots. That is, in a very important sense it is far more important for Whewell that an hypothesis be "correct" in some absolute sense than that it be suggestive. It is important to understand some of the implications of Whewell's demand for "true" hypotheses and theories, especially as they relate to the Scots' concerns regarding fruitful ones. Such an understanding can be gained by looking at Brewster and Whewell's opposing contentions regarding James Watt's claim to the discovery of the com­ pound nature of water. In a letter dated 26 April 1783, Watt had written to Joseph Priestley offering an explanation of a series of experiments done by Henry Cavendish and Priestley rel­ ative to the residue of water left when inflammable air (hydrogen) was burned in dephlogisticated air (oxygen) and to the apparent production of dephlogisticated air when water was heated in an earthenware retort. Watt suggested that "dephlogisticated air is composed of water deprived of its phlogiston."24 Ten months later, Caven­ dish announced his opinion in almost identical words: "I think we must now allow that dephlogisticated air is in reality dephlogisticated water, or water deprived of its phlogiston."25 There were several differences in [the contexts of] 23 William Whewell, The Philosophy of the Inductive Sciences Founded Upon Their History, (London: John W. Parker & Son, 1847) 2nd ed., I, pp. 173-176. 24 Published in Robert Schofield, "James Watt's Letter to Joseph Priestley, 26 April 1783," Annals of Science, 10 (1954), 299. 25 Henry Cavendish, "Experiments on Air," Philosophical Transac­ tions, 74 (1784), p. 137.

COMMON SENSE AND THE EXACT SCIENCES

these two announcements, however. Whewell emphasized the fact that whereas in 1784 Cavendish had asserted the identity of phlogiston and inflammable air, Watt had held that phlogiston was but one imponderable component of inflammable air. This was absolutely crucial for Whewell, for among the criteria which he insisted upon with regard to true chemical theories was the maxim that imponderable fluids are not to be admitted as chemical elements of bodies. Since Watt's theory included the implicit assumption of imponderable phlogiston as a chemical component of water, it could be allowed no role in the true discovery of the composition of water. Cavendish's theory, Whewell argued, involved nothing "hypothetical or superfluous" and thus truly deserved to be known as the first statement of the composition of water. 26 Brewster felt Whewell's argument to be totally unjust, and projected an interesting counter-example involving the luminiferous ether whose existence he doubted: The weakness of Mr. Whewell's argument is, however, easily exposed. It was the fashion in Mr. Watt's day to consider the imponderable fluids of light and heat as chemical elements. It is the fashion of the present day, and one in which Mr. Whewell rejoices, to say that calcareous spar contains the imponderable element of the luminiferous ether; and we should not blame a chemist of the Cambridge school who should thus announce the composition of that mineral: —Lime . . . 56.25, Carbonic acid . . . 43.75, Luminiferous ether . . . Inappreciable, = 100. But we should greatly blame the historian or legislator of science were he to transfer the favour of having discovered the true composition of calcareous spar to some future chemist, who merely omitted the 26

William Whewell, Philosophy of the Inductive Sciences . . . , London, (1840), I, p. 402.

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inappreciable element of the liminiferous ether. And yet this is precisely the case of Mr. Watt.27 We might question the extent of parallelism between Brewster's hypothetical case and Watt's treatment at the hands of Whewell, but there can be no mistaking the fundamental point at issue. For Brewster the falsehood of a fruitful hypothesis in no way prejudiced the discoveries which may be suggested by its use, whereas for Whewell it did. In practice this meant that the followers of post-Reidian Scottish methodology were more willing than their positivistically or idealistically oriented colleagues to in­ vestigate the implications of hypotheses and systems to

which they were unwilling to ascribe reality or certainty. This will be demonstrated in detail later in connection with the development of gas theory and electromagnetic theory at the hands of J. J. Waterston, William Macquorn Rankine, and James Clerk Maxwell. But we can see the fruits of the Scots' unique attitude equally well in connec­ tion with the history of Daltonian atomism. Scottish-trained chemists, like Thomas Thomson and William Henry (who explicitly appealed to Dugald Stewart's Elements of Philosophy of the Human Mind to justify his speculative approach),28 provided Dalton with his greatest avenue of support and dissemination; the Positivists (with one notable exception)29 and Idealists alike refused to take Dalton's atomism seriously. This was either (1) because they could not accept the positing of invisible entities (the fundamental Positivist position); (2) because, like the Idealist, Davy, they were convinced of 27 David Brewster, "Whewell's Philosophy of the Inductive Sciences," p. 304. 28 See William Henry, The Elements of Experimental Chemistry, 9th ed. (London: Baldwin, 1832), I, p. xviii. 29 See W. H. Brock, The Atomic Debates (Leicester: Leicester Uni­ versity Press, 1967), pp. 15ff. Brock mentions Alexander Williamson, a disciple of Comte, who supported atomic theory.

COMMON SENSE AND THE EXACT SCIENCES

the basic identity of elementary particles and could not countenance the assumption of such a variety of elemental substances; or (3) because, like Whewell, they simply asserted that "chemical research has not afforded, nor can afford, any satisfactory evidence whatever for such hypothetical entities." 3 0 Brewster's—albeit restricted—acceptance of the undulatory theory deviated so much from the positions expressed by Brougham, Leslie, and even Playfair and Robison, on etherial theories, that there is a danger of seeing it more as a rejection of the traditional Scottish attitude toward hypotheses than as a close development of that tradition. But we can see positions very similar to Brewster's stated by his predecessors whenever their discussions moved away from the ether, with its traditional moral and religious associations. Henry Brougham, for example, although he bitterly disagreed with many of the basic assumptions of the Huttonian theory of the earth, wrote a favorable review of Playfair's Illustrations of the Huttonian Theory in 1803, introducing his considerations with the following apologia for speculative systems: It cannot be denied, however, that observations accumulate but slowly when unassisted by the influence of system. The observer never proceeds with more ardour than when he theorizes; and every effort to verify or disprove particular speculations necessarily leads to the evolution of new facts and to the extension of the limits of real knowledge. Hence, it seems to be the business of philosophy rather to point out the imperfections, to detect the errors, to restrain the presumptuousness of the theorist, than to extinguish altogether a spirit, which, however incomplete and insufficient may be the materials on which it has to work, must at least 30

Ibid., p. 9. Brock is quoting from Whewell's Philosophy .. ., 2nd ed., London. 1847, I, p. 422.

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SCIENTIFIC REVIEWS facilitate generalization, and render the approach to 31 truth less tedious. Even more explicit with respect to its advocacy of the pragmatic adoption of questionable hypotheses was John Leslie's eloquent 1796 assessment of Lavoisier's chemi­ cal system: We will not dissemble that the Lavoisierian system, with all its symmetry and elegance, is pregnant with notable defects; that it assumes points not strictly sup­ ported by evidence; that it often rests on analogies strained beyond their proper bounds; that it tacitly ac­ cepts certain principles which are commonly received indeed among chemists, but which are repugnant to accurate dynamics; and that it employs a nomenclature which is not always the simple communication of facts, nor fitted to become the general language of science. Still we are convinced that the modern chemistry infi­ nitely excels the hypothesis of phlogiston, in every modified form that this has lately assumed. Its humblest merit is to represent to the memory a most extensive series of facts reduced to luminous order; the spirit of accuracy and precision, which pervades it, contains the germ of perpetual discovery and improvement; and if it be destined to undergo the fate of preceding theories, it will at least have prepared the way for the true system of corpuscular philosophy, and will be ever regarded as one of the finest monuments of human G e n i u s . 3 2 In this conditional praise of the new French system of chemistry, just as in Brewster's later conditional accep­ tance of the undulatory theory of light, we see mirrored 31

Henry Brougham, review of"Illustrations of the Huttonian Theory of the Earth by John Playfair . . .," Edinburgh Review, 1 (1802-03), p. 201. 32 John Leslie, review οι "Experiments and Observations Relating to the Analysis of Atmospherical Air . . . by Joseph Priestley," Monthly Review, 21 (1796), p. 368. 187

COMMON SENSE AND THE EXACT SCIENCES

Dugald Stewart's insistence on hypotheses as indispensable aids to memory and as guides to further experiment and discovery. Similarly, we see Stewart's assurance that even false hypotheses will ultimately lead to their own improvement, if they are capable of suggesting sufficiently precise procedures for verification or falsification. ATTITUDES TOWARD THE FOUNDATIONS OF MATHEMATICS

Just as the Scottish reviews provide a record of the serious concern among scientists w.-th methodological issues emphasized in Common Sense Philosophy, they also provide an insight into the Scots' concern about the foundations of mathematics and the extent to which this concern was also connected with Common Sense doctrines. The clearest and, in a sense, most important example of Common Sense elements in a mathematical review appears in Henry Brougham's unfavorable analysis of Robert Woodhouse's On the Necessary Truth of Certain Conclusions Obtained by Means of Imaginary Expressions. This review raises the Scots' fundamental epistemological objection to much of analytic mathematics. The early unease among the British over the logical rigor involved in operating with infinitesimal quantities—an u n e a s e stimulated largely by Berkeley's Analyst of 1734—was abated by Lagrange's algebraic method of developing the calculus which appeared in the Tkeorie des Fonctions Analytique of 1797, and the Scots were well aware of Lagrange's success in overcoming such traditional objections. But Lagrange's techniques could not resolve the doubts about impossible quantities, and these doubts were made quite clear by Brougham. "No small part of the modern mathematics," he wrote, "depends on the doctrine of imaginary or impossible quantities." This being the case, he argued, one would expect that the grounds of belief in such entities would have been fully examined and any objections answered. 188

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The contrary, however, will, in reality, be found to be the case. Mathematicians have been more attentive to improve and extend their methods, than solicitous to examine the principles on which they are founded. Men of a scientific turn, who wish to reason as well as to compute, and who will not assent to the truth of the conclusion without fully comprehending every step in the reasoning that leads to it, have justly to complain of the mystery and paradox attending the use of impossi­ ble quantities. 33 The basis of Brougham's objection to imaginary quan­ tities is that they are literally "unintelligible" and that the mind cannot "proceed one step in the investigation of truth, without clearly comprehending the objects about which it reasons." 34 This is precisely the argument brought against them by Stewart. Furthermore, just as Stewart had argued that the appearance of such quantities arose only because the limiting conditions under which a problem is legitimately soluble are often disregarded, Brougham argued that they appeared when the conditions to be fulfilled by some problem involve a contradiction or when some impossible supposition is unwarily admit­ ted. 35 Brougham did have some complimentary words for Playfair's "On the Arithmetic of Impossible Quan­ tities" which had appeared in 1778. But Playfair had only shown that operations with imaginary quantities demonstrate an analogy with operations on real quantities if the latter are taken to relate to properties of a hyperbola, while the former are taken to refer to the parallel proper­ ties of a circle. Fewmen could be satisfied with analogical arguments to justify conclusions in that most certain of all sciences, mathematics. Very much the same attitude as that stated by Brougham 33 Henry Brougham, review of "On the Necessary Truth of Certain Conclusions obtained by Means of Imaginary Expressions, by Robert Woodhouse . . .," Edinburgh Review, 1 (1802-1803), p. 407. 34 Ibid., p. 410. 35 Ibid., p. 407.

COMMON SENSE AND T H E EXACT SCIENCES

was presented by John Leslie in 1824 in his historical "Dissertation Fourth: Exhibiting a General View of the Progress of Mathematical and Physical Science, Chiefly During the Eighteenth Century," which was prefixed to the seventh edition of the Encyclopaedia Britannica:36 It is indeed the reproach of modern analysis to be clothed in such loose and figurative language, which has created mysticism, paradox, and misconception. The Algebraist, confident in the accuracy of his results, whenever they become significant, hastens through the successive steps to a conclusion without stopping to mark the conditions and restrictions implicated in the problem. 3 7 Particularly obnoxious and dubious to Leslie was the algebraist's use of the concept of "imaginary" or "impossible" numbers: A disposition has also prevailed in modern times, of hastening to general conclusions, although the data be limited or imperfect. Such careless deductions are but awkwardly amended by the adoption of expedients more like the fictions of lawyers than the reasonings of sound logicians. The introduction of equal and impossible roots of equations served only to restrict the ordinary rules, which had been made too general, representing the number of roots as always equal to the index of the highest power. The involution or repeated multiplication of binomials will produce the successive orders of expressions, which pass into equations on the supposition that any one of them vanishes or has its parts mutually balanced. But the converse of this proposition will not always hold true. That every compound 36

Reprinted in Dugald Stewart, et al, Disserations on the History of Metaphysical and Ethical and of Mathematical and Physical Science (Edinburgh: A. & C. Black, 1835), pp. 575-677. All further references are to this printing. 37 IbId., p. 592.

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expression is resolvable into as many binomial factors as the index of its highest power signifies. . . . Impossible quantities are thus merely the symbolical exhibition of the binomial factors of a quadratic or trinomial expression which is irreducible. . . . Such notation may indicate the limits of a problem, and seems to originate in neglecting the previous statement of the limitations. 38 The appearance of complex numbers thus meant to Leslie, as to Stewart and Brougham, that there had been a failure to delineate the conditions under which a problem was legitimately solvable, and he refused to accept them as viable mathematical concepts signifying more than the inappropriateness of further investigation. From the presentation of his first mathematical paper in 1788 39 until his death in 1832, Leslie did not once apply algebraic analysis to a problem if complex numbers would have been involved. Leslie went even further and rejected the algebraist's concepts of "quantities less than nothing," or negative numbers. As far as he was concerned, the notion of negative number was literally nonsensical. Numbers were, strictly speaking, neither positive nor negative; they were evolved from a counting operation, and plus and minus signs could legitimately be used only to indicate whether a given number should be added to or subtracted from some other number. 4 0 Under certain clearly defined circumstances, plus and minus signs could be used to denote the sense of a line on a graph. But that use in no way legitimized the abstract use of negative quantities in nongeometrical, symbolic algebra. Thus, Leslie and others could admire Cartesian analytic geometry without accepting symbolic algebra. 38

Leslie, Dissertation Fourth, p. 593. Leslie, "On the Resolution of Indeterminate Problems," Transactions of the Royal Society of Edinburgh, II, 1790, pp. 193-212. 40 Leslie, Dissertation Fourth, p. 593. 39

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Leslie's attitude toward analysis illustrates how Common Sense epistemology can partly explain the hesitancy of Scottish mathematicians to orient themselves toward analysis rather than toward ancient geometry. Some of the greatest successes of analysis came from its ability to simplify trains of reasoning by having recourse to operations involving negative numbers and complex quantities, and there was no way in which these concepts could reasonably be interpreted so long as one maintained that every mathematical symbol should represent some primary quality of an object of the senses. It should be made very clear that the logical reservations held by the Scots with regard to analysis did not preclude their learning and using analytic techniques. Leslie, for example; read the works of Euler, the Bernoulli's, Lagrange, and Laplace. H e acknowledged that in many ways algebra had an "immense superiority over the ancient analysis [i.e., geometry]," 4 1 especially in providing techniques for solving physical problems; and he even used the Continental rather than the fluxional calculus in his major works in natural philosophy. 4 2 Similarly, Brougham published An Analytic View of Sir Isaac Newton's Principia,43 which tried to cast the propositions of the Principia in the analytical mode. Nevertheless, the philosophical predilection for the rigor of geometry did have an important influence. In conjuncton with the pedagogical considerations discussed above, it insured geometry the central and very nearly exclusive role in mathematical education well into the nineteenth century, 44 and this in turn insured that Scottish scientists 41

Ibid., p. 591. See John Leslie, An Experimental Inquiry into the Nature and Propagation of Heat (London: J. Mawman, 1804), p. 551, for his explicit justification for adopting Continental techniques. 43 Henry Brougham and A. I. Routh, An Analytic View of Sir Issac Newton's Principia (London: Longman & Co., 1855). •"Although Playfair, Leslie, and Wallace taught an occasional advanced mathematics class which dealt with Continental analysis, the 42

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were more aware of the existence of and better trained in geometrical techniques than most of their Continental and many of their British colleagues in the early nineteenth century. bulk of the first two years' work in mathematics was classical geometry and trigonometry. Only in 1837, when Cambridge-trained Phillip KeIland became professor of mathematics, did algebra and analysis begin to form the core rather than the periphery of the mathematics class.

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CHAPTER 8

John Leslie and Henry Brougham: Model Common Sense Scientists of the First Generation T H E BASIC aim of this book is to present and to establish the probability of a hypothesis regarding the development of the exact sciences—i.e., that many of the important characteristics of the exact sciences in Scotland, and subsequently throughout Britain, can be accounted for by the fact that Scottish scientists adopted a particular set of methodological and epistemological attitudes which were clearly articulated by a group of moral philosophers collectively known as the Common Sense School. So far, it has been established that a Common Sense philosophy of science, changing over time but distinguishable from contemporary alternatives, did exist, and that at least during the period from 1770 to roughly 1830, the major elements of this philosophy were known to Scottish scientists. Furthermore, insofar as science involves the professional training of potential scientists and the criticism of current research expressed in review literature, it should be clear that Common Sense considerations did play a significant role. But the central activity within the scientific endeavor remains the research done by individual scientists—or, more r e c e n t l y , by closely-knit groups of scientists—and it remains to be shown that the hypothesis is consistent with and helps to organize important characteristics of the research done by Scottish scientists. L E S L I E ON T H E N A T U R E O F E L E C T R I C I T Y

One of the clearest examples of a scientific study carried out in accordance with the dictates of Common Sense is 194

JOHN LESLIE AND HENRY BROUGHAM

John Leslie's first paper in natural philosophy, a 1791 study of static electrical effects published only in 1824 because of its initial rejection by the Royal Society of Edinburgh. Robert Schofield has recently argued that: The paper should not have been published even then, as it reveals all of the worst aspects of Leslie's scientific work, and few of the best. Primarily concerned with the action of electrified bodies on ambient air, it characteristically generalizes from this restricted base, without regard for phenomena left unexplained by a new theory. It shows no awareness of the instruction, presumably given him by Robison, on the electrical work of Aepinus and Cavendish, and the value of the whole is not enhanced by Leslie's ostentatious failure to change any of his opinions, during the thirty-three years between the paper's presentation and its publication. 1 In some respects, Schofield's criticisms are quite justifiable. By 1824, when the "Observations on Electrical Theories" 2 was finally published, the state of electrical studies had gone far beyond its contents, and Leslie had certainly failed to take account of intervening events. But when it was first written in 1791, it was not at all clear that Leslie's theory accounted for a narrower range of phenomena than older theories had. And I cannot agree that the paper demonstrated only the "worst" aspects of Leslie's work. The paper did generalize from a restricted experimental base. This was, however, characteristic not only of Leslie's work but of nearly all the scientific theorizing of the late eighteenth- and early nineteenth-century Scottish intellectual community. In fact, Francis Jeffery, 'Robert Schofield, Mechanism and Materialism: British Natural Philosophy in an Age of Reason, (Princeton: Princeton University Press, 1970), p. 283. 2 John Leslie, "Observations on Electrical Theories," Edinburgh Philosophical Journal, 11 (1824): 1-39.

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editor of the Edinburgh Revieiv, characterized Scottish philosophers and scientists generally and quite rightly as "rather indefatigable in argument, than patient in inves­ tigation; vigilant in observation of facts, but not as strong in their number, as skillful in their application."3 This characteristic was certainly responsible for some of the failures of Scottish science, but it was equally instrumen­ tal in contributing to its fruitfulness and in helping to generate its successes. Leslie's "On Electrical Theories" offers the opportu­ nity to see both the suggestiveness and the dangers of this characteristic approach. The structure of the paper is also particularly suitable for analyzing its dependence on Common Sense methodology. It begins by condemning all previous theories of the nature of electricity because of their failure to meet proper philosophical criteria. Next it develops a hypothesis consonant with Common Sense demands, presents several experimental tests to support the new hypothesis, and uses the theory created to ac­ count for the relative superiority of points over spherical knobs in drawing electrical sparks. Finally, it extends the theory by analogy to electrical conduction in solids, a topic essentially untouched by earlier authors. We have seen that the most pervasive effect of Common Sense ideas among Scottish scientists working in the first two decades of the nineteenth century was to discredit the etherial fluid as a medium to be used in accounting for gravitation or light propagation. In Leslie's hands an iden­ tical argument allowed him to reject all "fluid" theories of electricity, whether the fluids posited were composed of mechanistic effluvia acting by impacts, like those of Nollet, or Newtonian fluids composed of attracting and repel­ ling particles, like those of Franklin or Aepinus. Mechanistic impact theories were discarded out of hand because Leslie accepted the Boscovichian critique of impulse forces which was taught by his mentors in 3 Edinburgh

Review, 3 (1805), p. 156.

JOHN LESLIE AND HENRY BROUGHAM

natural philosophy—Robison and Playfair—as well as by his moral philosophy teacher, Stewart. Thus Leslie wrote: Some writers, indeed, are unwilling to admit the possi­ bility of action at a distance, and, like the poor Indian who placed the world on the back of a tortoise, they have recourse to some intervening medium. But is it more difficult to conceive an effect produced at the distance of 1000 miles [referring to gravitation] or at the 1000th part of an inch? Or have we ever any idea of the connexion between cause and effect, but that of constant concomitancy? To maintain, that no body can act where it is not, is in fact, to assert, that the same body can be in two places at the same time; which is a con­ tradiction of terms, and therefore completely absurd. 4 One key to this critique of mechanism comes from Hume's analysis of causality, but it does go beyond the Humian position in a critical way. For Hume demanded both immediate antecedence and consequence in time and contiguity in space to consider a sequence of events causal. It was only the later Common Sense philosophers and their colleagues in natural philosophy who were will­ ing to separate temporal from spatial immediacy as the primary concern and thus to provide for the concept of action at a distance. In this sense, the Scots even went beyond Boscovich, for Boscovich was never able to bring himself explicitly to deny the need for a body to be where 4 John Leslie, "Observations on Electrical Theories," pp. 17-18. The reader who looks at Leslie's paper will see that I have separated two aspects of what Leslie considered to be one argument. He did not distinguish between mechanistic and Newtonian fluids in his argument. I do so only because, though I believe the source of those parts of his argument which apply particularly to mechanistic theories was largely his reading of Stewart, an argument might be made that they came to Leslie from Playfair and Robison and are therefore independent of, although consistent with, Common Sense writings. The same kind of argument cannot be made with regard to other parts of his discussion which refer to "Newtonian fluids," a class fully endorsed at least by PIayfair.

COMMON SENSE AND THE EXACT SCIENCES

it acted, and his interpretation of matter indefinitely ex­ tended in space through its patterns of force allowed him to maintain the old Aristotelian requirement, though in a vastly modified form. While Leslie's opposition to mechanistic explanations and to some Newtonian fluids was shared by Robison and Playfair as well as by Stewart, his discussion in the 1791 paper depended directly upon his training in moral philosophy and not upon an inheritance from his natural philosophy teachers alone. Men believe in electrical fluids largely because they seem to see the flow of some material from one body to another in electrical sparks. But, according to Leslie, this visual impression does not warrant the inference of the existence of a special electri­ cal fluid. In order to justify his apparent denial of sensory evidence, Leslie draws upon arguments about the nature of visual information which comes directly from Reid and Stewart: If we examine the subject with attention, we shall be convinced that the only information which the eye ever conveys; is limited entirely to the quantity, the quality, and the direction of the rays which enter it. It is from the sense of feeling alone, which is diffused over the body, that we derive our ideas of figure and extent, of motion and force, which are the foundation of matter. 5 Visual impressions alone, then, tell us little about the nature of the matter with which they are presumably as­ sociated. And all we learn from seeing a spark is that light is being emitted from a certain region of space. Further­ more, we know from abundant experience that almost any body in nature can be made luminous by heat, by friction, or by chemical changes; it is reasonable to assume that the light which constitutes our evidence for an electrical spark is due merely to some kind of change in the state of 5 Ibid.,

p. 16.

JOHN LESLIE AND HENRY BROUGHAM

the air between the communicating bodies. Thus, Leslie concludes: In these cases [of electrical discharge], it is unnecessary to recur to the supposition of an electric fluid. No argu­ ment can be adduced to prove its existence. It is founded only on prejudice and on a fallacious inference drawn from the single and unassisted indication of the sense of sight. All fluid theories of electricity must be discarded, then, according to Leslie, because, even though they might be able to account for all the observed phenomena, they fail to fulfill the requirement that the substances involved can be observed. But there are yet two more reasons for rejecting fluid theories, based again on considerations made explicit by the Common Sense philosophers and adopted by Leslie in his paper. First, as Stewart and, later, Brown pointed out, the simplest theories capable of explaining a given phenomenon are to be preferred over the more complex, all other things being equal; to posit additional entities in a theory was clearly to add to its complexity and to make it less plausible. In this vein, Leslie queried: "What advan­ tage is gained by admitting an electric fluid? All that can be demonstrated is the emission of light; and is not the difficulty increased by regarding, not the body itself, but a fluid residing in it, as the source?" These questions, of course, were merely rhetorical and Leslie went on to assure his reader that "prudence calls us to stop where the link [in the chain of principles which direct the universe] appears the simplest, and not to strain beyond the limits of our faculties." 6 Secondly, Leslie argued, the introduction of an electri­ cal fluid to explain the phenomenon leads to a theory which is not even self-consistent. We wish to explain, for example, the light which we see accompanying electrical 6 Ibid.,

p. 18.

COMMON SENSE AND T H E EXACT SCIENCES

discharge, and we know that light results from a change in matter; yet, when we posit an electrical fluid, we are positing something which moves, unchanged, from one body to another and which, therefore, must not emit light. 7 "The existence of such a fluid is therefore illusory; it is unnecessary, and inconsistent even with mechanical principles." 8 In many circumstances, however, it was clear that electric virtue (whatever it might be) was somehow transferred from one body to another. And since this did not occur under all circumstances, and was thus not analogous to the universal property of gravity, it was apparent that some theory was n e e d e d to explain the phenomena associated with electrical communication. Leslie did have a hypothesis to put forward to replace the demolished fluid theories—a hypothesis suggested by a strong analogy between heat phenomena and electrical phenomena and demanding the supposition of no unobserved entities. Basically, Leslie argued that any electrified solid causes the immediately environing air to become similarly electrified. Because of the mutual repulsion of like electrified objects, the air flies off and in turn electrifies surrounding bodies with which it comes into contact. This process was seen as precisely parallel to the processes of heat convection which Leslie had been studying since 1789. At the time that Leslie began to write his paper on electricity he was completing work on an English translation of Buffon's Histoire des Oiseaux; and in the process of preparing a set of explanatory notes for the Buffon volumes, he had become interested in heat relations as they 7 In Leslie's words: "But does not the profuse discharge of luminous matter from any substance constantly indicate a change of properties? And, would not an alteration, even though temporary in the nature of an electric fluid, be inconsistent with the notions commonly received?" ("Observations on Electrical Theories," p. 18.) 8 Ibid., p. 19.

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influence the range and altitudes of birds' flight. Through his consideration of the cooling of birds in flight, Leslie came to see the principal process of heat transfer as one in which successive air particles impinge upon a warm ob­ ject, somehow absorb some heat, and then fly off to de­ posit heat on a distant colder object. He even tried to show that the amount of heat transferred was proportional to the velocity of the air currents flowing past the hot body and to the density (or pressure) of the air.9 Furthermore, he ex­ tended this analysis to account for heat transfer between still bodies in initially still air by arguing that the change in density of the air environing a hot object (due to its heating and consequent expansion) would induce what we now call convection currents which could carry the heated particles through the air or other environing fluid.10 An analogous explanation accounted beautifully for the first set of electrical phenomena which Leslie discussed in 1791. Leslie began his experiments by setting a sheet of tinfoil on an insulating block a few inches from and paral­ lel to the prime conductor of an electrostatic machine. He turned the crank of the machine, and when he brought the knob of a grounded discharging rod near the back of the sheet of tinfoil he was able to draw off sparks. Leslie argued that these results were best explained by assuming that the air between the prime conductor and the tinfoil, and subsequently between the tinfoil and the grounded rod, had transmitted electricity by a convective process very similar to that by which air transfers heat from a warmer to a colder body.11 a The Natural History of Birds, From the French of the Count de Buffon . . . (London: A. Strathan and T. Cadell, 1793), I, pp. 409-511. 10 Leslie first tried to publish his ideas about induced convection in 1793 in an essay, "On Heat and Climate." This essay, like "On Electrical Theories," was refused publication and did not appear until 1819 in Annals of Philosophy. SeeAn. Phil. (1819), pp. 13, 22, for his comments on convection. 11 John Leslie, "Observations on Electrical Theories," p. 4.

COMMON SENSE AND THE EXACT SCIENCES

Leslie's rigorous adherence to the Common Sense dic­ tum that no more causes are to be adduced to explain a group of phenomena than are necessary now led him to extend the same explanatory mechanism to cover all elec­ trical communication through fluids: . . . if the air, in consequence of the successive applica­ tion of its particles, be thus capable of making an elec­ trical communication, may we not infer, with a consid­ erable degree of probability, that, whenever a body acquires the electricity of a distant one, it derives this quantity merely from the motion and transference of the intervening aerial particles. 12 There is one major objection to this theory of Leslie's which he anticipated and disposed of with another argu­ ment that was fully consistent with, if not motivated by, his Common Sense methodological commitments. Almost all electricians in the eighteenth century looked on air as an insulator—a non-conductor of electricity—and, as such, it could not possibly play the role assigned to it by Leslie. Leslie, on the other hand, denied the validity of the entire distinction between conductors and non­ conductors because it violated a general analogy or rule of nature, based upon induction from a wide variety of facts. This rule—that every species of motion is impressed gradually and in time—only appeared to be violated in electrical phenomena because some materials, like met­ als, transmit electricity in such short times that they elude our observations, while others transmit electricity so slowly that our detectors are too crude to discover any transfer in the short times they are employed. In the mid­ dle range, however, electrical communications can easily be seen to show gradations in velocity. A plume of charged glass threads, for example, collapses much more slowly when grounded than does a plume of feathers, even though the latter takes a perceptible time. Men who 12 Ibid.,

p. 4.

JOHN LESLIE AND HENRY BROUGHAM

speak of impulsive forces in general have obviously created a category which has no foundation in nature. "But," said Leslie: the electricians have gone a more unjustifiable length: they have discriminated substances into Conductors and Non-conductors; whereas no body has been found incapable of communicating the electrical virtue. The only difference consists in the celerity with which the effect is produced; and were conductors properly classed, it would be found, in the descending range, that the velocity of transmission descends by insensible shades. To the class of exceedingly slow conductors, we must refer the atmospheric air itself.13 In spite of the apparently contrary evidence of Franklin and Aepinus, who had whirled charged balls through the air and blown streams of air past them with no noticeable diminution of charge,14 Leslie was convinced that the air had to be capable of conducting electricity. Although Leslie met the requirements of a legitimate hypothesis, his conjecture had to be tested for its detailed conformity to phenomena and for its ability to predict new phenomena and suggest new investigations. He contrived a series of experiments to test his new hypotheses. The flavoring and reasoning behind these experiments are best expressed in his own words: Let a round hole, near an inch in diameter, be made in the middle of a sheet of paper which is kept insulated at the distance of half a foot from the prime conductor, and let the metallic point be held about half an inch behind the middle of the hole; it will there continue totally dark. If the aperture be enlarged, the effect will be the same, only the point must be removed somewhat 13 Ibid.,

p. 3. I. B. Cohen, Franklin and Newton, (Philadelphia: American Philosophical Society, 1956), pp. 542-543, for a discussion of these experiments. 14 See

COMMON SENSE AND THE EXACT SCIENCES

further back; and if the aperture be increased to several inches in diameter, or if the paper be brought very near to the conductor, the point will resume its lucid spangle. This experiment is so conclusive that it scarcely needs any comment. The resistance which air meets in passing through a narrow aperture is very considerable; and therefore a small part only of the aerial current, which diverges in all directions from the prime conductor, can flow through the hole in the paper. This experiment evinces, that not only the transmission of air is necessary to produce the luminous appearance, but that in orderthatthe effect be sensible, there must also be a quick succession of the particles. Hence whatever tends to detain the air which has al­ ready flowed upon a body, or retard the reflex of the stream, must retard the electrical communication. Thus, let a pointed wire be stuck through the middle of a round card of two or three inches in diameter, and made to project on the other side a quarter or half an inch. Let the point, carrying this card, be advanced toward the prime conductor till it become lucid; take off the card, and the point will show its bright spangle, though now withdrawn to double or triple its former distance. By this little contrivance, the air remains heaped about the card, and its renewal at the point is obstructed. 15 Since each of these experimental tests demonstrated that the transport of electricity was diminished in circum­ stances that reduced the flow of air between the two bodies, the results increased the plausibility of Leslie's hypotheses. But Leslie had a much more impressive test for his newly developed theory. He sought to use it to explain why pointed conductors were capable of drawing or emitting electric sparks more easily than were conduc­ tors tipped with spherical knobs. This was a particularly 15 John

Leslie, "Observations on Electrical Theories," pp. 5-6.

JOHN LESLIE AND HENRY BROUGHAM

interesting topic since no contemporary electrical theory was capable of providing a satisfactory explanation. 16 Leslie showed that the electrical properties of points and knobs differ only in degree and that if one used conductors with spheres of successively smaller diameters, they acted more and more like points. Since this was the case, Leslie asked whether points and spheres might act differently with respect to electricity only because spheres provide a greater resistance to the aerial currents involved in electrical communication. 17 At this point, Leslie saw a way of providing evidence of his hypothesis in circumstances which were independent of the geometrical effects he was attempting to explain. If he could produce a rapid stream of air moving past a ball and if the ball then exhibited point-like electrical properties, he would have the evidence needed to establish fully his conjectures as a theory. The means to try such an experiment were directly at hand, for in his studies of heat he had already discovered that rapid convection currents were established about heated objects. With this in mind, he described the following experiment: Screw a red-hot metal ball, of about an inch in diameter, to the end of one of the branches of the discharging rod, and hold it at the distance of a foot from the prime conductor; on turning the cylinder, very intense sparks may be obtained at the other branch and the effect will, according to circumstances, be equal, or even superior, to that of a point. But, as the ball cools, the sparks will grow weaker and weaker, and at last will become hardly perceptible. 1 8 Once more Leslie's hypothesis seemed fully justified. As the ball was heated and streams of air moved around it ie See I. B. Cohen, Franklin and Newton, pp. 470-472, for a discussion of the status of explanations of the action of points in drawing electricity during the late eighteenth century. 17 John Leslie, "Observations on Electrical Theories," p. 7. 18 Ibid., p. 7.

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more rapidly, the electric virtue was also transmitted more rapidly. Of course, Leslie realized that it might have been some special property of the hot metal or some property of heated (as opposed to cool) air which caused the increase in electrical transmission; so he devised yet another experiment to dispose of these objections. H e generated the increased aerial current by placing a lighted candle between the prime conductor and the discharging rod, and still the the transmission of electricity increased in spite of the fact that there was no heated metal involved. Leslie argued, moreover, that the candle flame was far enough from both prime conductor and rod that the air near those two places could not have been significantly heated; the principle process of transfer of electrical virtue to the air and from the air to the rod could not have been influenced by temperature. This left the velocity of the air stream the only heat-dependent variable of concern. 1 9 It seemed clearly established, then, that the rate of electrical transmission was directly related to the velocity of aerial currents in the neighborhood of electrified bodies; that points did function more effectively in drawing electricity because they provided less resistance to aerial motion than did spherical knobs; and that, in general, electrical communication in gases could be explained by the convective process he proposed. This even explained the common observation of travelers that electrostatic generators worked poorly at high elevations; in such cases the aerial density would be diminished. 2 0 As a consequence, Leslie felt free to dispense forever with the "fiction" of special electrical fluids and to assert confidently that" . . . what was presumed to be the electrical fluid is only air endued with certain properties." 2 1 Leslie proceeded to show that his theory had important practical implications. Although it upheld those who ar19 20

Ibid., pp. 7-8, especially note * on p. 8. Ibid., p. 14. "Ibid., p. 9.

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gued that pointed lightning rods should be more effective than rods topped with knobs, it called into question the general efficacy of lightning rods by showing that only a small fraction of the electrified air mass associated with a thundercloud could come in contact with a single rod during the short duration of a lightning stroke no matter what shape the rod might have. 2 2 Finally, Leslie extended the analogy between heat and electricity to a consideration of electrical conduction in solids. Assuming that the quantity of electrical virtue and quantity of heat are analogous and that electrical intensity is analogous to temperature, he argued that a law similar to Newton's law of cooling should form a fundamental relation for the flow of electricity from points of high electrification to points of low electrification. " I have supposed that the rate of communication of electricity is proportional to the intensity. Perhaps this is not strictly true, though extremely probable: it is exactly so in the application of h e a t . " 2 3 Through an analysis of what this law should imply about the rate of electrical communication of solids of varying length, cross section, and constitution, Leslie de­ veloped a series of statements about electrical conduction in solids which can be summarized without distortion in the formula which we now know as Ohm's Law (i = {aplVjV, where I is the rate of flow of electrical quantity, V is the electrical intensity, L is the length of a conductor, a is the conductor's cross-section, and ρ is a constant which depends on the specific materials of which the conductor is composed). Once again, Leslie conducted a series of experiements to check the validity of his hypothesis: . . . These deductions are confirmed by experiement as far as the subject will admit. Thus, if a slip of paper, sufficient to discharge a Leyden jar in about a quarter of an hour, be rubbed slightly wth charcoal dust, it will 22

Ibid., p. 25-27.

23

Ibid., p. 31.

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perform the effect in ten seconds [I is proportional top]. If now reduced to one-half its breadth, it will require about double the time [I is proportional to a], and, if again shortened to one-half its length, the time will be nearly the same as the first. [I is proportional to HL]. If the charcoal dust be strewed thicker, the discharge will become more rapid, until the time interval can no longer be distinguished [Z is proportional to a]. 24 Leslie concluded this section of his paper by analyzing the rate of conduction through a series of conductors of varying cross-sections, lengths, and compositions, show­ ing that a compound conductor could be replaced, for purposes of analysis, with a resistance of uniform crosssection and conductivity. In this way, he arrived at most of the central results developed and made widely known by George Ohm thirty-three years later. 25 Leslie's 1791 paper was written in comparative igno­ rance of roughly contemporary work in electricity. It showed no awareness of Coulomb's 1785 paper, which established that electrical attractions and repulsions fol­ low inverse square laws, for example. But it did demon­ strate flashes of brilliance, and it was a piodel application of Common Sense methodological principles. Beginning with a critique of existing theories which depended upon an explicit application of Common Sense demands for legitimate scientific hypotheses and upon a Common Sense analysis of the nature of visual information, Leslie followed with a new hypothesis based on an analogy with heat phenomena and demanding the assumption of no unknown substances or unprecedented processes. This hypothesis was used to generate an extensive and de­ tailed set of experiements which provided confirmatory 24 Ibid.,

p. 32. a more extended discussion of Leslie's work on electrical con­ duction in solids and its relation to Ohm's work, see Richard Olson, "Sir John Leslie and the Laws of Electrical Conduction in Solids,"American Journal of Physics, 37 (1969), 190-194. 25 For

JOHN LESLIE AND HENRY BROUGHAM

evidence in a variety of situations. And it was applied, at least to Leslie's satisfaction, to a set of phenomena—the distinction between the electrical action of points and knobs—which had not been adequately explained. Furthermore, once the theory seemed convincingly demonstrated, he extended the analogy on which it was based to make the theory cover a much greater range of phenomena than that initially considered, thus providing a remarkable analysis of electrical conduction in solids. There were certainly a number of technical aspects of this paper which did not depend on a commitment to Common Sense methodology. It is unlikely, however, that someone holding the views expressed by Priestley and Hartley (that any hypothesis, however free a creation of the mind it might be, should be considered and accepted insofar as it explains the phenomena to be accounted for) could have been motivated to challenge the accepted theories. As Leslie himself admitted, " T h e hypothesis of an electric fluid is so natural, and so agreeable to the primary information of the senses, that scarce a doubt has ever been entertained of its reality." 26 By the last decade of the eighteenth century a vast number of electrical phenomena were well accounted for by fluid theories of one kind or another. Although in Thomas Kuhn' s terms this was still a period in which there was some competition between paradigms in the science of electricity, virtually all studies were being carried on in one of two traditions growing out of the effluvial theories of Nollet or the Newtonian fluid theories of Franklin and Aepinus. One could not expect acceptance for a theory which condemned the theoretical bases of the entire science of electricity unless there were some overwhelming justification. Without a strong belief that one must reject all hypotheses which did not conform to the criterion of independent observability of the Common Sense philosophers, there simply was no adequate reason to turn one's 26

John Leslie, "Observations on Electrical Theories," pp. 18-19.

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back on contemporary theories. Thus, although Leslie's paper was read before the Royal Society of Edinburgh on January 2 and March 5, 1792, it generated no interest whatsoever; it was denied publication in the Society's Transactions, appearing only in 1824 when a number of subsequent discoveries had rendered it obsolete. C O M M O N S E N S E E L E M E N T S IN L E S L I E ' S H E A T S T U D I E S

In spite of the public failure of his initial paper on electricity, Leslie in no way retreated from his basic philosophical positions. The same arguments that made him reject an unobservable electric fluid supported his much more influential work on heat, causing him to reject both caloric fluid and etherial vibration theories. He was forced by his methodological beliefs into his own idiosyncratic heat theory which, though it was adopted by almost no other scientists, led him to an impressive and extensive number of experimental discoveries about heat phenomena. 27 The central lines of Leslie's heat theory had already been worked out by 1793 when he transmitted a paper, "On Heat and Climate," to the Royal Society of London. 2 8 But the fundamental motivations behind the theory can best be understood by looking at chapters eight and nine ofAn Experimental Inquiry into the Nature and Propagation of Heat. Leslie began by stating and explaining the basis of his firm commitment to Boscovich's basic theory of natural philosophy. But he did so in such a way as to 27

For a much more detailed analysis of the development and successes of Leslie's heat theory than is warranted in the present context, see Richard Olson, "Count Rumford, Sir John Leslie, and the Study of the Nature and Propagation of Heat at the Beginning of the Nineteenth Century," Annals of Science, 26 (1970), pp. 273-304. 28 This paper, like his earlier paper on electrical theories, was refused publication and appeared only in 1819 when Leslie's reputation had been made. " O n Heat and Glimate," Anwais of Philosophy, 14 (1819), pp. 5-27.

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demonstrate that his belief in Boscovich's system is not based on the metaphysical principles which were so central to Boscovich, but rather on principles consonant with Scottish philosophy. A vast range of experience shows that a very small number of fundamental substances underlie the variety of forms we experience every day. Water, ice, and steam are all the same, as are charcoal and diamond; bright metals can be converted into dull, dustlike oxides; water and air alone seem to be capable of producing all the products of the animal and vegetable kingdoms. The analogy of nature and our natural supposition of simplicity thus lead us to believe that "the peculiar properties of bodies must result merely from the different arrangement and configuration of the parts. The substance is in all of them essentially the same; and the sublime scene of the universe owes all its magnificence and splendour to the variety of its composition." 2 9 Amidst all the changes bodies undergo, there is one property which remains unalterable—gravitation toward other bodies. Furthermore, the gravitational force due to every combination is merely the aggregate of the forces exerted by each component part. This gravitational virtue extends infinitely through space, and at sensible distances it is found to decrease as the inverse square of the distance. The same law cannot hold at shorter distances; for then all matter would simply collect into one dense spherical particle. Within a certain distance, then, the gravitational attraction must be superseded by other forces or we must admit that the inverse square attraction is merely the most easily observed portion of a general force law which is a more complex function of the distance from each particle. "The latter hypothesis," Leslie said, "is more agreeable to analogy." 30 At large distances, the force is properly described as an inverse square attraction, 29

John Leslie, An Experimental Inquiry into the Nature and Propagation of Heat, (London: J. Mawman, 1804), p. 117. 30 Ibid., p. 122.

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but at closer distances it must become repulsive and alternate between attractive and repulsive, ultimately becoming intensely repulsive near the center of the particle. Such a force law can account for all varieties of phenomena including the diffraction of light, chemical changes, the variety of geometrical configurations in crystals, and phase transformations. 31 Boscovich had argued from the law of continuity that the so-called particles which manifest themselves by the forces so described must be mere points; i.e., that the forces must become infinitely repulsive only at the mathematical center of the pattern of forces. But Leslie disagreed. One cannot tell from the observed evidence whether the repulsive forces approach infinity at the origin or at some finite but small distance from the origin. In fact, contrary to Boscovich's assumption, the analogy of most experience would lead us to expect that the ultimate particles are finite in size. Judged by Common Sense standards, the Boscovichian system, in the form adopted by Leslie, is an ideal hypothesis. It is developed out of a wide-ranging appeal to analogy, it brings virtually all natural phenomena within the compass of one elegantly simple hypothesis, and it avoids positing anything—including a presumed size or lack of it—which is not directly observable as a characteristic of matter. In particular, it discusses physical interactions without the need to assume special invisible intermedia; and it assumes nothing more about the causes of natural phenomena than the constant and invariable sequence so much emphasized by H u m e , Reid, and Stewart. It was not by chance that Leslie chose a theory with the above characteristics. H e explicitly echoed Stewart's opinion with respect to the mechanistic philosophy which Boscovich's theory managed to overcome: It is a remarkable and instructive fact in the history of philosophy, that impulsion should have been at one 31

Ibid., p. 122.

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period the only force that was admitted. .. . Gravitation sounded like an occult quality; it was necessary to as­ sign some mechanical cause; and if there were no visi­ ble impulses to account for the weight of a body, might not that office be performed by some subtle invisible agent? Such was the sway of metaphysical prejudice, that even Newton, forgetting his usual caution, suffered himself to be borne along. In an evil hour he threw out those hasty conjectures concerning aether, which have proved so alluring to superficial thinkers, and which have in a very sensible degree impeded the progress of genuine science. 32 Once the general outlines of his approach to natural philosophy were clearly stated, Leslie turned to the more specific question of the nature of heat by stating his objec­ tions to the two classes of contemporary heat theory —dynamic theories and fluid theories. The hypothesis that heat consists in certain intestine motions of ordinary matter (dynamic theory) is subject to at least two major criticisms. In the first place, it fails in any of its versions to provide sufficient detail about whether the degree of heat is determined by the magnitude, the frequency, or the force of the vibrations or to explain precisely what parts of the hot body are supposed to be vibrating—whether indi­ vidual atoms, aggregate particles, or the bodies as a whole. In the second place, if heat were vibratory motion, we would certainly notice resonance phenomena like those associated with sound. But no such phenomena exist; so heat cannot be a vibratory motion. 33 All heat phenomena can be accounted for by the sup­ position that "heat is an elastic fluid, extremely subtle and active." 34 But is it some special fluid as almost all caloric theorists believe? We would hardly expect Leslie to have accepted new, unobserved fluids in view of his 32 Ibid.,

p. 122. Experimental Inquiry, pp. 139-141. 34 Ibid., p. 150.

33 Leslie,

COMMON SENSE AND T H E EXACT SCIENCES

principles. Nor did he. "Is it a new and peculiar kind of fluid," he wrote, "or is it one with which from its other effects, we are already in some manner acquanted? If any such can be discovered that will strictly quadrate with the phenomena, the spirit of true philosophy, which strives to reduce the number of ultimate principles, would certainly persuade us to embrace it." 35 At this point, Leslie presented a hypothesis which he adopted in the early 1790's from James Hutton, whom he had probably come to know through their common friend, John Playfair. Since the 1770's, Hutton had been discussing a theory connecting heat and light which he finally published in 1794. Hutton wrote: "We conceive a substance (light) to be continually radiated from the sun. . . . Heat is represented as another modification of that solar substance in a body; it is a combination of the solar substance with gravitating matter." 3 6 Leslie repeated this suggestion in detail: "Heat, then is manifestly allied to light. Is it a modification of that fluid, or is it not the same matter, only in a state of combination with other bodies? The latter hypothesis is recommended by its simplicity, which is the great object of philosophical research." 3 7 Such a hypothesis fit perfectly with Leslie's general Boscovichian views and with his methodological precepts. Hutton's particles of "solar substance" or light were simply interpreted as Boscovich's most elementary units or very simple symmetrical combinations. Heat then became the aggregate formed w h e n a light particle was 35

Ibid., pp. 150-151. James Hutton, Dissertation Upon the Philosophy of Light, H'eat, and Fire, (Edinburgh: Cadell, Jr. and Davies, 1794), p. 33. John Playfair's biographical account of Hutton in The Works of John Playfair, Esq., (Edinburgh: Archibald Constable and Co., 1822), IV, pp. 33-118, made it clear that Hutton had been discussing this theory since the 1770s. In his first paper on heat, published in 1793, Leslie described Hutton as a personal friend. 37 John Leslie, "On Heat and Climate," Annals of Philosophy 14 (1819), p. 6. First written in 1793. 36

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trapped within the force pattern of a normal particle of matter and bound to it. 38 In this way, a theory of heat could be developed without the assumption of any special, new kind of fluid, and it could fit naturally into a simple and universal theory of natural philosophy. As was the case with his paper on electricity, Leslie used his theory—motivated largely by his methodological concerns and based on the ideas of Boscovich—to suggest a wide variety of experiments and to guide him to unique interpretations of experiments done by others. For example, it led him to deny the possibility of heat transmission through vacuity. If the very nature of heat demanded the presence of ordinary matter, there could be no way for heat to exist, let alone be transmitted, in the absence of matter. 39 Even the phenomena associated with heat radiation —as opposed to heat convection—had to involve ordinary matter somehow. Since Leslie was aware that heat radiation was distinct from and could not involve the macroscopic motion of any ordinary media, he was forced to develop his own odd combination of wave and material theory to account for radiant heat. 40 He argued that if a hot body is exposed to the air, the particles of air immediately adjoining the body absorb some of the heat from the body. This layer of air then expands, and the expansion is propagated in the form of a pulse just like a pressure wave of sound except that its frequency is not audible and the heat associated with the pulse is carried along (i.e., in modern terms, the expansions are not adiabatic as in the case of sound). After the initial heat pulse passes beyond the layer of air surrounding the body, the layer contracts and becomes ready to absorb a new portion of heat, initiating a 38

39 Ibid., p. 18. Ibid., p. 278-280. In Leslie's words: "We are therefore compelled to embrace the only alternative and to refer the diffusion [radiation] of heat to the vehicle of certain oscillations, or vibratory impressions, excited in that elastic and active medium [i.e., the air or other fluid surrounding a radiating body]." An Experimental Inquiry, p. 215. 40

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new cycle. 41 This theory allowed Leslie to explain the effects of a variety of properties of radiating surfaces, a feat unmatched by contemporary alternative theories. 4 2

S E L F - C O R R E C T I N G H Y P O T H E S E S AND T H E SEPARATION O F T H R E E M O D E S O F H E A T T R A N S F E R

So far, this chapter has been devoted to the way in which Common Sense considerations led Leslie to reject contemporary theory in electrical and heat studies and to develop counter-hypotheses which conformed to Common Sense demands. Furthermore, the emphasis has been on the way in which these alternative hypotheses led to experiments which would otherwise not have been done and to implications which demanded new approaches to interpreting a variety of phenomena. There were, however, other aspects of Common Sense methodological theory which informed Leslie's work. Among these, one of the most important had to do with how a scientist responds to experiments which do not provide results confirming predictions based on an initial hypothesis. Dugald Stewart had emphasized that one of the great values of hypotheses lay in their ability to generate experiments which would lead to their own correction, and Leslie had emphasized this aspect of hypotheses in his laudatory comments on Lavoisier's system of chemistry. In the Experimental Inquiry, Leslie provided a beautiful example of what he called this "usual progress of discovery," in which, "we learn by degrees to correct our primary notions." 4 3 His earliest work on heat had dealt with convection in fluids, and Leslie had become convinced that heat was not transmitted in fluids except by convection currents, most of which were self-induced. He wrote 41

John Leslie, An Experimental Inquiry, especially pp. 204-240. lbid., pp. 240-260, or see Olson, op. cit., pp. 291-294. 43 John Leslie, An Experimental Inquiry, p. 339. 42

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that " I n fluids, the diffusion of heat is, in general, quicker and more uniform [than in solids] because the irregular density of the mass occasions an intestine motion. . . . In fact, that share of heat which is communicated by the slow pervading of the aerial mass [by what we might now call conduction] may be totally neglected in every computa­ tion. It is by its motion alone that air transfers and dis­ seminates w a r m t h . " 4 4 Of course, in developing his work in the Experimental Inquiry Leslie discovered that this notion was incorrect. H e found that radiation was an important mode of heat transfer, but through the first part of his researches he continued to believe that only two modes of heat transfer, radiation and convection, were operative in fluids. It oc­ curred to him that there might be a way to verify this fact and to separate the contributions of radiation and convec­ tion in the cooling of hot bodies. Assuming that Newton's law of cooling (ΔΤ = A T 0 e - k t ) holds for all operative modes of cooling as long as the environment of a cooling body remains unchanged, Leslie used the time to reach ΔΤ = ΔΤο/2 to estimate the initial rate of cooling. When Leslie compared the relative rates of cooling in still air and in different winds for blackened and polished balls, he found that the influence of the wind was totally i n d e p e n d e n t of the nature of the surface, and was propor­ tional to the wind velocity. 4 5 T h e knowledge that convective processes are i n d e p e n d e n t of the nature of the surface allowed him to make his next important step. H e assumed that the deviation from the expected radiational cooling of the black and metallic spheres in a still room (prior exper­ iments showed that heat should radiate eight times as rapidly from the blackened as from the polished surface) was caused by air currents induced in their vicinity and that the cooling effects of the induced currents were inde­ p e n d e n t of the nature of the surface. Using this assump44 45

John Leslie, "On Heat and Climate," pp. 13, 27. John Leslie, An Experimental Inquiry, pp. 282-283.

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tion, Leslie was able to separate the radiational cooling in macroscopically still air from the induced convective cooling and to show that at ordinary room temperatures in stagnant air the cooling of a metallic body arises largely from induced convection currents, while the cooling of a blackened body is affected slightly more by radiation than by convection. 46 So far, nothing contrary to expectations had occurred, but when he compared the cooling rates for bodies in still air with ΔΤ 0 = 20°C and ΔΤ 0 = 80°C, Leslie discovered that Newton's law of cooling does not hold for the convec­ tive mode of heat transfer. So he was led to modify his initial assumption and to extend his investigation in new directions. A very simple argument allowed him to ex­ plain why convective processes should deviate from Newton's law. The amount ofheat carried by each particle in a convection current must be proportional to ΔΤ, but the velocity of the induced current should also be propor­ tional to the variation in density caused when the fluid expands; and this in turn will be proportional to ΔΤ. Thus the net effect will be to make the amount ofheat transmit­ ted by a convective process proportional to (ΔΤ)2 rather than ΔΤ. Guided by this argument, Leslie did an addi­ tional series of experiments on the cooling of polished and blackened bodies as ΔΤ approached zero, and made the further discovery that there was a small amount of cooling that neither depended on the nature of the surfaces nor declined rapidly enough to be due to convection. Thus, he concluded: . . . besides the heat abstracted from the ball by the pulsatory [radiative] and regressive [convective] mo­ tions there is some other mode by which it is dispersed, at the rate of the 180th part each second. The portion of heat thus consumed is most certainly not annihilated; neither is it transported to a distance by any species of elastic motion excited in the encircling 46 Ibid.,

pp. 269-276.

JOHN LESLIE AND HENRY BROUGHAM

fluid. It is, therefore, absorbed the contiguous shell of matter, and afterwards slowly diffused through the extended mass. 47 That is, it is conducted away by the gas. Several portions of Leslie's arguments were crude, but he was able to delineate the three modes of heat transmission which we know as radiative, convective, and conductive, and to estimate their relative importance in a variety of circumstances some sixty years before the conductive power of gases was generally admitted. 4 8 Leslie provides an almost ideal model of the early Common Sense scientist, and the reception of his work was characteristic of that accorded to other first-generation Common Sense scientists as well. Because his work almost invariably began by attacking the most widely held theories with a philosophical critique which could be appreciated only by one who accepted most of the tenets of Scottish epistemology, Leslie was completely unsuccessful in convincing a sizeable number of scientists to take his theories seriously. His early papers on both electricity and heat were rejected and ignored; although his Experimental Inquiry was widely read and heralded for the experimental results it offered, its theoretical portions were largely ignored. As we shall see, the works of Henry Brougham which depended upon Common Sense considerations met an even less favorable response, though perhaps more deservedly.

H E N R Y BROUGHAM AND T H E R E F R A C T I O N AND DIFFRACTION OF LIGHT

Just as many of Leslie's studies were dominated by the conscious search for analogies among various phenomena, the first two papers in natural philosophy 47

lbid., p. 318. See Stephen G. Brush, "The Development of the Kinetic Theory of Gases VII, Heat Conduction and the Stefan-Boltzman Law," a draft 48

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COMMON SENSE AND T H E EXACT SCIENCES

written by Henry Brougham were an attempt to discover analogous relationships between the bending of light within bodies (refraction or, in the eighteenth-century term, refrangibility) and the bending of light outside of bodies (reflection and diffraction or, in Brougham's word, flexion). "It has alway appeared wonderful to me," he wrote, "since nature seems to delight in those close analogies which enable her to preserve simplicity and even uniformity in variety, that there should be no dispositions in the parts of light, with respect to inflection and reflection, analogous or similar to their different refrangibility. In order to ascertain the existence of such properties, I began a course of experiments and observations, a short account of which forms the substance of this paper." 4 9 In almost all his experiments, Brougham thought he was investigating the bending or flexion of light (1) around small objects, (2) through narrow apertures formed by sharply defined boundaries, or (3) by parallel grooves or "veins" which appeared naturally or were scored on reflecting surfaces. In modern terms, we would say he was observing the interference or diffraction patterns of light. But Brougham was writing before Young's elucidation of interference; more importantly, he was already disposed—because of his philosophical background—to deny the possibility of any waves in the ether. This is best shown in his attempt to replace Newton's explanation of the natural colors of bodies by one suggested by his observations: paper privately circulated by the author from the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, pp. 11-15, for a more detailed analysis of Leslie's success in separating the three modes of heat transfer. 49 Henry Brougham, "Experiments and Observations on the Inflection, Reflection, and Coloured Light," Phil. Trans., 86 (1796), p. 237. Brougham's second paper was a continuation of the first, "Further Experiments and Observations on the Affections and Properties of Light," Phil. Trans. 87 (1797), pp. 352-385.

220

JOHN LESLIE AND HENRY BROUGHAM

The consideration of the foregoing phenomena inclines me to think, that on the principles which have been laid down, the colours of natural bodies may be explained. The celebrated discovery of Newton, that these depend upon thickness of their parts, is degraded by a compari­ son with his hypothesis of the bits of rays and waves of ether. Delighted and astonished by the former, we gladly turn from the latter; and unwilling to involve in the smoke of unintelligible theory so fair a fabric, founded on strict induction, we wish to find some con­ tinuation of experiments and observations which may relieve us from the necessity of the supposition. 50 In place of etherial and undulatory speculations about the forces to which light is subject in the presence of matter, Brougham invoked an explanation patterned on the ideas of Boscovich. 51 Light is supposed to be particu­ late in nature, and the varying sizes of light particles are supposed to correspond to spectral colors. Furthermore, a pattern of forces is supposed to extend beyond the geometrical surface of any body so that light of any given size (color) will be repelled at certain distances and at­ tracted at others. This being the case, the path of any particle approaching a surface which has, for example, two regions of repulsion and one of attraction may be represented by Figure 2 (after Brougham's Figure 2, Plate 9, Phil. Trans. Abridged, 17, p. 727). Let A C D E B be the surface and FGHIJKLbe the path of the light. In a region near G the light will be repelled (deflected) and turned away from the normal to A B. In a region near H it will be attracted (inflected) and pulled back toward the normal, and in a region near I it will be so strongly repelled (reflected) that it is turned around to escape along the path I J K L. Because 50 "Experiments and Observations on the Inflection, Reflection, and Coloured Light," reprinted in PHI. Trans. Abridged, 17 (for 1797), p. 750. 5l Ibid., p. 730.

COMMON SENSE AND T H E EXACT SCIENCES

different-colored particles have varying sizes (corresponding to the varying masses of particles of different matter), their paths will be slightly different. Thus, in any given region of deflection or inflection, a beam of white light should be decomposed into a spectrum; i.e., different colors should have different flexibilities analogous to their differing refrangibilities. In his second paper, Brougham explained why, in spite of the fact that flexion, like refraction, separates light, we cannot produce a spectrum by ordinary reflection. 52 This 52

See "Further Experiments and Observations on the Affections and Properties of Light," Phil. Trans. Abridged, 18, (for 1797), pp. 199-200.

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JOHN LESLIE AND HENRY BROUGHAM

is true essentially because, as Figure 2 shows, the paths of all colors are symmetrical about the line I E, which includes the point of reflection. Under certain special circumstances, however, Brougham's theory implied that reflection might produce a spectrum. Experiments done on the bending of light around small objects and on the patterns formed by light reflected at grazing incidence from concave mirrors seemed to confirm the theory. 53 The colored fringes produced when light was passed at grazing incidence over one edge of a concave mirror and then reflected from the opposite side appeared very similar to the phenomenon of Newton's rings, and this led Brougham to a reinterpretation of the production of fringes in thin plates. Like Leslie, Brougham was led to overemphasize vastly the significance of a small number of experiments by his attempt to follow the Common Sense demand for the incorporation of as many phenomena as possible into one explanatory scheme. Since the fringes produced by grazing reflections looked like those produced in thin plates, Brougham was convinced that they must be produced in the same manner. "The state of the case, then, seems to be this," he wrote, "when a phenomenon [i.e., colored fringes] is produced in a particular set of circumstances, and the same phenomenon is also produced in another combination, where some of the circumstances, before present, are wanting; we are entitled to conclude that the latter is the most general case, and must try to resolve the other into it." 54 Colored rings like those produced by Newton and supposed to arise in part because of the refraction and internal reflection of light within these rings seemed in Brougham's experiments to be produced by flexion alone. Thus, he felt fully justified in denying any role to refraction or internal reflection in the explanation of colored rings produced by thin plates. Within a few years of Brougham's papers, Young's un53

Ibid., pp. 203-208.

54

Ibid., p. 208.

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COMMON SENSE AND T H E EXACT SCIENCES

dulatory theory emphasizing interference phenomena was capable of dealing with all Brougham's observations with a much greater degree of quantitative precision. But Brougham was never able to deny his basic philosophical principles and accept the luminiferous ether for light to undulate in. He continued, even through the 1850s 55 to produce papers based on his old theory of flexion. G. B. Airy incorrectly, but with understandable reason, wrote of the last of these papers, "It is written in entire ignorance both of the general principles of the great Undulatory Theory and of the algebraical and numerical results which have been deduced from it." Airy correctly continued, "The paper is more than twenty years behind the actual state of science." 5 6 That Brougham should have been fighting the undulatory theory nearly fifty years after it had begun to receive serious support and at least thirty years after even David Brewster had acknowledged its value is a testimonial not only to the stubbornness of the man but also to the power of the Common Sense principles which motivated and sustained his attitude. 55 See Henry Brougham, "Experiments and Observations upon the Properties of Light," Phil. Trans. 140 (1850), pp. 235-260; "Further Experiments on Light," Proceedings of the Royal Society of London, VI, 1852, pp. 172-174; and "Further Experiments and Observations on the Properties of Light," Proceedings of the Royal Society of London, VI, (1853), pp. 312-415. 5e Royal Society of London Archives, Referees' Report RR 2.36, ff. 1-2.

224

CHAPTER 9

Common Sense Concerns Once Removed: James D. Forbes and John James Waterston laid by the Edinburgh Moral Philoso­ phers, Dugald Stewart and Thomas Brown, on aspects of scientific methodology was not continued by John Wilson, who turned the chair of moral philosophy at Edinburgh into a chair of rhetoric and belles letters for the period between 1820 and 1850. 1 Thus, between 1820 and 1836, when William Hamilton assumed the chair of metaphysics and logic, students of natural philosophy at Edinburgh were not systematically exposed to the philosophy and methodology of science, and they showed a less self-conscious attitude toward the epistemological and metaphysical foundations of their scientific work than did those who immediately preceded or followed. Com­ mon Sense methodological ideas did not entirely disap­ pear from the curriculum, however. As long as John Leslie remained in the chair of natural philosophy (1819-1832) he continued to provide an emphasis on methodology. Furthermore, though Wilson's interests lay outside the sciences, he continued to have his students read the works of DugaId Stewart and Thomas Brown, and he provided an opportunity for those of his students who were also interested in natural philosophy to explore the connec­ tions between moral and natural philosophy in their class essays. For instance, James David Forbes, who was to become Leslie's successor as professor of natural THE EMPHASIS

1 See

SirAlexander Grant, The Story of the University of Edinburgh (London: Longmans and Co., 1884), II, pp. 345-347 for a discussion of Wilson's emphases and background.

COMMON SENSE AND THE EXACT SCIENCES

philosophy and a highly respected scientist of the nineteenth century, won first prize in Wilson's class of 1827-28 by writing "The Influence and Advantages of the Study of Astronomy on the Mind" and "On the Inductive Philosophy of Bacon, his Genius, and Atchievements [sic]."2 The second of these essays is particularly interesting because it expounds a scientific methodology to which Forbes adhered throughout his active scientific life—a methodology based on Bacon's Novum Organum but con­ sciously modified by insights derived from Stewart, Playfair, and John Gregory.3 In particular, Forbes fol­ lowed Stewart in believing that Bacon's emphasis on the role of analogies in science had been insufficiently recog­ nized and exploited. Thus, he wrote that "To reason by strict analogy from small to great effects is the only open­ ing through which Natural Philosophy can ever arrive at firm conclusions."4 Similarly he argued that "The opera­ tion of analogical inquiry is, then, the most important and difficult part of the process of induction and [one] which, as I have just maintained, is yet far behind the author's [i.e., Bacon's] view of its perfection." 5 ANALOGICAL INQUIRY IN FORBES' WORK

Forbes' early emphasis on the role of analogical insights in the process of scientific discovery, with its obvious source in Common Sense discussions of Baconian philos­ ophy, is especially fascinating because his most important scientific discoveries—those of the polarization and total internal reflection of heat, the temperature dependence of heat conductivity in metals, and the viscous theory of the 2 "Moral

Philosophy Essays," 1827-1828, Item 4, Box V-VI, in Cor­ respondence and Papers of James David Forbes at St. Andrews Univer­ sity Library. 3 Ibid. Stewart is cited on pp. 13, 24, 30 and 32, Playfair on pp. 14, 20 and 26, and Gregory on p. 25. 4 Ibid., p. 6. 5 Ibid., p. 18.

JAMES FORBES AND JOHN WATERSTON

motion of glaciers—all depended upon a conscious and explicit exploitation of analogies. Although Forbes began to publish a series of wellreceived papers on descriptive geology even before he became a student at Edinburgh, 6 he initiated his most important physical investigations when John Leslie died in 1832 and he took over not only Leslie's natural phil­ osophy class but also his series of investigations of radiant heat. Late in 1834 Forbes began a series of investiga­ tions stimulated largely by Marcello Melloni's discovery that non-luminous heat was refracted in its passage through rock salt. 7 The refraction of heat implied the exis­ tence of a strong analogy between radiant heat and light and suggested to Forbes that he should seek to determine whether heat could also be polarized like light. "The importance of this subject," he wrote, "will be estimated when we consider the very definite laws to which the polarization of light is subjected, and the accuracy with which they are represented on the undulatory hypothesis. If heat, when wholly deprived of light, be subjected to similar modifications, our progress in acquiring a knowl­ edge of the true nature of heat will be greatly advanced by our previous analogical acquaintance with the laws of light" 8 Forbes justified his emphasis on analogical relations by reiterating and expanding upon the considerations of his early Baconian essay: 6 See "Remarks on Mount Vesuvius," Edinburgh Journal of Science, VII (1827), p. 11, and a series of eight "Physical Notices of the Bay of Naples," Edinburgh Journal of Science, IX (1828), pp. 189-213; X (1829), pp. 108-136; X (1829), pp. 245-267; I n.s. (1829), pp. 124-141; I n.s. (1829), pp. 260-286; II n.s. (1830), pp. 326-350; III n.s. (1831), pp. 246-278. 7 Macedonio Melloni, "Memoir on the Free Transmission of Radiant Heatthrough different Solid and Liquid Bodies; presented to the Royal Academy of Sciences of Paris on the fourth day of February, 1833." Taylor's Scientific Memoirs Vol. 1, 1837. 8 James D. Forbes, "On the Refraction and Polarization of Heat," Transactions of the Royal Society of Edinburgh, 13 (1835), p. 147.

COMMON SENSE AND THE EXACT SCIENCES

The importance of analogies in science has not, per­ haps, been sufficiently insisted upon by writers on the methods of philosophizing. A clear perception of connexion has been by far the most fertile source of discovery. That of gravitation itself was only an ex­ tended analogy. The undulatory theory of light has been preeminently indebted to the coordinate science of acoustics, which afforded to Dr. Young the most plausible basis of his curious and original investiga­ tions; and unless that science had existed, it may be doubted whether such a speculation would have been invented, or, if invented, would have been listened to. The penetrating sagacity of M. Fresnel, in his prosecu­ tion of the subject, has led him to draw from mechanical and mathematical analogies, accurate representations of laws which no strict reasoning could have enabled him to arrive at. Of this, his marvelous prediction of the circular polarization of light by two total reflections in glass, is the most prominent example, a conclusion which no general acuteness could have foreseen, and which was founded on the mere analogy of certain in­ terpretations of imaginary expressions. The mere reasoner about phenomena could never have arrived at the result—the mere mathematician would have re­ pudiated a deduction founded upon analogy alone. 9 In the course of a long series of investigations on radiant heat, Forbes succeeded in proving not only that heat could be polarized and that it could be totally internally reflected like light, but also that all the complex relation­ ships derivable from the undulatory theory and estab­ lished for light were true of radiant heat. 10 Thus, his mi9 Ibid.,

p. 147. Emphasis mine. '"Following "On the Refraction and Polarization of Heat," Forbes published "Researches on Heat" Trans. Roy. Soc. Edin., 13 (1836), pp. 446-471; "On the Undulatory Theory of Heat, and on the Circular Polarization of Heat by Total Reflection," Phil. Mag., 12 (1838), pp. 545-559,3 (1838), pp. 97-113,180-192; and "Researches on Heat, Third Series," Trans. Roy. Soc. Edin., 14 (1840), pp. 176-207—all of which

JAMES FORBES AND JOHN WATERSTON

nute investigation of the analogy of light and radiant heat set the stage for the subsequent identification of thermal and luminous radiations. THE GENESIS OF FORBES' VISCOUS THEORY OF GLACIER MOTION

Forbes began his second major series of scientific in­ vestigations in the summer of 1841, and once again the key to his success was his sensitivity to analogical rela­ tions and his attitude toward their exploitation. At the invitation of Louis Agassiz, he joined a party of Swiss naturalists on the Lauter-Aar glacier in Switzerland. 11 During his short stay there, Forbes observed a previously unnoticed set of vertical bands or strata which ran parallel to the length of the glacier, permeating the glacial ice. 12 This discovery in itself was of minor significance, but it stimulated Forbes' interest in glacial phenomena, and when he returned to Edinburgh, he wrote a lengthy and important essay review of the recent literature on glaciers and their role in geological change. 13 continued to develop and amplify the analogy between light and radiant heat. 11 See John Campbell Shairp, Peter Guthrie Tait, and A. AdamsReilley, Life and Letters of James David Forbes, (London: Macmillan and Co., 1873), p, 256 ff., for a discussion of Forbes's first Alpine trip. 12 See James D. Forbes, "On a Remarkable Structure Observed in the Ice of Glaciers," Edinburgh New Philosophical Journal, 32 (1842), pp. 391-393. 13 Review ot "1. Memoire sur la Variation de la Temperature dans Ies Alpes de la Swisse, par M. Venetz . . . 2. Naturhistorisehe Alpenreise, parF.J.Hugi . . . 3.Notice sur la Cause Probable de Transporte Ies Blocs Erratiques de la Suisse, par M. J. de Charpentier . . . 4. Discours prononce a I'ouverture des stances de la Societe Helvetique des Sci­ ences Naturelles a Nuefschatel, Ie J 4 Juillet 1837, par L. Agassiz . . . 5. Htudes sur la Glaciers, par L.L. Agassiz . . . 6. Theorie des Glaciers de la Savoie, par M. Le Chanoine Rendu ... 7. Essai sur Ies Glaciers, et sur Ie Terrain Erratique du Bassin du Rhone, par Jean de Charpentier . . . 8. Etudes Geologiques dans IesAlpes, par M. L. A. Necker . . ."Edinburgh Review, 75, (1842), pp. 49-105.

COMMON SENSE AND THE EXACT SCIENCES

In order to prepare his reader for an analysis of theoreti­ cal discussions of glaciers, Forbes first sought to "present to the reader a picture of what a glacier is, and of the curious and beautiful appearances and transformations which it exhibits." 14 In the process of this description, he developed an analogy which he was to exploit in a new and insightful way: A glacier, in the customary meaning of the term, is a mass of ice, which, descending below the usual snow line, prolongs its course down the cavity of one of those vast gorges which furrow the sides of most mountain ranges. It is better represented by a frozen torrent than by a frozen ocean None who has seen or even clearly conceived a lava-stream, can fail to find in it the nearest analogue of a glacier. Stiff and rigid as it appears, no one can doubt that it either flows or has flowed. . . . The glacier, therefore, moves progressively, or if the reader pleases, it flows. 15 Forbes was by no means the first to point out the visual similarites between glaciers and rivers, but the visual analogies had not been taken seriously by those who had tried to understand the mechanisms underlying glacial motion. One widely held theory initiated by Benedict de Saussure supposed that the glacial mass, lubricated un­ derneath by water produced by its own melting, simply slid downward as a result of its own gravity, much like a great slab or rock. The only serious rival to this gravita­ tional theory—the dilation theory—supposed that during summer days the water melting on top of the glacier infil­ trated the mass through vertical fissures. This water was supposed to refreeze and expand at night, pushing the glacier outward in the direction of least resistance —which was obviously downward. In his 1842 review, Forbes showed that neither of these theories was satisfac­ torily established. 16 But at this point he was not yet will­ ing to press his own analogy between the flow of glaciers 14 Ibid.,

p. 53.

15 Ibid.,

pp. 53^4.

16 Ibid.,

pp. 70-77.

JAMES FORBES AND JOHN WATERSTON

and that of rivers or lava. Instead, he returned to the Alps in the summer of 1842 to collect exact data on the motion of glaciers, and on July 24 he made a further observation which fully convinced him that, "a glacier moves like a sluggish river, and under the same laws." 1 7 On August 22 he wrote: One afternoon I happened to ascend higher than usual above the level of the Mer de Glace, and was struck by the appearance of discoloured bands traversing its surface. . . . These dirt-bands perfectly resemble those of froth and scum which every one has seen upon the surface of slowly moving foul water; and their figure at once gives the idea offluid motion, freest in the middle, and obstructed by friction towards the sides and bottom. 18 With these analogies motivating his investigation, Forbes went on to establish (1) that the different portions of any transverse section of a glacier move with varying velocities and fastest in the center, (2) that those circumstances which increase the fluidity of a glacier—namely, heat and wetness—invariably accelerate its motion, and (3) that the structural surfaces occasioned by fissures which have traversed the interior of the ice are also the surfaces of maximum tension in a semi-solid or plastic mass lying in an inclined channel. 1 9 Thus, he was able to conclude by presenting what he considered to be a legitimate theory of glacial motion: "A glacier is an imperfect fluid, or a viscous body, which is urged down slopes of a certain inclination by the mutual pressure of its parts." 2 0 Forbes could not work out the details of his theory because knowledge of the motion of imperfect fluids was 17

John Campbell Shairp, et. al., Life of Forbes, p. 526. "Third Letter on Glaciers," printed in. Life of Forbes, p. 527. 19 Quoted in Life of Forbes, p. 509. From Travels Through the Alps of Savoy, (1843). T h e detailed evidence on these three points was presented in a three-part article, "Illustrations of the Viscous Theory of Glacier-Motion," Phil. Trans. 136 (1846), pp. 143-210. 20 Ibid., p. 365. 18

231

COMMON SENSE AND THE EXACT SCIENCES not sufficiently advanced in the 1840s. But virtually all subsequent investigations of glacial motion have in­ volved technically sophisticated elaborations of Forbes' basic idea. THE COMPLEMENTARITY OF PHYSICAL INSIGHT AND MATHEMATICAL THEORY Just as his early essay on Bacon presaged Forbes' later sensitivity to analogical arguments, it also provides an insight into his attitude toward both the value and the limitations of mathematics. In discussing Bacon's failure to consider mathematics seriously enough, Forbes wrote: It may be remarked generally, with regard to the practi­ cal employment of the Baconian Method, that in the exact branches of Natural Philosophy, an instrument has been extensively used, to the advantages of which Bacon did not, perhaps, assign a sufficiently important place in his system—Geometrical Investigation —which, of all other methods, has most enlarged our Generalization and Analogies. It has saved many of the more circuitous operations of the first steps of Induction and brought our conclusions quicker to the "Experimentum Crucis," that most important means of enquiry. But desire to attain this facility has ever led the cultivators of the sciences depending less upon mathe­ matical demonstration to overlook the slow but sure progress which the inductive system when fully pur­ sued, promised them and led them to outstrip in theory their experimental knowledge, a procedure which will ever lead into an abyss of confusion and uncertainty. 21 Forbes was in close agreement with Reid and Stewart. Like them, he emphasized the immense value of quantita­ tive, mathematical investigations for generating knowl­ edge in some fields of natural philosophy, but he retained 21 "Moral

Philosophy Essays," (see note 2), pp. 39-40.

JAMES FORBES AND JOHN WATERSTON

a belief that it was inappropriate and perhaps mpossible to shortcut the direct empirical and analogical method of induction by appealing to mathematical arguments in all cases. In his early essay, for example, Forbes took particular exception to the Daltonian atomists, who, he thought, based their theories on "the appearance of unattainable precision and the introduction of algebra into an investigation where it can have no place." 2 2 Forbes later changed his mind about Daltonian atomism and admitted that it was Dalton's attempt to represent the conditions of mixed gases "geometrically and atomically" 23 which allowed him to develop an extremely fruitful theory. But he never relinquished his feelings about the limitations of mathematics. H e insisted, for instance, that if any mathematical theory of glacier motion were to be taken seriously, it would have to be rigorously controlled in such a way that it represented not only the macroscopic phenomenon of glacial motion but also the internal mechanisms. Similarly, he demanded that the boundary conditions used in the mathematical theory conform strictly to the physical conditions being represented. In an important sense, he followed his philosophical teachers in rigidly restricting the latitude of mathematical model-builders while he allowed those who investigated physical analogies or models much greater freedom. One can sense this attitude clearly in his response to William Hopkins' attempts to provide a mathematical theory of glaciers. 24 "From general physical considerations, and from an experimental study of plastic 22

Ibid., pp. 38-39. James D. Forbes, A Review of the Progress of Mathematical and Physical Science in More Recent Times, and Particularly Between the Years 1775 and 1850, (Edinburgh: Adam and Charles Black, 1858), p. 140. This essay was initially published as a preliminary dissertation to the eighth edition of the Encyclopedia Britannica. 24 William Hopkins, "On the Motion of Glaciers," Philosophical Magazine, 26 (1845), pp. 1-16, "On the Mechanism of Glacial Motion," Philosophical Magazine 26 (1845), pp. 146-169, 237-251, 328-334. 23

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COMMON SENSE AND T H E EXACT SCIENCES

bodies, I was well aware that Mr. Hopkins' mode of treatment was applicable only to a body possessing properties, or placed under conditions, which I was perfectly certain that a glacier had not, or was not, placed in. I regarded his solutions, therefore, (I refer to his early papers in the Cambridge Trans, and Phil. Magazine) as irrelevant mathematical excercitations. His later writings I have not studied, as I perceive that he had made no enlargement of his physical basis of reasoning." 2 5 An even more forceful caution against mathematicism appeared in Forbes' 1858 review of the third edition of Whewell's History of the Inductive Sciences. Forbes again acknowledged the importance of mathematics in mechanics and physical astronomy but warned against those who were carried away by the beauties and apparent certainty of mathematics. In cases where the abuse of which we speak has obtained amongst modern writers, of making—to use a homely phrase—the facts of nature mere pegs on which to suspend festoons of algebraic drapery, the evil may be said to extend beyond the region of trifling, for the theorist commonly falls into positive mistake. Sound mathematics lead to false results if applied to insufficient or wrongly assumed data, and the general public is misled by an array of proof altogether fallacious and delusive. 2 6 Forbes' cautious attitude toward mathematical theories probably had little influence on his work. By his own admission, he was not "mathematically strong enough" to develop mathematical theories even where he might have felt them appropriate. But his insistence that mathematical formulations always be supplemented and controlled 25 Letter to P. G. Tait, January 12, 1865, reprinted in Life of Forbes, pp. 514-515. Emphasis mine. 26 James D. Forbes, "The History of Science; and Some of Its Lessons," Fraser's Magazine for Town and Country 57 (1858), p. 292.

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by physical insights was transmitted to his more technically able students, James Clerk Maxwell and P. G. Tait, and in their hands this insistence played a critical role.

F O R B E S AND T H E D E C L I N E O F T H E COMMON SENSE TRADITION IN S C O T T I S H E D U C A T I O N

Forbes shared, emphasized, and passed on to his students Common Sense methodological concerns relating to the importance of physical analogies and the insufficiency of over-mathematicized approaches to natural philosophy. But it is also true that he played a greater role than any other single individual in bringing to an end that curious blend of moral and natural philosophy which characterized the science of early nineteenth-centruy Scotland. Forbes gave a new thrust to the institutional forms of Scottish education which ultimately destroyed the pattern of philosophically based liberal education and the production of philosophically trained and oriented scientists. The story of Forbes' attempts at educational reform and his running fight with William Hamilton, the last of the Common Sense School, to dethrone moral philosophy from its preferred place in Scottish education is clearly told in George E. Davies' The Democratic Intellect: Scotland and Her Universities in the Nineteenth Century,21 and I cannot hope to reproduce its details here. It is enough for our purposes to say that while Forbes saw the worth of specific methodological considerations, he did not assimilate the general spirit of Scottish philosophy with its emphasis on broad liberal education and its belief in the primacy of the philosophy of the mind. H e was deeply impressed by the scientific commitment of William Whewell, John Herschel, and Charles Babbage, whom he came to know well in connection with his role in 27

Second edition, Edinburgh, 1964.

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COMMON SENSE AND THE EXACT SCIENCES

the formation of the British Association for the Advancement of Science. H e saw himself as a professional scientist, and he saw his principle role in the university not as a molder of "men-o'-parts" but as a producer of professional scientists. Thus, he pressed strongly for the institution of Cambridge-like written examinations to replace the somewhat casual oral examination which had characterized the Scottish tradition. H e raised the level of teaching in natural philosophy, and he successfully fought to change the traditional geometrical emphasis of the mathematics class by urging the appointment of Cambridge-trained Phillip Kelland to the professorship of mathematics in 1837. We can hardly fault Forbes for his attempts to upgrade the quality of Scottish education and to place Scottish students in a better competitive position relative to Oxbridge graduates for obtaining jobs in a rapidly industrializing and professionalizing society. On the other hand, it is clear that, after his accession to the natural philosophy chair at Edinburgh in 1832, the interesting and often fruitful mutual reinforcement of ideas which earlier students had received in their integrated studies of moral philosophy, natural philosophy, and mathematics became increasingly rare. William Hamilton fought this trend until his death in 1856, b u t when he died the old ideals of Scottish education died with him. Ideas which had entered science at least in part from the Scottish philosophical tradition continued to influence British science through the nineteenth century. But the influence was transmitted through the scientific writings of men like Maxwell and Rankine, and explicit training in philosophy ceased to b e an important factor in Scottish and British science. J O H N JAMES WATERSTON

During the class session of 1826-1827, the year before Forbes entered Leslie's and Wilson's classes, one of the 236

JAMES FORBES AND JOHN WATERSTON

most brilliant and pathetic of nineteenth-century scientific figures, John James Waterston, was medalist in natural philosophy. 2 8 There is no record of his attendance in Wilson's moral philosophy class, but as in the case of Brewster there is fairly clear evidence that he read the major works of the Common Sense School. The first reference in his one book-length monograph, Thoughts on Mental Functions,29 is to Reid's Enquiry into the Human Mind on the Principles of Common Sense, and we shall see that the methodological discussions prefixed to his early papers demonstrate a thorough, though critical, understanding of the methodological ideas of Stewart and Brown. After several years' work in London as a draftsman and civil engineer, Waterston accepted the post of naval instructor to the East India Company's cadets in Bombay. There he wrote Thoughts on Mental Functions,30 as well as "The Physics of Media Composed of Free and Perfectly Elastic Molecules in a State of Motion," which was condemned to the archives of the Royal Society of London in 1845, only to be rediscovered by Lord Rayleigh and published in 1892. Again in 1852 he failed to get the Royal Society to publish a paper on the behavior of saturated vapors. So in 1857 he returned to Edinburgh, apparently expecting circumstances more favorable to his research and its publication. Between 1857 and 1868 Waterston published some twenty papers, mostly on molecular physics and chemis28 Virtually all biographical information about Waterston comes from the memoir of Waterston by J. S. Haldane in The Collected Papers of John James Waterston (London: Oliver and Boyd, 1928). Though some of his papers remain in the hands of Charles D. Waterston, now head of the Department of Geology in T h e Royal Scottish Museum, many of the sources used by Haldane seem to have disappeared. 28 Originally published by Oliver and Boyd in 1843, reprinted in his Collected Papers. The reference is on p. 3. in Collected Papers. 30 See Stephen G. Brush, "John James Waterston and the Kinetic Theory of Gases," American Scientist 49, (1961), pp. 208-209, for a summary of the elements of kinetic theory presented in this book.

237

COMMON SENSE AND T H E EXACT SCIENCES

try, and all appearing in Philosophical Magazine, one of whose editors was David Brewster. As we have seen, Brewster's philosophical beliefs made him much more sympathetic to the speculative nature of the basic assumptions which characterized Waterston's work than any of his powerful British contemporaries. In fact, Brewster had once written to James Forbes advising him, "Forget entirely all that you have heard of Lord Bacon's Philosophy. Give full reins [sic] to your imagination. Form hypotheses without number." 3 1 Of course, he went on to insist that Forbes "put them all to the test of experiment," but his basic sympathy toward a controlled hypothetical method was well established. The outstanding characteristic of all Waterston's post1831 papers was the way in which he attempted careful experimental investigations of the implications of his theories. Thus, it seems likely, as Haldane has suggested, that it was at Brewster's urging that Waterston's papers were published in his journal. 32 This speculation is reinforced by the fact that when Brewster died in 1868, even this outlet was closed to Waterston. Twice more during the 1860s, papers which Haldane assesses as valuable contributions to contemporary science were rejected—this time by the Royal Astronomical Society. Finally, on a June morning in 1883, Waterston went for a walk and either fell or jumped into the waters of the Firth of Forth. No trace of his body was ever found. WATERSTON'S G O A L : T H E R E D U C T I O N O F ALL P H E N O M E N A T O M A T T E R IN M O T I O N

Waterston's first paper, "An Exposition of a New Dynamic-Chemical Priniciple," published in 1831, was at 31 Letter from Brewster to Forbes, Melrose, November 13, 1830, University Library, St. Andrews. Correspondence and Papers of James David Forbes, incoming letter 1830/35, p. 2. 32 See Waterston's Collected Works, pp. lvi and lxii. I am informed by E d Morse, who is currently working on a biographical study of Brewster

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JAMES FORBES AND JOHN WATERSTON

once a very simple and an alarmingly ambitious attempt to provide a unitary theory of all natural phenomena. The Scottish tradition in which he had been trained had long looked forward "to that period when all that is concealed under the veil of mystery shall finally be exposed in the sublime grandeur and simplicity which so eminently characterizes the works of nature." 3 3 To this background of long-term expectations of unity, Waterston added an extensive reading of the works of Hans C. Oersted, a physicist who had emphasized the connection between electrical and chemical forces in his Identity of Electricity and Chemical Affinity of 1813 and who had established the connection between electricity and magnetism in 1821. In fact, Waterston chose to preface his first paper with an illuminating quotation from Oersted's article, "Thermo-Electricity," in the Edinburgh Encyclopedia: "The new discoveries, in short, reveal to us the world of secret motions, whose laws are probably analogous to those of the universe, and which deserve to be the subject of our most earnest meditations." 3 4 Like Oersted, who was a student of Kant, Waterston was deeply struck by recent discoveries which demonstrated the intimate connection between heat, electricity, magnetism, light, and chemical phenomena. But Waterston was almost certainly ignorant of the Kantian dynamical philosophy underlying the sentiments expressed by Oersted. When he interpreted Oersted's statement about the analogy between chemical, electrical, and thermal laws and "those of the universe," the latter phrase meant to him the laws of gravitation in the most straightforward Newtonian sense, and it implied nothing about the fundamental epistemological bases of our knowledge of matter as it did for the Idealists. Thus, Waterston began the subat the University of California at Berkeley, that the editorial correspondence from Philosophical Magazine which might have been able to confirm or refute this conjecture was lost during World War II. 33 34 Waterston's Collected Works, p. 531. Ibid., p. 53.

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COMMON SENSE AND THE EXACT SCIENCES

stance of his paper by speculating about the relation be­ tween gravitation and the phenomena of optics, heat, electricity, magnetism, and chemistry. He acknowledged that no experiment had been able to demonstrate an electrical, chemical, or thermal influence upon gravity or vice versa. But, he argued, experiment does not warrant the conclusion that there are no interconnections. Speak­ ing of attempts to measure the weight of heat, he wrote: The magnitude of the results may, like the parallax of the fixed stars, be placed far beyond the range of our means of observation, without at the same time justify­ ing doubts which may be entertained either of the inti­ mate connection of gravitation and caloric, or of the real magnitude of these heavenly bodies. Is it not more consonant a reason to consider them as inseparably combined in their operations? We know that both pow­ ers surround every particle of matter, exist in the same space, and generate motion at the same time and in the same place; may we not, therefore, with justice con­ clude that so far from acting independently, gravitation may communicate to heat all the properties by which it is distinguished, and that they may both be examples of the same elementary force exhibited through different media? 35 At this point, Waterston offered a simple example or, in his word, "analogy" designed to establish the plausibility of his supposition that gravitation may give rise to other kinds of phenomena and to suggest the fundamental mechanism of transference of force or power from one mode to another. If we cons ider a body falling to the earth, it gradually accumulates a quantity of momentum which is visibly lost when it arrives at the ground. In this instance the momentum, before it is transferred to the falling body, is invisible; why may not, therefore, the same momentum after collision, be again reduced to 35 Ibid.,

p. 533.

JAMES FORBES AND JOHN WATERSTON

the same invisible state without being actually destroyed? The manner in which it appears and disappears is certainly different, b u t the latter may b e governed by laws as unalterably fixed as the former, a l t h o u g h from t h e c o m p l e x i t y of t h e att e n d i n g c i r c u m s t a n c e s t h e i r i n f l u e n c e c a n n o t so readily be appreciated. Thus, after collision, in the above example, u n d u l a t i o n s or vibratory motions are always observed to take place. These changes are influenced by the nature of the composing substance, which again is an immediate consequence of the peculiar molecular forces of the ultimate constituent parts. Since we have reason to suppose that their molecular forces are, like gravitation, subject to fixed laws and are of like importance and universality, it becomes highly probably that they are alone the invisible agents which abstract this momentum of collision, without any evidence of its existence being afterward perceived. 3 6 It is extremely important to understand what Waterston thought this example illustrated in order to gain an insight into his overall attempt to remake natural philosophy. He was fully aware that it made no sense to talk about invisible momentum existing before it is transferred to a falling body, as long as one believes only in the conservation of momentum in its usual vectorial sense. In fact, Waterston was urging scientists to take seriously Descartes' notion of the conservation of "the absolute quantity of motion in the universe" as well as the conservation of momentum in its present technical sense. He knew that the absolute quantity of motion seemed to diminish in all inelastic collisions. But, he agrued, this apparent loss of motion may be due only to the fact that we cannot detect internal motions within bodies which have collided. 37 The reference in his example to undulations and vibrations felt as a result of the impact of falling bodies is thus a plausible argument for the transference of motion from the macrosphere of 36

Ibid., p. 536.

37

See ibid., p. 534.

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COMMON SENSE AND THE EXACT SCIENCES

falling bodies to the microsphere of molecular motions. If it is true that the momentum of a falling body is transferred at the termination of its fall into invisible motions of the constituent parts of matter, then it would also seem plausible by analogy that before it was manifested in the macro-motion of the falling body, it existed in the invisible motions of some other medium—perhaps an ether. In that case, even gravity might be said to be caused by matter in motion, and the phenomena of heat, chemical change, electricity, etc., might merely be the manifestation of motions of particles of differing shapes and sizes. Thus, Waterston wrote that his suppositions "induce a lively hope that matter and motion alone will be found sufficient to explain all the phenomena attending the grand cycle of nature's operations, and that that system of unity and simplicity which the advancement of discovery is always bringing further into view, will at length be completely unfolded, and all the physical sciences eventually traced to the varied development of these two principles." 3 8 He knew that any assumption of the existence of a gravitational ether controverted Common Sense teachings about the nature of causation, but he justified his approach on grounds which might also have found their justification in the Scottish tradition. In a clear reference to ideas presented most forcefully by Thomas Brown, Waterston wrote: This last doctrine [that a subtle fluid or ether is supposed to transmit gravitational force from one region of space to another] has b e e n reckoned by some unphilosophical, by introducing a clumsy mode of explaining that, which certain refined metaphysical speculations on causality do not require to b e explained. But, although the cause which is sought, may not on these metaphysical principles be necessary, yet it will always remain inconceivable how two bodies in an absolute vacuum will move towards one another in 38

Ibid., p. 535.

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JAMES FORBES AND JOHN WATERSTON

accordance with the laws of gravitation; and it is certainly preferable to adopt the contrary opinion, more especially if we discover a certain arrangement of the fluid which will explain the development of an attractive and repulsive energy on the most simple and evident mechanical principles. 3 9 Although this statement specifically argues for an explanation of phenomena which Stewart, Brown, and Reid had chosen to believe inexplicable, its general tone is more in line with than opposed to Scottish philosophical principles. Had he been seeking merely an ad hoc explanation of gravitational phenomena, Waterston's attempt would have been violating Common Sense canons of method. But his theory sought to correlate an extremely wide range of phenomena within a single explanatory structure; this was an explicit goal of Common Sense Philosophy. In a sense, Waterston realized that he was substituting one inconceivable process—the perfectly elastic collision of particles subject only to the laws of conservation of momentum and vis viva—for another —the distant attraction between two bodies—as the basis for theorizing. This seemed a perfectly justifiable step, however, in light of the greater generality it seemed to promise. Although Waterston's theory presumed the existence of invisible entities, there were mitigating circumstances. His invisible entities were not assigned any special and unprecedented qualities. In place of the myriad qualitatively distinct types of fluids which were uniformly decried by such Common Sense natural philosophers as Robison, Playfair, and Leslie, Waterston proposed to consider ensembles of particles possessing only qualities uniformly attributed to matter—size, shape, and inertial mass. Furthermore, he had more than adequate precedent for this kind of presumption of invisible material particles in Thomas Brown's explicitly atomistic writings. 39

Ibid., pp. 535-536.

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COMMON SENSE AND T H E EXACT SCIENCES

Once he had stated the general aim of his paper—to provide an explanation of all natural phenomena based on the impact mechanics of perfectly elastic particles—Waterston went on to provide an outline of the detailed development of such a proposal, claiming that the outline would have to be filled in later as the mathematical details were worked out. He began by assuming the existence of an infinite number of cylindrically shaped, perfectly solid particles, each endowed initially with an indefinite rect i l i n e a r motion. In t i m e , h e a r g u e d , t h e p r i m i t i v e momentum would be distributed through collisions among rectalinear and rotational motions. Though he did not prove a formal equipartation theorem, it is fairly clear that the tendency of his argument was to show that equal energies would eventually b e transferred into rotational and rectilinear modes of motion. If one now placed an extensive rigid plane surface in this medium of randomly-moving translating and rotating cylinders, the transformation of rotational into rectilinear momentum at the surface would necessitate the development of a new equilibrium distribution of particles such that the mass density would be a monatonically increasing function of distance from the plane. 4 0 If one then introduced a second plane parallel to and at any given distance from the first, he would observe an attractive force between the two planes. This force would be proportional to the masses of planes of uniform thickness and would probably be inversely proportional to the square of the distance between the planes as long as the distance was great relative to the size of the cylinders. Thus, it seemed to Waterston that the inverse square law of attraction associated with gravity could be accounted for by the action of his medium of cylindrical particles upon plates ofrelativelylarge size. Furthermore, he showed that when the distance between plates becomes small relative to the 40

Ibid., pp. 539-541. Waterston's argument is extremely intuitive. A careful mathematical investigation does not seem to warrant his conclusion.

244

JAMES FORBES AND JOHN WATERSTON size of the cylindrical particles, "polar forces will be de­ veloped. .. while other peculiar changes relating to chem­ ical phenomena will simultaneously take place. 41 Finally, if a third set of particles intermediate in size between the elemental cylinders and the relatively large plates was introduced into the theory, a new set of phenomena which "appear to coincide remarkably with the known proper­ ties of heat" were generated. Gravitational, chemical, and thermal phenomena all seemed to flow from Waterston's provisional theory. Un­ fortunately, he was unable to confirm his intuitive argu­ ments, so the subsequent development of a cylindrical particulate ether hinted at in this early paper never materialized. The basic assumption that some form of matter-in-motion explanation could account for major realms of natural phenomena, however, remained the source of his later development of a kinetic theory of gases. WATERSTON'S KINETIC THEORY OF GASES AND ITS COGNITIVE STATUS Because his ether theory of 1831 was never more than a highly speculative suggestion, Waterston was not forced into considering the cognitive status of a successful theory generated by his hypothetical method. His 1845 "Physics of Media That are ComposedofFree and PerfectlyElastic Molecules in a State of Motion," 42 on the other hand, was capable of providing a mechanistic account of virtually all phenomena to which it seemed applicable. In his introduction to this paper, Waterston expressed an attitude toward his creation which was fully consonant with the methodological dicta of the later Common Sense philosophers. Once more he asked his reader to assume a medium composed of perfectly elastic particles subject 41 Ibid.,

p. 542. the Physics of Media that are Composed of Free and Perfectly Elastic Molecules in a State of Motion," in The Collected Scientific Papers of John James Waterston, p. 207-319. 2 "On

COMMON SENSE AND THE EXACT SCIENCES

only to the laws of conservation of vis viva and momen­ tum; but this time, he continued, "whether gases do con­ sist of such particles or not, it seems worthwhile to inquire into the physical attributes of media so constituted, and to see what analogy they bear to the elegant and symmetrical laws of aeriform bodies. 43 Thus Waterston joined with Dugald Stewart and David Brewster in focusing attention on the suggestiveness rather than on the reality of scien­ tific hypotheses. Waterston began his investigation by deriving a series of results about the characteristics of a homogeneous medium composed of "a vast multitude of small particles of matter, perfectly alike in every respect, perfectly elastic as glass or ivory, but of size, form, and texture that requires not to be specified rather than that they are not liable to change by mutual action." 44 These particles were as­ sumed to be moving within a container formed by per­ fectly elastic walls so that the total vis viva of the ensem­ ble would remain constant. Defining the density of this medium as the number of particles per unit volume, he proved (1) that the elastic force (e) of a medium, as rep­ resented by the weight or pressure required to confine it, is directly proportional to the number of molecular im­ pacts that take place against a unit surface in a unit time with a constamy velocity; (2) that the elastic force (e) of a medium with a constant mean molecular velocity (ν) is proportional to its density (Δ3); (3) that the elasticity of a medium having a constant density is proportional to the mean square molecular velocity, or to the vis viva of the medium; and (4) that under a constant pressure, the den­ sity is inversely proportional to the vis viva or mean square molecular velocity. With these results proved, he argued: We cannot fail of being sensible of the analogies that subsist between these synthetical deductions and the chief properties that distinguish aeriform fluids. . . . 43 Ibid.,

p. 214.

44 Ibid.,

p. 215.

JAMES FORBES AND JOHN WATERSTON

Thus, the laws of Mariotte and of Dalton and GayLussac are represented by the formula (448 - t) Δ 3 = e; in which t = temperature, Fahrenheit scale;A 3 = den­ sity, and e = elasticity. The law of elasticity, in the hypothetical medium is represented by the formula υ 2 Δ 3 = e; in which υ 2 is the mean square molecular velocity; Δ 3 = density, and e = elasticity. The first expresses physical laws that have b e e n found to belong to a certain existent form of matter. The second expresses laws that have b e e n proved to belong to a certain possible form of matter. The cause of the effect represented by (448 - t) in the first is unknown, but has, at various times, by eminent authorities, b e e n referred to molecular motion. The corresponding term, υ 2 , of the second represents molecular motion. 4 5 In the second section of his paper, Waterston showed that if two or more of his hypothetical media, each com­ posed of particles with a distinct molecular weight and possessing equal elasticities and mean vis vivas, were brought into contact with one another, then they would diffuse through one another, exchanging velocities by impact in such a way that the mean square velocities of the particles would remain inversely proportional to the specific weights of the molecules. Media in equilibrium of pressure and vis viva would have equal numerical density; so their specific gravities would be proportional to their specific molecular weights; and they would dif­ fuse themselves through their common volume with ve­ locities inversely proportional to the square roots of their specific gravities. 4 6 Again, the analogies with observed gaseous p h e ­ nomena and with certain chemical generalizations were remarkable. The specific gravities of gases at the same pressure and temperature were, according to Daltonian 45

Ibid., pp. 223-228.

46

Ibid., pp. 223-228.

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COMMON SENSE AND THE EXACT SCIENCES

theory, proportional to their atomic weights, and equal volumes did seem to contain equal numbers of molecules. Thus, Waterston's work and Daltonian atomism were mutually supportive. Furthermore, Thomas Graham had shown that the velocity of gaseous diffusion is inversely proportional to the square roots of their specific gravities, confirming yet another of Waterston's predictions. Next, Waterston sought to derive a set of relations for his media which could be compared with the observed relations between the specific heats of gases at constant volume and constant pressure and with the mechanical equivalent of heat recently investigated by Joule. In his derivation of the ratio between the vis viva required to produce increments of molecular vis viva in the medium under constant pressure and constant volume, he made an arithmetical mistake which led to a ratio of 4 to 3. This ratio agreed very closely with that experimentally determined by James Ivory, Gay-Lussac, and Clement and D e s o r m e s . 4 7 Moreover, w h e n he a s s u m e d that t h e specific heat of his medium was similar to that of air, he was able to show that the mechanical effect of 673 pounds falling through one foot would generate an increase of one degree Fahrenheit in a pound of water. 48 This result seemed in relatively close agreement with the 800 footpounds calculated by Joule in his early experiments. Thus once more, Waterston's theory seemed to provide very close analogies with observed effects. On two more important sets of phenomena, Waterston's theory was capable of generating quantitative results in close agreement with accepted observable results. An investigation of the density and temperature distribution in a vertical cross-section of one of Waterston's media which was subject to gravitational forces led him to expect a linear decrease of temperature of one degree for every 310 feet of elevation. Near the earth's surface a variety of complicating factors appeared to mask this effect, but observations of temperatures at high altitudes made by 47

Ibid., pp. 231-242.

48

Ibid., p. 24.

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JAMES FORBES AND JOHN WATERSTON

Gay-Lussac in a balloon flight near Paris showed a de­ crease of one degree for every 316 feet of elevation, dem­ onstrating a remarkable agreement with Waterston's calculations. 49 Similarly, Waterston was able to calculate the velocity with which impulses would be transmitted through his medium; and this calculation provided a ve­ locity of sound within roughly 2% of that observed by Moll and Goldingham. 50 Only on one topic did a clear discrepancy arise between Waterston's calculations and observed phenomena. When he tried to calculate the resistance which should be afforded to a surface moving through his media, Waterston obtained results four times those observed. In retro­ spect it is easy to see that Waterston's calculations should have been applicable only to surfaces of very small extent relative to the mean free paths of the molecules of his media; whereas the observed values of resistance came from experiments which did not come close to meeting this criterion. Waterston did not recog­ nize the problem in this manner. Instead, he developed a plausibility argument dependent on the assumption that the perfect elasticity of his medium was not shared by real solid objects moving through it. This argument led him to expect that the resistance to imperfect sur­ faces should be substantially less than that calculated for ideal elastic surfaces, and it allowed him to retain a belief in the widespread applicability of his hypothesis. 51 THE RESPONSE TO WATERSTON'S KINETIC THEORY

Tο one imbued with the later Common Sense sympathy toward suggestive hypotheses—as long as their highly provisional cognitive status was recognized—Waterston's paper should have had great appeal. But there were few in the British sceintific hierarchy during the first half of the nineteenth century who could accept this approach. Their 51Ibid.,

50Ibid., p. 263. pp. 242-249.

COMMON SENSE AND T H E EXACT SCIENCES

emphasis was on a form of induction much more closely tied to non-speculative reasoning and to observational or experimental procedures. Thus, when Waterston's paper was reviewed, one referee, John William Lubbock, wrote that "the paper is nothing but nonsense, unfit even for reading before the Society." 52 The other referee, Baden Powell, wrote that the paper "exhibits much skill and many remarkable accordances with the general facts, as well as numerical values furnished by observation. . . . The original principle itself involves an assumption which seems to me very difficult to admit, and by no means a satisfactory basis for a mathematical theory." 5 3 Consequently, the paper was rejected. Only after the German theoretician Clausius had published his two impressive papers on kinetic theory in 1857 and 1859—they too appeared in English translation in Philosophical Magazine, perhaps at Brewster's urging 54 — were such speculations given widespread and serious consideration in Britain. 55 Then, as we shall see, the Scottish-trained and Common Sense-oriented James Clerk Maxwell and William J. M. Rankine pursued the subject most actively. A direct connection between conscious methodological considerations and the development of molecular theories will be much clearer in the cases of Maxwell and 52 Ibid., p. 209. The attribution of this statement to Lubbock was made by Sir Harold Hartley and N.H. Robinson. See Stephen Brush, Kinetic Theory, I., (Oxford: Pergamon Press, 1965), p. 17. 53 Ibid., p. 209. Powell also identified as in note 52. 54 See Rudolf Clausius, "The Nature of the Motion Which We Call Heat," Philosophical Magazine, 14 (1857), pp. 108-127, and "On the Mean Length's of the Paths Described by the Separate Molecules of Gaseous Bodies," Philosophical Magazine, 17 (1859), pp. 81-91. 55 See L. Scott Wilson, The Conflict Between Atomism and Conservation Theory 1644-1860. (London and New York, 1970), pp. 273-275. In addition to Waterston, both John Herapath and James P. Joule had, of course, developed aspects of kinetic theory prior to 1850, but Scott cogently argues that their works were largely ignored, though they were not suppressed as were Waterston's, until after the renewed interest stimulated by Clausius.

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JAMES FORBES AND JOHN WATERSTON

Rankine than it is in the case of Waterston. But a look at Waterston's theory and its reception or rejection is worthwhile in two ways. Waterston's emphases on the desire, for unification of natural philosophy, on the inves­ tigation of physical analogies, and on the minimal impor­ tance of assigning a real existence to his hypothetical media demonstrate that at least one early development of kinetic theory was associated with a constellation of methodological beliefs which could have been derived from Common Sense writings. Since there is evidence that Waterston was aware of the Common Sense me­ thodological tradition, it is reasonable to hypothesize that this tradition did play a significant role in forming his beliefs. Perhaps more importantly, the pattern of rejection and publication of Waterston's work supports the contention that the scientific style attributed to British physicists by Pierre Duhem was historically connected with Scottish philosophy. Only Philosophical Magazine, whose policy was set at least in part by the Scot, Brewster, seemed open to the publication of articles based on admittedly hypo­ thetical considerations; it was not until after the works of Rankine and Maxwell had stressed the importance of models and physical analogies that they came to dominate British scientific theorizing.

C H A P T E R 10

Sir John Herschel's

Preliminary

Discourse on the Study of Natural Philosophy

and the

Common Sense Tradition I T IS FAIRLY clear that until the third decade of the nineteenth century, Common Sense considerations had a direct impact upon scientific activity almost exclusively in connection with scientists educated in or working at the University of E d i n b u r g h . 1 But in 1830 John F . W. Herschel, the Cambridge-trained son of Sir William Herschel, published his Preliminary Discourse on the Study of Natural Philosophy; this work made the basic tenets of Common Sense methodology available to a much wider segment of the scientific community. To my knowledge, the Preliminary Discourse, which has been frequently characterized as "the first attempt by an eminent man of science to make the methods of science explicit," 2 has never been interpreted in connection with the writings of the Scottish Common Sense philosophers. But I hope to show that on such topics as the nature of mathematics, the analysis of causation, the interpretation x

There is a possible exception to this statement which I have not yet investigated. Scottish philosophy had a major place in American higher education, and in his book, American Science in the Age of Jackson (New York: Columbia University Press, 1968), George Daniels makes a series of strong arguments for believing that the influence of Reid and Stewart, with the latter's emphasis on analogy, was crucial in the formation of American science. See especially chapters 3-8. 2 See Curt J. Ducasse, "John F. W. Herschel's Methods of Experimental Inquiry," in Ralph M. Blake et al., Theories of Scientific Method: The Renaissance Through the Nineteenth Century (Seattle: University of Washington Press, 1966), p. 153. 252

HERSCHEL AND THE COMMON SENSE TRADITION

of phenomena, and the function of hypotheses in science, Herschel's ideas were so similar to those of the Scottish school that there is little doubt of a direct relation. Furthermore, I hope to show that even his illustrative materials often came directly from Thomas Brown's Lectures on the Philosophy of the Human Mind. Even the context of the publication of Herschel's Preliminary Discourse was closely related to an outgrowth of Common Sense considerations. In 1827, the Society for the Diffusion of Useful Knowledge, a group formed largely at the instigation of Henry Brougham, began to publish a series of semi-popular scientific tracts under the general title of The Library of Useful Knowledge. T h i s s e r i e s was i n t r o d u c e d by B r o u g h a m ' s Discourse on the Objects, Advantages, and Pleasures of Science, which presented an overview of the sciences very much in the Common Sense vein. Shortly thereafter, Dyonisus Lardner, stimulated in part by the same desire to enlighten the British public and in part by the desire to exploit the commercial potential suggested by The Library of Useful Knowledge, projected his own series under the rubric of The Cabinet Cyclopedia and talked Herschel into writing both an introductory volume to parallel Brougham's introductory Discourse—i.e., The Preliminary Discourse on the Study of Natural Philosophy, which appeared in 1830—and a volume on astronomy, A Treatise on Astronomy, which appeared in 1833. Like Brougham's Discourse, Herschel's Preliminary Discourse began with a discussion of the advantages of scientific study, emphasizing the material utility of science, the religious solace to be discovered in natural theology, the potentials for the application of scientific methods to the solution of social problems, and the sheer aesthetic pleasure to be derived from the search for knowledge. Also like Brougham's work, Herschel's concluded with an attempt to provide a rational classification of the natural sciences. But in between his paean to the 253

COMMON SENSE AND THE EXACT SCIENCES

advantages of science and his scheme of classification Herschel included an extensive and influential discussion "of the principles on which physical science relies for its successful prosecution, and the rules by which a systematic examination of nature should be conducted," 3 which had no parallel in Brougham's discussion.

HERSCHEL ON THE NATURE, UTILITY, AND DISTINCTIVENESS OF MATHEMATICS

In chapter two of the first section of his Preliminary Discourse, Herschel undertook an analysis of the relation of the abstract sciences—like logic and the various branches of mathematics—to the natural sciences. Since natural philosophy involves the applications of such terms as "motion," "velocity," "quantity," "number," and "order," Herschel pointed out, it is valuable for the prospective natural philosopher to have some experience with mathematics as a prerequisite to his study of natural phenomena. H e continued: But there is yet another recommendation of such sciences as a preparation for the study of natural philosophy. Their objects are so definite, and our notions of them so distinct, that we can reason about them with an assurance, that the words and signs used in our reasonings are full and true representatives of the things signified; and consequently that when we use language or signs in argument, we neither, by their use, introduce extraneous notions, nor exclude any part of the case before us from consideration. . . . It is widely different with words expressing natural objects and mixed relations . . . some, nay most, have two or three meanings; sufficiently distinct from each other to make a propos3

John Frederick William Herschel, A Preliminary Discourse on the Study of Natural Philosophy, a facsimile of the 1830 edition with a new Introduction by Michael Partridge (New York and London: Johnson Reprint Corporation, 1966), p. vi.

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HERSCHEL AND THE COMMON SENSE TRADITION

tion true in one sense and false in another, or even false altogether; yet not distinct enough to keep us from confounding them in the process by which we arrived at it, or to enable us immediately to recognize the fallacy when led to it by a train of reasoning, each step of which we think we have examined and approved. . . . It is, in fact, in this double or incomplete sense of words that we must look for the origin of a very large portion of the errors into which we fall. Now, the study of the abstract sciences, such as arithmetic, geometry, algebra, etc., while they afford scope for the exercise of reasoning about objects that are, or at least, may be conceived to be, external to us; yet being free from these sources of error and mistake, accustom us to the strict use of language as an instrument of reason, and by familiarizing us in our progress towards truth to walk uprightly and straight forward on firm ground, give us that proper and dignified carriage of mind which could never be acquired by having always to pick our steps among obstructions and loose fragments, or to steady them in the reeling tempest of conflicting meanings. 4 Herschel's concern about the uncertainty and ambiguity of many terms used in natural philosophy might well have had its direct source in Bacon's discussion of the so-called Idols of the Market Place, where he emphasized the fact that many errors in philosophy arise out of the fact that words are ill-defined and ambiguous. 5 But this same c o n c e r n was frequently voiced by C o m m o n Sense philosophers, and it was only in the writings of Campbell, Reid, Stewart, and Brown that the concepts of mathematics were cited as ideal models for guiding us in the strict use of language. Brown, for example, had provided a very clear precedent for Herschel's emphasis in his Lectures on the Philosophy of the Human Mind: 4

IHd., pp. 19-22. See Francis Bacon, The New Organon and Related Writings, ed. Fulton H. Anderson (Indianapolis: Bobbs-Merrill, 1960), Aphorisms LIX and LX, pp. 56-58. 5

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It is by the diffusive tendency of its spirit, almost as much as by its own sublime truths and the important applications of these to physics, that the study of geometry has been of such inestimable advantage to science. Those precise definitions which insure to every word the same exact signification, in the mind of every one who hears it pronounced, and that lucid progress in the development of truth after truth. . . are unquestionably of the utmost benefit to the mathematical student, while he is prosecuting his particular study, without any contemplation of other advantages to b e reaped from them. But there can be no doubt that they are, at the same time, preparing his mind for excellence in other enquiries of which he has no conception; that he will ever after be less ready to employ, and be more quick-sighted than he would otherwise have been in detecting vague and indefinite phraseology, and loose and incoherent reasoning. 6 Herschel had not thought so extensively about the origins of mathematical concepts as had his Common Sense predecessors, and he showed no awareness of the subtleties which led Stewart, for instance, to distinguish b e t w e e n the certainties of geometry and of algebra. Nonetheless, his attitude toward the origin of mathematical knowledge was identical with the abstractionist doctrine of Reid and Stewart that made mathematical knowle d g e somehow d e p e n d e n t upon b u t not tainted by experience. Herschel wrote: Indeed, the axioms of geometry themselves may be regarded as in some sort an appeal to experience, not corporeal, but mental. When we say, the whole is greater than its part, we announce a general fact, which rests, it is true, on our ideas of whole and part; but, in abstracting these notions, we begin by considering them as 6

Thomas Brown, Lectures on the Philosophy of the Human Mind, first American edition (Andover: Mark Newman, 1822), I, pp. 70-71.

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subsisting in space, and time, and body, and again, in linear, and superficial and solid space. Again, when we say, that equals are equal, we mentally make compari­ sons, in equal spaces, equal times, etc.; so that these axioms, however self-evident, are still general proposi­ tions so far of the inductive kind, that, independently of experience, they would not present themselves to the mind. 7 On one further point relating to the distinction between the abstract mathematical sciences and the natural sci­ ences, which depend upon a more direct and extended appeal to experience, Herschel showed a remarkable agreement with Common Sense sources. Like all the Common Sense philosophers, he made the point that mathematical truths seem to be necessary rather than con­ tingent; once mathematical terms are defined, their rela­ tions can be discovered without further appeal to experi­ ence. Knowledge of natural phenomena, on the other hand, is always contingent—that is, dependent upon im­ mediate experience. "A clever man, shut up alone and allowed unlimited time, might reason out all the truths of mathematics, by proceeding from those simple notions of space and number of which he cannot divest himself without ceasing to think. But he could never tell, by any effort of reasoning, what would become a lump of sugar immersed in water." 8 This choice of illustrative example is particularly il­ luminating since Thomas Brown, writing of the same dis­ tinction between the contingency of our knowledge of nature and the necessity attained in the abstract sciences, had used the solubility of sugar in water as a prime exam­ ple of a fact which no amount of a priori speculation could have predicted. 9 Even the technique of postulating a man locked up in a room, capable of developing mathematical 7 John 9 See

84-85.

8 Ibid., p. 76. Herschel, Preliminary Discourse, p. 95. Brown, Lectures on the Philosophy of the Human Mind, I, pp.

COMMON SENSE AND T H E EXACT SCIENCES

knowledge but not a knowledge of natural events, was almost certainly borrowed from the Scottish tradition. Henry Brougham had used it in his Discourse, with which H e r s c h e l ' s Preliminary Discourse was d e s i g n e d to compete. 1 0

H E R S C H E L O N CAUSATION AND T H E ANALYSIS O F P H E N O M E N A

Herschel discussed and used the word "cause" in several different ways in the Preliminary Discourse,11 and each of these usages, as well as Herschel's analysis of the relations which subsist among them, closely parallels Common Sense discussions of causation. According to Herschel, the first and most fundamental meaning of cause comes from our own awareness of the act of will or effort w h e n we seek to p r o d u c e an effect: We are conscious of a power to move our limbs, and by their intervention other b o d i e s ; . . . And even when such exertion produces no visible effect (as when we press our two hands together, so as just to oppose each others efforts), we still perceive, by the fatigue and exhaustion, and by the impossibility of maintaining the effect long, that something is going on within us of which the mind is the agent, and the will the determining cause.12 10 Brougham wrote: " l f a man were shut up in aroom with pen, ink, and paper, he might be thinking, discover any of the truths of arithmetic, algebra, or geometry; it is possible in his discovering all that is now known of these sciences; and if his memory were as good as we are supposing his judgment and conception to be, he might discover it all without pen, ink, and paper, and in a dark room. But we cannot discover a single one of the fundamental properties of matter without knowing what goes on around us, and trying experiments upon the nature and motion of bodies." See his Discourse on the Objects, Advantages, and Pleasures of Science in The Critical and Miscellaneous Writings of Henry Lord Brougham, (Philadelphia; Lea and Blanchard, 1841), Vol. 2, pp. 101-102. n C u r t Ducasse, et al., Theories of Scientific Method, pp. 164-173. 12 JoIm Herschel, Preliminary Discourse, Section 77, p. 86.

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The notion that in its ultimate and most proper sense causation belongs only to intelligent and willing agents is identical with Reid's contention, and it plays a fundamental role in the metaphysical thought of Herschel as well as Reid. It allows both to infer the existence of a Divine Will as the underlying first cause of all phenomena. There is nothing about Herschel's early statements on causation as an act of will that would link him with Reid rather than Berkeley, who also argued that the source of our notion of causality lies in man's consciousness of his own purposive action. But a reference to causation in his later Treatise on Astronomy clearly connects Herschel's belief with the realism of the Scottish school rather than with the idealism of Berkeley. Whatever attempts may have been made by metaphysical writers to reason away the connexion of cause and effect, and fritter it down into the unsatisfactory relation of habitual sequence, it is certain that the conception of some more real and intimate connexion is quite as strongly impressed upon the human mind as that of the existence of an external world. . . . It is our own immediate consciousness oieffort, when we exert force to put matter in motion, or to oppose and neutralize force, which gives us this internal conviction of power and causation so far as it refers to the material world, and compels us to believe that whenever we see material objects put into motion from a state of rest, or deflected from their linear paths, and changed in their velocities if already in motion, it is in consequence of such an EFFORT, somehow exerted, though not accompanied with our consciousness. . . [falling bodies] are therefore urged [to the earth's surface] by a force or effort, the direct or indirect result of a consciousness and a will existing somewhere, though beyond our power to trace. . . . 13 13

Quotedby Walter Cannon, "John Herschel and the Idea of Science," Journal of the History of Ideas, 22 (1961), p. 227 from Herschel's Treatise on Astronomy (Philadelphia, 1834), pp. 221-222.

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The important thing to note is the identical cognitive status Herschel gives here to our belief in causation and to our belief in the existence of an external world. These beliefs are not merely habitual, as they were for Hume, nor are they really separable, as they were for Berkeley (who accepted the first while denying the second). For Herschel as for the Scottish Common Sense School, they are both inescapable beliefs "impressed upon the mind" by an "internal conviction" which, though it may be given plausibility by being referred to our immediate consciousness, is susceptible of no more fundamental justification. Just as Herschel expressed the opinion that causation in its most proper sense was connected with intention, he also followed Reid in denying this notion of causality an important role in natural philosophy. For Reid the denial was necessary because the material entities studied by the natural philosopher were assumed to be passive rather than active agents, and the mechanisms by which the wills of active agents were transmitted into physical phenomena were completely undiscoverable. All a natural philosopher could do then was to "acquiesce in a law of nature according to which the effect is produced, as the utmost that natural philosophy can reach, leaving what can be known of the agent, or efficient cause, to metaphysics or natural theology." 1 4 Similarly Herschel wrote of our own consciousness as an active causal agent: But how obscure is our knowledge of the process going on within us in the exercise of this important privilege in virtue of which alone we act as direct causes, we may judge from this, that when we put any limb in motion, the seat of the exertion seems to be in the limb, whereas it is demonstrably no such thing, but either in the brain or in the spinal marrow; the proof of which is that if a little fibre called a nerve, which forms a 14

ReJd, Works, p. 76. Emphasis mine.

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communication between the limb and the brain, or spine, be divided in any part of its course, however we may make the effort, the limb will not move. (78) This one instance of the obscurity which hangs about the only act of direct causation of which we have an immediate consciousness, will suffice to show how little prospect there is that, in our investigation of nature, we shall ever be able to arrive at a knowledge of ultimate causes, and will teach us to limit our views to that of laws, and to the analysis of complex phenomena by which they are resolved into simpler ones, which, appearing to us incapable of further analysis, we must consent to regard as causes. 1 5 Although Herschel apparently went beyond Reid in offering two different aims for a science which has abdicated the search for "ultimate" or Reid's "efficient" causes, his reference to laws as a primary goal of scientific investigation shows his basic agreement with Reid. His additional emphasis on the analysis of complex phenomena, he said, was really only the suggestion of a technique for enabling us to recognize phenomena whose laws might be most easily discovered; 1 6 even that technique seems to have been suggested by Thomas Brown's Lectures on the Philosophy of the Human Mind. In connection with his discussion of causation, Brown had adduced the extended example of a man listening to the sounds of a violin, breaking this phenomenon into a series of steps. The complex physical phenomenon fairly clearly begins with the bow touching the strings of the violin and concludes with the "hearing" of a melody. But Brown said that men soon learn that there are a series of intermediate phenomena making u p the whole. First, the bow excites vibrations within the violin. Second, the violin transmits its vibrations to the air. Third, the vibrations are propagated through the air to the ear. Fourth, the 15 16

John Herschel, Preliminary Discourse, pp. 87-88. Emphasis mine. Ibid., p. 97.

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vibrations are somehow transmitted to the organ of hearing. Fifth, there is some mechanism of communication to the auditory nerve and brain, and, finally, there is an "affection of the mind which constitutes the particular sensation." 1 7 Each time we state an intermediate phenomenon, we are said to state a cause of the overall complex phenomenon. We say "that these vibrations of air are the cause of the sound, by communicating vibration to parts of the ear, and that the vibrations of the ear are the cause of the sound, by affecting, in a particular manner the nerve of hearing, and the brain in general. . . ." 18 In most of these cases, if we wished we could further analyze each intervening phenomenon, referring the vibration of the air, for example, to the impacts of the individual particles constituting it. But we must eventually reach some irreducible phenomenon. Thus, Brown said: "When we come to the ultimate affection of the sensorial organ, which immediately precedes the sensation of the mind, it is evident that we cannot say of it, that it is the cause of sound, by exciting anything intermediate, since it then could not itself be that by which the sound was immediately preceded. It is the cause, however, exactly in the same manner as all the other parts of the sequence were causes merely by being the immediate and invariable antecedent of the particular effect." 19 For Brown, then, all causes Were merely invariable antecedents of particular effects. Herschel's discussion of the analysis of phenomena and the notion of causation followed Brown's example almost step by step, although he placed a somewhat greater emphasis on the distinction between ultimate and proximate causes. In section (79) of the Preliminary Discourse he wrote: What we mean by the analysis of complex phenomena into simpler ones, will best be understood by 17 Brown, Lectures on the Philosophy of the Human Mind Vol. 1, p. 107. 18 19 Ibid., p. 109. Ibid., p. 110.

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an instance. Let us, therefore, take the phenomenon of sound, and, by considering the various cases in which sounds are produced, we shall find that they all agree in these points: First, the excitement of a motion in the sounding body. Secondly, the communication of this motion to the air or other intermedium which is interposed between the sounding body and our ears. Thirdly, the propagation of such motion from particle to particle to particle in such intermedium in due succession. Fourthly, its communication, from the particles of the intermedium adjacent to the ear, to the ear itself. Fifthly, its conveyance in the ear, by a certain mechanism, to the auditory nerves. Sixthly, the excitement of sensation. 20 In sections (80) and (81), he argued that the phenomena of steps one through five are all capable of further analysis leading to the ultimate phenomenon of matter in motion. Such phenomena cannot be further analyzed; their behavior can only be described by the laws of motion and law of equilibrium.21 In section (82), he pointed out, as Brown had, the irreducibility of the casual relation between the physiological state of the nerves and brain and our sensation of sound, 2 2 and in section (83), he acknowledged, as Brown had, that we can never be certain when we have reached a truly "ultimate" phenomena or cause. But this makes little or no practical difference; for, "in a modified and relative sense, we may still continue to speak of causes, not intending thereby those ultimate principles of action on whose exertion the whole frame of nature depends, but of those proximate links which connect phenomena with others of a simpler, higher, and more general or elementary kind." 2 3 Up to this point, Herschel had said nothing about the circumstances which allow us to decide how to determine when something can legitimately be considered a proxi20 21

Herschel, Preliminary Discourse, p. 88. 22 23 Ibid., p. 89-91. Ibid., p. 91. Ibid., p. 92.

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mate cause; but in two later sections, (138) and (145), he made it clear that his proximate cause was nothing other than Brown's invariable antecedent phenomenon: "Ex­ perience having shown us the manner in which one phenomenon depends on another in a great variety of cases, we find ourselves provided, as science extends, with a continually increasing stock of such antecedent phenomenon, or causes." 24 Furthermore, in order to de­ termine what antecedent phenomena may be causes, he says that "we must have regard to the characters of that relation which we intend by cause and effect [which are] .. . invariable connection, and, in particular, antecedence of the cause and consequence of the effect unless pre­ vented by some counteracting cause. . . . " 25 Though Herschel provided some refinements to this definition, his was essentially the same as that used by all Common Sense philosophers in considering the physical meaning of causation. EXPLANATORY VERSUS GENERALIZING FUNCTIONS OF SCIENCE, AND THE ROLE OF HYPOTHESES

So far, we have seen that according to Herschel the major aim of scientific inquiry is to analyze complex phenomena into simpler ones for which proximate causes may be discovered. The scientist may assume these prox­ imate causes to be incapable of further analysis, in which case he immediately attempts to provide a complete gen­ eral description (a lawful account) of the phenomena at­ tributable to the cause in question. Or he may seek to analyze the phenomena by which the proximate cause produces its effect into more fundamental causes until he comes to some ultimate cause of which he can give only a lawful account. In this formulation, while the analysis of phenomena precedes the formulation of laws, it is the 24 Ibid., 25 Ibid.,

Section (138), p. 144. Emphasis mine. Section (145), p. 151.

HERSCHEL AND THE COMMON SENSE TRADITION

latter process which is fundamental, since it provides the ne plus ultra of scientific inquiry. The first chapter of the second part of Herschel's Preliminary Discourse reflects this ultimate emphasis on the scientist's search for laws of phenomena. We are told (88) that there is a general method for discovering general laws or "axioms of nature." 26 Most of the second through sixth chapters of Part II are then concerned with defining the character of a law of nature and examining the induc­ tive process by which such laws or "general facts" are generated out of particular facts and successively or­ ganized into groups of superior generality "till at length by continuing the process, we arrive at axioms of the highest degree of generality of which science is capable." 27 The ultimate aim of science is to form lawful generalizations which function both "as a kind of artifical memory" 28 and as a guide to the interconnectedness of all phenomena. 29 In his emphasis on generalizations and their induction from particular phenomena, Herschel continued in the tradition started by Bacon and given almost exclusive emphasis by the Common Sense philosophers Reid and Gregory. But there is a second point of view expressed in the methodological portion of Herschel's Preliminary Discourse which emphasizes an explanatory aspect of scientific knowledge. According to this view, which had many parallels in Stewart's and Brown's discussions of the function of hypotheses and theories, men often seek an understanding of phenomena which goes beyond mere generalization to the discovery of immediate causes. "The first thing that a philosophic mind considers, when any new phenomenon presents itself, is its explanation, or reference to an immediate producing cause. If that cannot be ascertained, the next is to generalize the phenomenon, and include it, with others analogous to it, in the expres26Ibid., 28Ibid.,

27Ibid., p. 102. pp. 96-99. 28Ibid., Section (93), p. 101-102. Section (92), p. 101.

COMMON SENSE AND T H E EXACT SCIENCES

sion of some law, in the hope that its consideration, in a more advanced state, may lead to the discovery of an adequate proximate cause." 3 0 For Herschel, as for Stewart and Brown, the explanatory function of science is particularly important in motivating theories which connect large numbers of lower-order "general facts," and it is the search for explanations which leads to hypotheses. "The immediate object we propose to ourselves in physical theories is the analysis of phenomena, and the knowledge of the hidden processes of nature in their production." 3 1 This object naturally involves the discovery of the structure and mechanisms of nature through which the hidden processes are carried out. As did Brown, Herschel pointed out that we may be frustrated in the attempt to obtain such knowledge by direct induction from phenomena because our senses may not be capable of detecting the elements involved in the structure of nature, due to their extremes in size. 32 We might, of course, simply stop seeking to understand the underlying causes of phenomena for this reason; if we did, we would still have a "perfect comprehension of the whole subsequent process." 3 3 We might, on the other hand, choose to theorize further by forming a hypothesis about events for which we have no direct evidence. The procedures for seeking scientific knowledge by projecting and testing hypotheses are more dangerous and potentially misleading than is the straightforward process of induction carried on first among facts to establish laws and then among laws to form more general laws. 34 But so long as hypotheses are subjected to certain restrictions and are never mistaken for more than provisional suggestions, they "often have an eminent use: and a facility in framing them, if attended with an equal facility 30

Ibid., Section (137), p. 144. Emphasis mine. Ibid., Section (202), p. 191. 32 Herschel, Preliminary Discourse, Section (202), p. 191. 33 Ibid., Section (206), p. 194. 34 IWd., Section (217), pp. 204-205. 31

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in laying them aside when they have served their turn, is one of the most valuable qualities a philosopher can possess." 35 At the very least, hypotheses "afford us motives for searching into analogies" and enable us "to generalize a step farther and group together several [general] laws under a more universal expression." 36 But they may be much more important: It may happen (and it has happened in the case of the undulatory doctrine of light) that such a weight of anal­ ogy and probability may be accumulated on the side of an hypothesis, that we are compelled to admit one of two things; either that it is an actual statement of what really passes in nature, or that the reality, whatever it might be, must run so close a parallel with it, as to admit of some mode of expression common to both, at least insofar as the phenomena actually known are con­ cerned. Now this is a very great step, not only for its own sake, as leading us to a high point, in philosophical speculation, but for its applications; because whatever conclusions we deduce from any hypotheses so sup­ ported must have at least a strong presumption in their favour: and we may be thus led to the imagining of many useful and important contrivances, which we should never otherwise have thought of, and which, at all events, if verified in practice are real additions to our stock of knowledge and to the arts of life. 37 Herschel thus joined Stewart and Brown in emphasiz­ ing the fruitfulness and suggestiveness of hypotheses rather than their certainty or truth. He likened a hypo­ thetical structure to a scaffolding 38 and emphasized the fact that knowledge obtained through its use is not de­ pendent on the lasting capabilities of its provisional structure. 35Ibid.,

36Ibid., p. 196. Section (216), p. 204. Section (208), pp. 196-197. 38Ibid., Section (216), p. 204. 37Ibid.,

COMMON SENSE AND THE EXACT SCIENCES

Nonetheless, also like Stewartand Brown, Herschel did not believe that hypotheses regarding hidden causal agents and mechanisms underlying phenomenon may be arbitrarily selected. He emphasized precisely those re­ quirements imposed upon hypotheses by the Common Sense tradition. Any supposed cause must have an inde­ pendently verifiable existence and must be shown to be operative in phenomena analogous to those under inves­ tigation. He said that the agents which play a role in a hypothetical theory "are not to be arbitrarily assumed; they must be such as we have good inductive grounds to believe do exist in nature, and do perform a part in phenomena analogous to those we would render account of; or such, whose presence in the actual case can be demonstrated by unequivocal signs." 39 Furthermore the laws which regulate the action of the supposed causes may not be merely conjectural; they must themselves be established either through prior induction or by a process which involves the empirical verification of modes of action assumed to exist. 40 On only one relatively minor point regarding the use of hypotheses in science did HerscheI disagree with his Common Sense predecessors. He was more willing to develop relatively complicated hypotheses. Thomas Brown, in particular, was adamantly opposed to the intro­ duction of hypotheses which were less simple than the phenomena to be explained. According to Brown, the imperfections of our sense which sometimes warrant our presumption of intermediate phenomena underlying those which we can directly observe also generates an illusion that for every chain of events we have discovered, there must be some intervening mechanism. Thus we often complicate simple phenomena by positing mechanisms which do nothing to make them more intel­ ligible, and we must always be on guard against our desire 39Ibid., 40Ibid.,

Section (209), p. 197. Sections (209) and (210), pp. 197-199.

HERSCHEL AND THE COMMON SENSE TRADITION

to gratify our "passion for the complicated"41 and reject any hypotheses which do not truly simplify our knowledge. Brown applied this warning especially to the phenomena of gravitation, rejecting etherial speculations, and Herschel followed him with regard to this one set of phenomena. 4 2 But Herschel did not accept the general principle. He defended Ampere's molecular-current theory of magnetism, writing: This, we might say, is too complex, it is artificial, and cannot be granted: yet if the admission of this or any other structure tenfold more artificial and complicated will enable any one to present in a general point of view a great number of particular facts—to make them a part of one system, and enable us to reason from the known to the unknown, and actually to predict facts before trial—we would ask, why should it not be granted? 4 3 Herschel's argument is particularly interesting for two reasons. First, it is such a direct answer to the argument raised by Brown that, given all their similarities of view, there can be little doubt that it was stimulated by Brown's commentary. Secondly, this particular argument provides a way of judging the direct influence of the Scottish methodological discussions upon such men as Rankine, who read and followed Herschel on many points but who explicitly adopted Brown's counter-argument with regard to the simplicity appropriate to hypotheses. In spite of this one area of disagreement regarding the characteristics of acceptable hypotheses, and in spite of Herschel's unique discussions of the nature of induction (which I have suppressed in my arguments), the range of agreement between Herschel and the Common Sense school on both epistemological issues and methodologi41

Brown, Lectures on the Philosophy of the Mind, p. 118 ^Herschel, Preliminary Discourse, Section (214), p. 202. 43 Ibid., Section (215), p. 203.

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cal questions warrants placing Herschel squarely within the Common Sense tradition. After the publication and widespread dissemination of Herschel's work, it is next to impossible to judge from most scientific works whether methodological ideas were directly adopted from the Scottish tradition or whether they were more closely connected with Herschel's Discourse. Only the extensive methodological discussions of Rankine and the writings of Maxwell, which display some of the idiosyncratic terminology of Hamilton's formulation of scientific method, provide significant, direct evidence of Scottish sources after the third decade of the nineteenth century.

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CHAPTER 11

The Methodological Writings of William John Macquorn Rankine I T IS NOT surprising that the greatest of Scottish physicists—in terms of lasting international reputation —were trained under James D. Forbes, the man who began to professionalize scientific training at Edinburgh. But it is somewhat ironic to find that two of these men, William John Macquorn Rankine (1820-1872) and James Clerk Maxwell (1831-1879), were among the most consciously philosophical or "metaphysical" products of the long Edinburgh tradition. The strong interaction between the methodological concerns of Scottish moral philosophy and the scientific work done by natural philosophers thus had its most outstanding flowering precisely at the time when the institutional basis for the tradition of interconnections was coming to an end. It is tempting to suggest that this impressive manifestation of the Scottish philosophical tradition in science was due to the personal influence of William Hamilton, because it is clear that Maxwell was immensely impressed by his teacher of logic and metaphysics. But there is no evidence that Rankine came into contact with him, and Rankine's clear and incisive synthesis of elements from the Common Sense tradition was in many ways just as impressive as Maxwell's more subtle but diffuse set of methodological considerations. During the sessions of 1836-1837 and 1837-1838, Rankine attended classes in natural philosophy, chemistry, natural history, and botany at the University of Edinburgh. 1 Although there is no record of his attendance 1 AImOSt all biographical information about Rankine comes from P. G. Tait's Memoir in The Miscellaneous Scientific Papers of William John

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in Hamilton's logic or metaphysics classes, he did record in his personal journal that he was reading much metaphysics, including such authors as Aristotle, Hume, Locke, and Dugald Stewart. 2 At the same time, he indicated a special interest in questions of scientific method by writing a prize-winning essay on "Methods of Physical Investigation" for Forbes' advanced natural philosophy class in 1837-1838. 3 Between 1838 and 1848, Rankine turned most of his attention to his work as a civil engineer on a series of railway and waterworks projects, but as early as 1842 he began to develop a new hypothesis about the molecular basis of elasticity in gases and vapors. 4 By late 1849, the experimental work of Regnault seemed to verify his earlier speculations; in December of that year Rankine submitted two remarkable papers ("On the Centrifugal Theory of Elasticity as Applied to Gases and Vapours," and "On the Mechanical Action of Heat Especially in Gases and Vapours") to the Royal Society of Edinburgh. 5 These papers introduced the careful mathematical development of the hypothesis of molecular vortices into British physics. Not only did this hypothesis allow Rankine to derive a version of the second law of thermodynamics from a mechanical model but it also provided Rudolf Clausius, and through him Ludwig Boltzman, with a crucial clue to the interpretation of the second law in Macquorn Rankine (London: Charles Griffin, 1881), pp. ixxx-xxxvi, and from Sir James B. Henderson, Macquorn Rankine: An Oration (Glasgow: Jackson, Wylie and Co., 1932). 2 See Tait's Memoir, p. xxi. 3 Ibid., p. xxi. 4 See "On the Centrifugal Theory of Elasticity as Applied to Gases and Vapours," Phil. Mag., 2 (1851), pp. 509-542. Reprinted in Miscellaneous Scientific Papers, pp. 16-48. Rankine mentions his 1842 start on the developments presented in this paper on p. 16 of the reprint. 5 Both papers were read to the Society on 4 February 1850, but the first was published in Phil. Mag. (see note 4), and the second appeared in the Transactions of the Royal Society of Edinburgh, 20 (1853), pp. 147-180. See also Miscellaneous Scientific Papers, pp. 234-278.

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terms of kinetic theory. 6 Perhaps most importantly, Rankine's hypothesis of molecular vortices provided the direct stimulus for William Thomson's (Lord Kelvin) vor­ tical interpretation of magnetism in 1856. 7 Thus it heads the immensely important tradition of molecular models which characterized much of late Victorian physics. After developing the implications of his hypothesis in a series of papers published in the early 1850s, however, Rankine made an interesting change of direction in 1853. In a paper, "On the General Law of the Transformation of Energy," presented to the Philosophical Society of Glasgow, 8 he reformulated his thermodynamic considera­ tions in terms of much more general and abstract ideas and brought them into an hypothesis-independent form which fit more neatly into the positivistically oriented tradition of classical thermodynamics. His reasons for making this change were clearly discussed in "Outlines of the Science of Energetics," presented to the Philosophi­ cal Society of Glasgow in 1855. 9 This paper, together with his retrospective paper, "On the Use of Mechanical Hypotheses in Science and Especially in the Theory of Heat" published in 1864, contains a fascinating justifica­ tion of his methodology and an eloquent summary of Common Sense and HerscheIian attitudes.

RANKINE'S HYPOTHESIS OF MOLECULAR VORTICES

For our purposes, the disappearance of Rankine's stu­ dent essay on "Methods in Physical Investigation" is a tragedy. All his extant methodological discussions post­ date the development of the scientific theories to which 6See Edward Daub, "Atomism and Thermodynamics," Isis, 58 (1967), pp. 293-303. 1See Robert H. Silliman, "William Thomson: Smoke Rings and Nineteenth Century Atomism," Isis, 54 (1963), pp. 461-474, especially p. 468. 8 Miscellaneous Scientific Papers, pp. 203-208. 9Ibid., pp. 209-229.

COMMON SENSE AND THE EXACT SCIENCES

they explicitly refer, so there is no certain way of knowing that his methodological beliefs preceded, much less directed, his scientific work. Furthermore, in these writings, Rankine never mentioned the sources of his methodological beliefs. In his most important discussion of method in "The Outlines of Energetics," he coined a new terminology, so his formulation of methodological statements shows few verbal similarities with traditional Common Sense discussions. Nonetheless, there is sufficient internal evidence to support a belief that his ideas on method were largely derived from those of Stewart, Brown, and Herschel. And the subjects of his methodological statements were so closely related to his own scientific work that it is hard to imagine that these ideas did not provide guidance to his work. Rankines essay "On the Use of Mechanical Hypotheses in Science" deals centrally with the assumptions of his early work and will, therefore, be discussed first. Since this paper is a conscious justification of Rankine's hypothesis of molecular vortices, moreover, we shall look initially at the hypothesis and the implications drawn from it in the two papers Rankine presented to the Royal Society of Edinburgh in 1849. As presented in his early papers, Rankine's hypothesis of molecular vortices involved four fundamental assumptions: (1) Each atom of matter consists of a nucleus or central point enveloped by an elastic atmosphere which is retained in its position by attractive forces. The elasticity due to heat, then, arises from the centrifugal force of the atmospheres revolving or oscillating about their nuclei or central points. 1 0 (2) The quantity of heat is thevisviva of the molecular revolutions or oscillations. 11 (3) The vibration which, according to the undulatory hypothesis, constitutes radiant light and heat is a motion 10

"On the Centrifugal Theory of Elasticity as Applied to Gases and 11 Vapours," Miscellaneous Scientific Papers, p. 17. IbId., p. 17.

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of the atomic nuclei or centers and is propagated by means of their mutual attractions or repulsions. 1 2 (4) The absorption of light and of radiant heat consists in the transference of motion from the nuclei to their atmospheres, and, conversely, the emission of light and of radiant heat is the transference of motion from the atmospheres to the nuclei. 1 3 Such a set of assumptions seemed to Rankine to offer great advantages over the hypothesis of a luminous ether as a basis for an undulatory theory of light and radiant heat. Unlike a fluid ether, a lattice formed by the small, massy, and mutually attractive nuclei could easily be given elastic properties to sustain transverse vibrations. 14 Similarly, the great velocities of light and radiant heat were a natural consequence of assuming the vibrating masses to be very small compared with the forces which acted upon them, and the influence which crystalline bodies exerted on light and heat seemed more intelligible if the vibrations constituting them were supposed to be those of atomic nuclei whose positions d e p e n d e d on the form of crystallization. 18 But totally aside from these supposed advantages, the theory was capable of generating a very detailed set of testable consequences with regard to thermal phenomena. By considering the static interactions between the atmospheres of atoms, for example, Rankine was able to devise a theory which predicted the deviation of the elasticity of real gases from the predictions of ideal gas laws. 16 Similarly, he was able to calculate the maximum pressure of a vapor in contact with its liquid and to show that his 12

13 14 Ibid., p. 18. Ibid., p. 18. IbId., p. 18. Ibid., p. 18. Though the optical implications of Rankine's theory were of less lasting interest than the thermodynamic implications, Rankine did follow up these suggestions in two subsequent papers: "On the Vibrations of Plane-Polarized Light," read before the Royal Society of Edinburgh, Dec. 2,1850 and published in Phil. Mag. for June (1851), and "A General View of an Oscillatory Theory of Light," read to the British Association for the Advancement of Science at Hull, Sept. 10, 1853 and 16 published in Phil. Mag. for December, 1853. Ibid., pp. 27-39. 15

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theory accounted almost perfectly for the results determined for water vapor and mercury by Regnault and for alcohol, ether, turpentine, and petroleum by Andrew Ure. 1 7 Turning to the dynamic relations obtaining within molecular vortices, Rankine dealt with the mutual conversion of heat (in the form of molecular rotational vis viva) and the mechanical work expended in producing macroscopic changes of state in gases. H e developed a theoretical expression for the specific heats of different gases at constant volume and constant pressure, and showed that if certain constants in his equations were evaluated by using results on the ratio of Cp to Cv for atmospheric air, the specific heats for oxygen and hydrogen were accurately predicted by his theory. 1 8 Then he showed that Dulong's discovery "that equal volumes of all substances in the state of perfect gas, at the same pressure and at equal and constant temperatures, being compressed by the same amount, disengage equal quantities of heat," followed from his theory; 19 he made a calculation of the mechanical equivalent of heat which seemed to agree with Joule's experimental value w h e n the problems of the experiment were accounted for.20 Next, Rankine derived an expression for the temperature dependence of the total and latent heats of evaporation of vapors which approach the conditions of an ideal gas. Then he used the theory to calculate the limit of efficiency of a steam engine, assuming steam to be a perfect gas. 21 Finally, in a supplementary paper presented to the Royal Society of Edinburgh in December of 1851, he generalized his discussion of energy conversion and effi17

Ibid., pp. 40-47. T h e comparison of the theory derived from the hypotheses of molecular vortices with experimental results on vapor pressures appeared in a separate paper published earlier. See "On an Equation Between the Temperature and the Maximum Elasticity of Steam and other Vapours," Miscellaneous Scientific Papers, pp. 1-12. 18 "On the Mechanical Action of Heat, Especially in Gases and Vapours," Miscellaneous Scientific Papers, pp. 253-258. 19 20 21 Ibid., p. 258. Ibid., p. 259. IMd., pp. 265-278.

276

MACQUORN RANKINE ciency and showed that both Joule's principle (a variant of the law of conservation of energy) and Carnot's principle (the second law of thermodynamics) followed from the dynamical relations of his molecular vortex theory. 22 The most remarkable aspect of this final result is that the equation representing the expansive work done in a closed cycle (a cycle in which the working substance, whatever it may be, is returned to its initial state at the end) shows that "the proportion of the original latent heat of expansion finally transformed into expansive power, is a function of the temperatures alone [i.e., the initial tem­ perature and the final temperature attained at the end of the expansive phase of the cycle], and is therefore inde­ pendent of the nature of the body employed." 23 Thus it seemed possible that the results derived from Rankine's molecular vortex theory might have a validity which transcended that of the model from which they arose. METHODOLIGICAL JUSTIFICATION FOR THE MOLECULAR VORTEX THEORY In his long discussion of the use of hypotheses in sci­ ence, Rankine used his own hypothesis of molecular vor­ tices to illustrate the necessary properties of acceptable hypotheses. He began by discussing the characteristics which enable an hypothesis to "simplify" science in the sense understood by Brown and Stewart. Speaking of the hypothesis of molecular vortices, he wrote: That hypothesis, like the wave theory of light, the hypothesis of atoms in chemistry, and all other physical hypotheses whatsoever, substitutes a supposed for a real phenomenon, viz., invisible motion for tangible heat; the object being to deduce the laws of the real phenomenon from those of the supposed one. If the 22 "On the Centrifogal Theory of Elasticityand Its Connection with the Theory of Heat," Miscellaneous Scientific Papers, pp. 62-64. 23 Ibid., pp. 63-64.

COMMON SENSE AND THE EXACT SCIENCES

supposed phenomenon were more complex, or less completely known in its laws than the real one, the hypothesis would be an encumbrance, and worse than useless. But such is not the case with the hypothesis of molecular motions as applied to heat. The laws of motion are at once simpler and more thoroughly known than those of any other phenomenon; and as the hypothesis in question enables the known laws of the mechanical action of heat to be deduced from the laws of motion, it tends towards the simplification of science. 2 4 This demand that any supposed explanatory phenomenon should be simpler than the phenomenon which it explains, provides one of Rankine's few divergences from Herschel's methodological dicta. The requirement that it be more thoroughly known than the phenomenon it is intended to account for is, of course, one of the central demands that had led earlier Common Sense philosophers as well as their scientific counterparts to reject etherial explanations of such phenomena as gravitation. Brown, for instance, had complained of the introduction of unknown substances (not only substances which were invisible, like those atoms which he did suppose to exist, but substances whose properties were also not clearly and independently understood) because "though they correspond exactly with the preceding and succeeding phenomena, no advantage will result, as these are not rendered more explicable." 2 5 Similarly, Playfair had rejected an etherial theory of gravitation because the actions at a distance implied by the phenomena of gravitating bodies was no more inexplicable than the contact action of bodies assumed in most etherial explanations; and Leslie had criticized fluid theories of electricity because they all 24 "On the Use of Mechanical Hypotheses in Science, and Especially in the Theory of Heat," Proceedings of the Philosophical Society of Glasgow, 5 (1864), pp. 126-127. 25 Brown, Observations on Dr. Darwin's Zoonomia, pp. xiv-xv.

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seemed as complex and questionable as the phenomena they were intended to account for. Rankine rejected the luminiferous-ether theories of his contemporaries for much the same reason. No familiar mechanisms were capable of providing the combination of elasticity and tenuousness supposed to belong to the etherial medium, so the positing of an ether provided no real advantage in explaining the phenomena of light and radiant heat. His own hypothesis of molecular vortices, on the other hand, was a simple model whose properties were all derived from the highly developed and universally accepted science of mechanics—a science which was familiar to all scientists, which seemed to involve no logical gaps, and which seemed to depend upon no hypotheses itself. Rankine emphasized not only that his model was internally simple but also that it was capable of organizing an extremely wide range of phenomena and thus provided a second kind of "simplification of science." This kind of simplification had been thoroughly discussed by Stewart, who argued that "the probability of an hypothesis increases in proportion to the number of phenomena for which it accounts" as well as in proportion "to the simplicity of the theory by which it explains them." 2 6 In fact, for Rankine, as for Stewart and Herschel, the fact that hypotheses enabled one to deduce a variety of phenomena from a small number of basic principles provided one of the strongest motivations for developing hypotheses in the first place. Rankine next turned to the question of assessing the probability of hypotheses whose internal characteristics made them likely candidates for consideration. Like virtually all commentators on the hypothetical method, Rankine asserted that "an hypothesis is absolutely disproved by any facts that are inconsistant." 27 And, like all Common 26

Stewart, Works, in, p. 311. "On the Use of Mechanical Hypotheses . . . ," Proc. Phil. Soc. Glasgow, 5 (1864). 27

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Sense philosophers, he insisted that "no hypothesis is capable of absolute proof by any amount of agreement between its results and those of observation; such agreement can give at best only a high degree of probability to the hypothesis." 2 8 Probing more deeply into the question of what warrants our confidence in an hypothesis, he continued: It is not sufficient that there should be a mere loose and general agreement between its results and those of experiment. Any ingenious and imaginative person can frame such hypotheses by the dozen. The agreement should be mathematically exact, to that degree of precision which the uncertainty of experimental data renders possible, and should be tested in particular cases by numerical calculation. The highest degree of probability is attained when an hypothesis leads to the prediction of laws, phenomena, and numerical results which are afterwards verified by experiment; as when the wave theory of light led to the prediction of the true velocity of light in refracting media, of the circular polarization of light by reflection, and of the previously unknown phenomena of conical and cylindrical refraction; and as when the hypothesis of atoms in chemistry led to the prediction of the exact proportions of the constituents of innumerable compounds. 2 9 There is, of course, nothing in this discussion of the probability of hypotheses which unequivocally labels Rankine as a student of Common Sense methodology. But each of his points was in complete conformity with the beliefs of the Common Sense philosophers, and his emphasis on predictive capability as a crucial component of acceptable hypotheses had been given a particularly strong expression in the works of Stewart. Summing up the merits of his hypothesis, Rankine once more paralleled Stewart's beliefs about the primary func28

Ibid., p. 127.

29

IbId., p. 127.

280

MACQUORN RANKINE

tions of hypotheses in science. Stewart had written of any proper scientific theory, including one which may be generated by hypotheses, both that it "enables us to arrange facts already known" and that "it furnishes the means of ascertaining, by synthetic reasoning, those which we have had no access to determine by direct observation." 3 0 Rankine wrote: I think I am justified in claiming for the hypothesis of molecular vortices, as a means of advancing the theory of mechanical action of heat, the merit of having fulfilled the proper purposes of a mechanical hypothesis in physical science, which are, to connect the laws of molecular phenomena by analogy with the laws of motion, and to suggest principles, such as the second law of thermodynamics, and the laws of the elasticity of imperfect gases, whose conformity to fact may be afterwards tested by direct experiment. 3 1 This statement also agrees with Herschel's comments on the use of hypotheses, but its emphasis on the notion of the analogical status of the laws of motion seems more closely related to earlier Scottish formulations. Herschel was prone to speak of the reduction of one kind of phenomena to another, while Stewart merely maintained the existence of analogies between well-known phenomena and those to be explained.

RANKINE'S D I S T I N C T I O N B E T W E E N ABSTRACTIVE AND H Y P O T H E T I C A L M E T H O D S FOR F O R M I N G PHYSICAL T H E O R I E S

Rankine's discussion of hypotheses in "On the Use of Mechanical Hypotheses in Science . . . " was fully consistent with the major considerations of such philosophers as 30

S tewart, Works, ill, p. 251. "On the Use of Mechanical Hypotheses in Science," p. 132. Emphasis mine. 31

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COMMON SENSE AND THE EXACT SCIENCES

Stewart and Brown. But his clearest debt to a particular methodologist is that to Herschel for the principal arguments developed in the introductory sections of "Outlines of the Science of Energetics," the 1855 paper in which he presented his most abstract formulation of what we now call classical thermodynamics. 3 2 Not only did Rankine adopt almost all Herschel's terminology, emphasizing the distinction between abstract science and physical theory and calling the laws of nature axioms, but he also extended and exploited Herschel's distinction b e t w e e n explanatory t h e o r i e s , w h i c h u s u a l l y hypothesized the existence of causal mechanisms, and those theories which merely sought increased generality of the laws of nature through a straightforward process of induction. It was Rankine's emphasis (shared withHerschel) on the greater certainty of abstractive, or merely generalizing, theories that led him to try to transcend the immensely successful hypotheses of molecular vortices and to present thermodynamics as a series of generalizations unconcerned with causal mechanisms. Rankine b e g a n " T h e O u t l i n e s of E n e r g e t i c s " (as Herschel had begun the Preliminary Discourse) with a discussion of what distinguishes a physical theory from an abstract science. According to Rankine, both fully developed physical theories and abstract science consisted of 1) definitions, 2) axioms or first principles, and 3) propositions which are consequences of the first principles and definitions. Then he went on to state the differences in a way which shows a strongly Herschelian viewpoint: First, . . . in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena; and an axiom states a mutual relation amongst such notions, or the names 32 "Oufiines of the Science of Energetics," read before the Philosophical Society of Glasgow, May 2, 1855, and published in Vol. 3 of the Proceedings of that Society. Reprinted inMiscellaneous Scientific Papers, pp. 209-228.

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MACQUORN RANKINE

denoting them: while in a physical science, a definition states properties common to a class of existing objects, or real phenomena; and a physical axiom states a general law as to the relations of phenomena. 3 3 The suggestion here that the entities of abstract sciences have their ultimate origin in experience b u t are defined without regard to a correspondence with real existences is clearly one which Herschel as well as Reid and Stewart had presented. Furthermore, although Herschel had not made the distinction between physical definitions and physical axioms as clear as Rankine did, Rankine's terms are perfectly consistent with Herschel's usages. Herschel had emphasized that "we frame a definition . . . [whenever] we perceive that two or more phenomena agree in so many or so remarkable points, as to lead us to regard them as forming a class or group, if we lay out of consideration, or abstract, all the circumstances in which they disagree, and retain in our minds those only in which they agree." 3 4 Similarly, he had emphasized that the most important way of regarding a law or axiom of nature was as "anouncing a relation" 3 5 between two or more phenomena. Rankine continued his analysis of the differences between abstract and physical sciences by pointing out that: . . . in an abstract science the propositions discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science." 3 6 33

IbId., p. 209. ^Preliminary Discourse, Section 89, p. 98. Emphasis mine. 35 Ibid., Section 91, pp. 100-101. ^Miscellaneous Scientific Papers, p. 209. Emphasis mine.

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COMMON SENSE AND THE EXACT SCIENCES

Thus Rankine, like Herschel and his Common Sense colleagues, emphasized the differences between the deductive methods of abstract science—which begin from the most general and most complex—and the methods of physical science—which begin with the complex generalizations from immediate experience and move toward the most general and simple laws and definitions. Turning to the development of physical theories, Rankine next argued that there are two quite distinct methods of formulating knowledge. Amplifying and emphasizing the distinctions Herschel had made between attempts to generalize and attempts to explain phenomena, Rankine defined the abstractive method as one in which "a class of objects or phenomena is defined by describing . • ., and assigning a name or symbol to, that assemblage of properties which is common to all the objects or phenomena composing the class, as perceived by the senses, without introducing anything hypothetical." 3 7 H e defined the hypothetical method as one in which "a class of objects or phenomena is defined according to a conjectural conception of their nature, as being constituted, in a manner not apparent to the senses, by a modification of some other class of objects or phenomena whose laws are already known." 3 8 Rankine did not wish to renounce the hypothetical method. H e argued that in many cases "a hypothetical theory is necessary, as a preliminary step, to reduce the expression of the phenomena to simplicity and order, before it is possible to make any progress in framing an abstractive theory." 3 9 In other words, it provides a "scaffolding" which may be essential to the erection of the final edifice. But he was aware that hypothetical theories have two major drawbacks—one epistemological, one pragmatic. First, " e v e n those h y p o t h e s e s whose consequences are most fully confirmed by experiment never can, by any amount of evidence, attain that degree of 37

IbId., p. 210.

38

IbId., p. 210.

284

39

IbId., p. 213.

MACQUORN RANKINE

certainty which belongs to observed facts." 40 Second, successful hypotheses tend to be endowed with the au­ thority which belongs only to facts, "and a tendency has, consequently, often evidenced itself to explain away, or set aside, facts inconsistent with these hypotheses, which facts, rightly appreciated, would have formed the basis of true theories." 41 Again following Herschel, Rankine argued that mechanics, or the science of forces and motions, is the only science which has been throughly pursued along abstractive (for Herschel, purely inductive) lines. 42 Cer­ tainly, however, it would be desirable to have a more general abstractive theory capable of embracing the wide range of materials from traditional dynamics, heat, optics, electricity, and physical chemistry which his hypothetical theory of molecular vortices had been able to organize. Instead of supposing the various classes of physical phenomena to be constituted, in an occult way, of mod­ ifications of motion and force, let us distinguish the properties which those classes possess in common with each other, and so define more extensive classes de­ noted by suitable terms. For axioms, to express the laws of those more extensive classes of phenomena, let us frame propositions comprehending as particular cases the laws of the particular classes of phenomena com­ prehended under the more extensive classes. So shall we arrive at a body of principles, applicable to physical phenomena in general, and which, being framed by induction from facts alone, will be free from the uncer­ tainty which must always attach, even to those mechan­ ical hypotheses whose consequences are most fully confirmed by experiment 43 40 Ibid.,

41 Ibid., p. 212. p. 212. p. 210-211. For Herschel's discussion of the special inductive status of mechanics (or dynamics in his terminology), see Preliminary Discourse, Section 188, pp. 179-180. 43 Miscellaneous Scientific Papers, p. 213. 42 Ibid.,

COMMON SENSE AND THE EXACT SCIENCES

The science so constructed was, of course, Rankine's science of energetics, or classical thermodynamics. In Rankine's methodological writings, we find the clearest and most fully developed expression of—and in his scientific works the clearest manifestations of—key Common Sense doctrines of scientific method. Physical hypotheses, when properly selected to conform to requirements of simplicity and independent existence, provide the central method for suggesting experiments and extending knowledge. Such hypotheses should be exploited to organize our understanding only until such time as they are falsified by divergences between prediction and experience, and they should always b e considered as a preliminary step rather than as a final consequence of scientific investigation; for they can never offer the degree of certainty which we strive to attain. The ultimate aim of the scientist is to seek ever more general laws which, though they may have been discovered by using hypotheses, can always be justified by direct appeal to a straightforward process of induction or generalization which involves no extra-experiential suppositions.

286

C H A P T E R 12

Culmination of the Tradition: Metaphysics and Method in the Works of James Clerk Maxwell NOT ONLY was James Clerk Maxwell (1831-1879) among the most brilliant and original scientists of the nineteenth century; he was also more consciously and continuously aware of the metaphysical and methodological bases of scientific work than were any of his contemporaries. In both its extent and its degree of sophistication, his knowledge of the philosophy and psychology of science was awesome, and his philosophical training seems to have played a key role in determining the strategies which made his work so fruitful. After a youth spent largely on his father's estate in Aberdeenshire, interrupted by six years of term-time attendance at the Edinburgh Academy, where he became a prize mathematics student, Maxwell entered the University of Edinburgh in 1847. There he enrolled in the natural philosophy classes of J. D. Forbes, the second mathematics class of Philip Kelland, the chemical course of J. Gregory, the moral philosophy class of George Wilson, and also in the logic and metaphysics courses of William Hamilton. Maxwell's major interests were already oriented toward science. He had had his first mathematical paper, "On the Description of Oval Curves, and Those Having a Plurality of Foci," published in the Proceedings of the Royal Society of Edinburgh in 1846, 1 while he was still a student at parties Clerk Maxwell, "On the Description of Oval Curves and those Having a Plurality of Foci," Proceedings of the Royal Society of Edinburgh, 2 (1846), pp. 89-93.

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Edinburgh Academy. And as a student at Edinburgh he continued independent studies of polarized light, galvinism, rolling curves, and the compression of solids, publishing papers on the latter two topics in 1849 and 1850. 2 But in spite of this concentration on science, he devoted a great deal of effort to Hamilton's courses, referring to Hamilton's lectures as "the most solid" 3 he was hearing. Hamiltonian metaphysical doctrines formed a lasting and influential impression upon the young scientist. But, important as particular Hamiltonism ideas were for Maxwell, even more critical was Hamilton's general insistence that psychological, epistemological, and metaphysical questions all deserve consideration from the natural philosopher. From the time Maxwell wrote a paper, "On the Properties of Matter," for Hamilton's metaphysics course—a paper in which he set out the geometrical properties of matter and those which can be known through the various senses 4 —he showed a constant awareness of the epistemological grounds upon which knowledge of and beliefs about the nature of matter are based. His own theories were frequently formulated in light of explicit concerns with psychological needs and sensory limitations—limitations which restrict knowledge to aspects of relations between objects rather than to their existence in an absolute sense. It is particularly important to recognize that Maxwell's metaphysical and methodological concerns were not short-lived interests stimulated by a brilliant teacher and soon forgotten in the course of his active scientific life. In 1850, when he left Edinburgh to begin studying at Cambridge, his first letter to his friend Lewis Campbell outlined five current projects. One was to read "Kant's Kritik of Pure Reason in German, . . . with a determination to make it agree with Sir W. Hamilton," 5 and another was to 2

Lewis Campbell and William Garnett, The Life ofJames Clerk Maxwell with a Selection from His Correspondence and Occasional Writings (London: MacMillan and Co., 1882), pp. 106-197. 3 5 Ibid., p. 116. "Ibid., pp. 109-113. Ibid., p. 135.

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JAMES MAXWELL

study the metaphysical principles of moral philosophy with an emphasis on Hobbes' Leviathan. In 1855 his letters home referred to the writings of Hegel and of Comte; 6 in 1856 he presented an illuminating paper, "Are there Real Analogies in Nature?" to the Apostles' Club—a highly selective Cambridge intellectual society which he was invited to join in 1853. That he retained such an interest long beyond his student days is evident not only in his scientific work and the semi-popular scientific articles he wrote, but also in the fact that when he returned to Cambridge in 1871 he joined with several of his old friends from the Apostles* Club to form a new club for philosophical discussions. The papers he delivered to this group between 1873 and 1878 have been preserved, and two of them deal with critical metaphysical or methodological problems raised by scientific investigation. In the first, "Does the Progress of Physical Science Tend to Give any Advantage to the Opinion of Necessity (or Determinism) over that of the Contingency of Events and the Freedom of the Will?," dated 11 February, 1873, he investigated the implications of statistical theories which call into question the determinist assumptions associated with earlier scientific theories. 7 In the second, on "Psychophysiks," he dealt with epistemological problems relating to current psychological theories. 8 To the end of his life, Maxwell retained a keen interest in metaphysics and epistemology, independent of his professional scientific work.

" A R E T H E R E R E A L A N A L O G I E S IN N A T U R E ? "

We have seen that William Hamilton, like Thomas Brown, insisted that scientific knowledge—as opposed to beliefs, which might be held for a variety of reasons—is severely restricted or conditioned by sensory and mental 6

Ibid., p. 205.

'Ibid., pp. 434-444.

289

8

IbId., pp. 452-463.

COMMON SENSE AND THE EXACT SCIENCES

limitations. For both men this meant that virtually all scientific knowledge was of relations between objects and/or events. Brown chose to place greatest emphasis on the invariable relationships of temporal and spatial con­ tiguity, arguing that only these constitute causal relations, but Hamilton placed more emphasis on the second-order relationship of similarity or analogy among first-order re­ lations. For example, Hamilton argued that the only proof of the existence of a God whose primary attribute is a free intelligence comes from an analogy with "the relation in which we find intelligence to stand in the order of the human constitution," 9 and he insisted that the highest function of science is to trace out the analogy of apparently unconnected observations. 10 Maxwell's adherence to Brown's and Hamilton's belief in the relational aspect of all scientific knowledge and to Hamilton's emphasis upon analogical or metaphorical in­ sights into such relations is central to his greatest work in electromagnetism and kinetic theory. His most critical development of these doctrines was begun in a lecture on analogies presented to the Apostles' Club in 1856 at roughly the same time that he began to exploit the method of physical analogies in his first great paper, "On Faraday's Lines of Force." 11 Overall, Maxwell's lecture is an extremely confusing, if not confused, attempt to assess whether analogies are merely imposed by us upon phenomena or whether they exist in nature independent of the investigator. Maxwell's answer to this question—there are some real analogies between natural entities which we are capable of recognizing because our senses and intellect are properly constituted, but not all analogi9 Hamilton,

Lectures, I, p. 22. '"Hamilton, Discussions, p. 243. llt On Faraday's Lines of Force" was read to the Cambridge Philosophical Society, December 11, 1855 and published in their Transactions on February 11, 1856. Maxwell's lecture, "Are there Real Analogies in Nature?" was delivered before the Apostles in February of 1856.

JAMES MAXWELL

cal arguments are thereby justified— 12 is important for two reasons. Itjustifies the general search for analogies in science which is supposed to be a study of the real natural world. At the same time, it retains a demand for justifying any particular analogy to insure that it expresses a real rather than an imagined relationship. Maxwell's clearest statement of the value of analogical reasoning and the fundamental problems of justification which it raises occurred near the end of his lecture, after he had discussed attempts to draw moral implications from physical phenomena: Whenever [men] see a relation between two things they know well, and think they see there must be a similar relation between things less known, they reason from one to the other. This supposes that although pairs of things may differ widely from each other, the relation in the one pair may be the same as that in the other. Now, as in a scientific point of view the relation is the most important thing to know, a knowledge of one thing leads us a long way towards a knowledge of the other. 13 In this statement we see an immediate reflection of the relational emphasis of Hamilton's epistemology and the analogical emphasis of both Hamilton and James D. Forbes. So far Maxwell had emphasized only the positive value of analogy, but he continued: If all that we know is relation, and if all the relations of one pair of things correspond to those of another pair, it will be difficult to distinguish the one pair from the other, although not presenting a single point of resemb­ lance, unless we have some difference of relation to 12 Maxwellneverformulatedhis conclusion in this manner. Instead, he offered examples of real analogies and of unjustified ones and left the reader to form his own conclusions. SeeLife of Maxwell, pp. 235-244, for the entire text of Maxwell's lecture. l3 Campbeil and Garnett, Life of Maxwell, pp. 242-243.

COMMON SENSE AND THE EXACT SCIENCES

something else, whereby to distinguish them. Such mistakes can hardly occur except in mathematical and physical analogies, but if we are going to study the constitution of the individual mental man, and draw all our arguments from the laws of society on one hand, or those of the nervous tissue on the other, we may chance to convert useful helps into Wills-of-the-whisp. 14 Here Maxwell made a point by way of illustration which Dugald Steward had explicitly dealt with—that analogies are of greatest value when they are varied occasionally so that no one analogy imposes a narrowness of scope and vision upon our considerations. Only by discovering negative analogies can we avoid mistaking similarities for identities and remain aware of the complexity of relation­ ships among phenomena. Finally, Maxwell concluded by pointing out the fun­ damental provisionality or condition of all attempts to "discover" analogies: Perhaps the "book," as it has been called, of nature is regularly paged; if so, no doubt the introductory parts will explain those that follow, and the methods taught in the first chapters will be taken for granted and used as illustrations in the more advanced parts of the course; but if it is not a "book" at all, but a magazine, nothing is more foolish to suppose than that one part can throw light on another. 15 Like all his Common Sense predecessors, Maxwell was inclined to assume that nature was more like a book than a magazine. Like Hamilton alone, Maxwell also accepted a constant responsibility to test his own belief. Thus, every analogy he explored demanded independent testing against experience. Each was the starting point of a scien­ tific investigation, never merely the result. The Apostles' Club essay on analogy contains important Hamiltonian elements beyond the analysis of the rela14 Ibid.,

p. 243.

15 Ibid.,

p. 243.

JAMES MAXWELL

tional and analogical aspects of science. Hamilton had insisted that, although we are capable of at least relational knowledge about real natural events through a combination of sensation and reasoning, even the most elementary interpretation of phenomena presupposes an act of intelligence and abstraction. Maxwell reiterated this idea in writing: Now the very first notion of number implies a previous act of intelligence. Before we can count any number of things, we must pick them out of the universe and give each of them a fictitious unity by definition. Until we have done this, the universe of sense is neither one nor many, but indefinite. But yet, do what we will, nature seems to have a horror of partition. Perhaps the most natural thing to count " o n e " for is a man or human being, but yet it is very difficult to do so. Some count by heads, others by souls, others by noses; still there is a tendency to run together into masses or to split up into links. The dim outlines of phenomenal things all merge into one another unless we put on the focusing glass of theory and screw it up sometimes to one pitch of definition, and sometimes to another so as to see down into different depths through the great millstone of the world. 16 Like Brown's discussion of the "fictitious" unity given to a piece of glass, this passage emphasizes the active human element in interpreting phenomena and separating out those elements upon which we choose to focus. But Maxwell's separation of a particulate unity from an indeterminate whole of primitive perception is really the converse of Brown's assertion that we synthesize wholes from ensembles of particles. Hamilton was more prone to emphasize the wholeness of experience from which aspects were abstracted and individuated; it was from Hamilton that Maxwell probably inherited his sensitivity to the priority of the complex perception and to the possi16

Ibid., pp. 236-237.

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bility of alternative modes of analyzing and defining its components prior to reasoning about it. The importance of Maxwell's consciousness of the priority of the whole in our perception clearly had a bear­ ing on his preference for Faraday's "field" point of view in electricity as opposed to the French and German theories which focused on actions at a distance between particles. This connection is most evident in a passage from his massive Treatise of Electricity and Magnetism, which first appeared in 1873. We are accustomed to think of the universe as made up of parts, and mathematicians usually begin by consider­ ing a single particle, and then conceiving its relation to another particle and so on. This had generally been supposed to be the most natural method. To conceive of a particle, however, requires a process of abstraction, since all our perceptions are related to extended bodies, so that the idea of the all that is in our consciousness at any given instant is perhaps as primitive an idea as that of any individual thing. Hence there may be a mathematical method in which we proceed from the whole to the parts instead of from the parts to the whole. For example, Euclid in his first book, conceives a line as traced out by a point, a surface as swept out by a line, and a solid as generated by a surface. Buthe also defines a surface as the boundary of a solid, a line as the edge of a surface, and a point as the extremity of a line. 17 In much the same way, Maxwell continued, we may de­ fine "potential of a material system" as a certain function of the masses and positions of an ensemble of particles, or we may consider the potential, ψ, to be primary and give mass, M, a meaning determined only by M =

Ψ dV

17 James Clerk Maxwell, A Treatise on Electricity and Magnetism, reprint of3rd, 1891 edition (New York: Dover Publications, 1954), Vol. 2, pp. 176-177.

JAMES MAXWELL

In electrical investigations, we may consider as primary either the distances between bodies and the charges associated with them or quantities which are continuous through space. Faraday took the second approach in each example, as did Maxwell in his electromagnetic researches. As Maxwell suggested in his comments on the need to multiply analogies, however, he insisted upon adjusting his "glass of theory" sometimes to one pitch of definition and sometimes to another. Thus, although his bias was in favor of field theories in physics, he was more than willing to explore the implications of particulate impact or action-at-a-distance viewpoints in his papers on kinetic theory. Even in his work on electricity and magnetism, where field concepts dominated, he varied his theoretical point of view from paper to paper. He concentrated on a purely geometrical definition of lines of force in "On Faraday's Lines of Force," 1 8 he exploited a specific mechanical model in "On Physical Lines of Force" which was published five years later in 1861, 19 and he provided general dynamical definitions of field variables in "A Dynamical Theory of the Electromagnetic Field," which appeared first in 1864. 20 The changing theoretical bases of Maxwell's successive papers on electricity and magnetism depended upon a conscious attempt to vary his theoretical focus and did not merely reflect a temporal change in his views about the 18 "On Faraday's Lines of Force" in The Scientific Papers of James Clerk Maxwell, ed. W. D. Niven (New York: Dover Publications, 1965), reprinted from the Cambridge University Press edition of 1890, Vol. 1, pp. 156-229. 19 "On Physical Lines of Force" was first published in Phil. Mag. for March, April, and May, 1861 and January and February, 1862. Reprinted in Scientific Papers, Vol. 1, pp. 451^513. 20 "A Dynamical Theory of the Electromagnetic Field" read before the Royal Society of London, December 8, 1864 and published in Phil. Trans., Vol. 155 (1865). Reprinted in Scientific Papers, Vol. 1, pp. 527— 597.

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proper way of doing science. One of the clearest bits of evidence on this point comes from the second section of "On Faraday's Lines of Force" in which Maxwell attempted to set forth a mathematical theory of Faraday's electrontonic state (that condition into which all bodies, including a supposed etherial medium, are placed by the presence of magnets and currents, and the changes of which give rise to currents or tendencies toward currents). Maxwell admitted in this discussion that there was already a widely accepted physical theory based on actionat-a-distance notions that will account for the phenomena which he is hoping to interpret. He continued: What is the use then of imagining an electrotonic state of which we have no distinctly physical conception, instead of a formula of attraction which we can readily understand? I would answer, that it is a good thing to have two ways of looking at a subject, and to admit that there are two ways of looking at it. 21 Additional evidence comes from the fact that Maxwell was clearly aware of the dangers of using particular mechanical models before he adopted the mechanical point of view in "On Physical Lines of Force." In "On Faraday's Lines of Force," for example, he had written that when "we adopt a physical hypothesis, we see phenomena only through a medium, and are liable to that blindness to facts and rashness in assumption which a partial explanation encourages." 2 2 Yet he believed that so long as we are conscious of these limitations and dangers, the method of physical hypothesis offers a special insight into phenomena which warrants its use at a certain stage in the investigation; he chose to exploit this viewpoint in "On physical Lines of Force." Similarly, although he rejected action-at-a-distance approaches to physics in his dynamical theory of electricity and magnetism of 1864, he ^Scientific Tapers, Vol. 2, p. 208. ^Scientific Papers, Vol. 1, pp. 155-156.

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exploited them in "On the Dynamical Theory of Gases" in 1866. 23 Finally, though the approach to electricity and magnetism which had been developed in "A Dynamical Theory of the Electromagnetic Field" continued to domi­ nate his later Treatise on Electricity and Magnetism, he returned in An Elementary Treatise on Electricity, to a further exploitation of the purely geometrical approach of "On Faraday's Lines of Force." 24 Even within the Treatise, as P. M. Heiman has shown, Maxwell did not use one consistent approach but alternated between an ap­ proach which considered "lines of force" as primary and one which employed "particulate polarization." 25 Maxwell presented a psychological justification for his emphasis on a variety of scientific approaches which not only demonstrates the psychologizing tendency of the whole Scottish Common Sense tradition but also provides an interesting insight into the analysis of British as against Continental scientific styles undertaken later by Pierre Duhem. Inhis 1870 address as Presidentofthe Mathemat­ ical and Physical Sections of the British Association for the Advancement of Science, Maxwell wrote: There are men who, when any relation or law, however complex, is put before them in a symbolical form, can grasp its full meaning as a relation among abstract quan­ tities. Such men sometimes treat with indifference the further statement that quantities actually exist in nature which fulfill this relation. The mental image of the concrete reality seems rather to disturb them than to assist their contemplations. But the great majority of mankind are utterly unable, without long training, to retain in their minds the unembodied symbols of the pure mathematician. . . . 23 Scientific

Papers, Vol. 2, pp. 26-78. Clerk Maxwell, Elementary Treatise on Electricity, ed., W. Gamett (Oxford: Oxford University Press, 1881), section 65. 25 See P. M. Heimann "Maxwell and the Modes of Consistent Repre­ sentation," Archive for History of Exact Science, 6 (1970), pp. 171-213 passim. 24 James

COMMON SENSE AND THE EXACT SCIENCES

There are, as I have said, some minds which can go on contemplating with satisfaction pure quantities pre­ sented to the eye by symbols, and to the mind in a form which none but mathematicians can conceive. There are others who feel more enjoyment in follow­ ing geometrical forms, which they draw upon paper, or build up in the empty space before them. Others, again, are not content unless they can project their whole physical energies into the scene which they conjure up. They learn at what rate the planets rush through space, and they experience a delightful feeling of exhilaration. They calculate the forces with which heavenly bodies pull at one another, and they feel their own muscles straining with the effort. To such men momentum, mass, and energy are not mere abstract expressions of the results of scientific inquiry. They are words of power, which stir their souls like the memories of childhood. For the sake of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid colouring of a physical illus­ tration, or in the tenuity and paleness of a symbolical expression. 26 Few, if any, scientists of any age have shown such a great awarenees and toleration of—much less a commit­ ment to—diversity in modes of scientific expression. This is not to say that Maxwell showed no preference for one approach over another in his own work. At least in part because of his Common Sense training, he preferred the methods of geometrical imagery or physical illustration over the abstract mathematical approach. This preference dictated the style and even the content of much of his work. 27 26 Scientific

Papers, Vol. 2, pp. 219-220. do not propose to analyze in detail Maxwell's works on elec­ tromagnetic theory. P. M. Heimann's "Maxwell and the Modes of Consistent Representation," Archive for History of Exact Sciences, 6 (1970), 27 I

JAMES MAXWELL E M B O D I E D M A T H E M A T I C S AND PHYSICAL A N A L O G I E S

In his lecture to the Apostle's Club, Maxwell spoke very generally of analogies. But beginning with his introductory comments on "On Faraday's Lines of Force," he placed particular emphasis in his scientific writings on what he called "physical analogy." According to Maxwell, the mass of experimental evidence and the number and complexity of descriptive mathematical formulae known to apply to electrical and magnetic phenomena in 1855 was so great as to overtax the memory and effectively prohibit further progress. This being the case, he wrote: The first process therefore in the effectual study of the science, must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis. In the first case we entirely lose sight of the phenomena to be explained; and though we may trace out the consequences of given laws we can never obtain more extended views of the connexions of the subject. If, on the other hand, we adopt a physical hypothesis, we see the phenomena only through a medium, and are liable to that blindness to facts and rashness in assumption which partial explanation encourages. We must therefore discover some method of investigation which allows the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which that conception is borrowed, so that pp. 171-213, provides an excellent account, although it emphasizes concerns which are of marginal importance to my argument and does not interpret dynamical theory as based on a general analogy with other material systems. See also Mary Hesse, "Logic of Discovery in Maxwell's Electromagnetic Theory," (draft of a paper presented to a conference on "Foundations of Scientific Method: the Nineteenth Century," at Indiana University, November 19-22, 1970).

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it is neither drawn aside from the subject in pursuit of analytical subleties, nor carried beyond the truth by a favorite hypothesis. In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other. 28 Two characteristics of this formulation of the nature and role of physical analogies point directly to its sources in Common Sense Philosophy. Maxwell's assertion that the principal function of analogy is to simplify and arrange phenomena enough to bring them within easy range of the memory and intellect is precisely the same as that initially made by Dugald Stewart and reemphasized by Rankine only two years before Maxwell's discussion. But even more characteristic of the Common Sense school is Maxwell's dissatisfaction with a purely analytic mathematical understanding. Maxwell was uneasy about losing sight of the phenomena to be explained and sought a method "which allows the mind at every step to lay hold of a clear physical conception." 2 9 That this preference was consciously related to Common Sense concerns is most clearly seen from comments which appeared in his review of William Thomson and P. G. Tait's classic textbook, Elements of Natural Philosophy (1873). Maxwell began his review by writing that nearly all texts in physical science had been written by men with one of two pionts of view. The first type emphasized mathematics and saw the progress of science in the reduction of phenomena to mathematical formulae. The second type emphasized experiments and immediate observation of phenomena "until the student becomes at length able to perform and describe experiments of his ^Scientific Papers, Vol. 1, pp. 155-156.

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29

IbId.

JAMES MAXWELL

own." But neither had followed a third and more fruitful method—that fortunately chosen by Thomson and Tait: Each of these types of men of science is of service in the great work of subduing the earth to our use, but neither of them can fully accomplish the still greater work of strengthening their reason and developing new powers of thought. The pure mathematician endeavours to transfer the actual effort of thought from the natural phenomena to the symbols of his equations, and the pure experimentalist is apt to spend so much of his energy on matters of detail and calculation, that he has hardly any time left for the higher forms of thought. Both of them are allowing themselves to acquire an unfruitful familiarity with the facts of nature, without taking advantage of the opportunity of awakening those powers of thought which every fresh revelation of nature is fitted to call forth. There is, however, a third method of cultivating physical science, in which each department in turn is regarded, not merely as a collection of facts to be coordinated by means of the formulae laid up in store by the pure mathematician, but as itself a new mathesis by which new ideas may be developed. Every science must have its fundamental ideas —modes of thought by which the process of our minds is brought into the most complete harmony with the process of nature—and these ideas have not attained their most perfect form as long as they are clothed with the imagery, not of the phenomena of the science itself, but of the machinery with which mathematicians have been accustomed to work problems about pure quantities. 3 0 Just as Hamilton had insisted that in geometry we have the advantage over algebra in being able to "[feast] at each turn with glances of the earth and of the heavens, while we inhale the pleasant breeze, and gather new strength at ""Scientific Papers, Vol. 2, pp. 324-325.

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every effort we put forth," 31 Maxwell insisted that by physically clothing our mathematical conceptions we provide the "opportunity of awakening those powers of thought which every fresh revelation of nature is fitted to call forth." It was the desire to provide physical imagery to underlie even nominally "mathematical" concepts that most clearly differentiated Maxwell's approach to the use of analogies in physics from the purely formalist approach of Fourier and the French Positivists, who hoped to reduce physics to analysis. Throughout his entire career, from his first formal exposure to mathematics in the Edinburgh Academy, Maxwell showed a preference for geometrical methods or "embodied mathematics." At Cambridge he was a student of the great tutor of analysis William Hopkins, but even there he retained his geometrical orientation. Fellow-students commented that in Hopkins' lectures, "whenever the subject admitted of it he had recourse to diagrams, though the rest might solve question more easily by a train of analysis." 32 Furthermore, Maxwell continued to write purely geometrical papers almost until the end of his active scientific life. 33 It is in connnection with his work in physics that Maxwell's predilection for something more than analytic formulations had its greatest importance, however. In "On Faraday's Lines of Force" as we have already seen, one of Maxwell's intentions was to develop a so-called physical analogy which would illuminate Faraday's investigations of electricity and magnetism. The analogue Maxwell chose for this first exploration—the motion of an 31 Quoted by George Elder Davie in The Democratic Intellect, 2nd ed. (Edinburgh: Edinburgh University Press, 1964), p. 127. 32 LiJe of Maxwell, p. 175, note 1. 33 As late as May 9,1872, Maxwell read a paper, "On the Condition that in the transforming of any figure by curvilinear coordinates in three dimensions, every angle in the new figure shall be equal to the corresponding angle in the original figure," to the London Mathematical Society. Scientific Papers, Vol. 2, pp. 297-300.

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imponderable, incompressible fluid—is particularly in­ teresting because its choice seems to have been dictated almost solely by his desire to develop geometrical in­ sights. He admitted that the fluid he was considering did not have a real physical existence: "It is merely a collec­ tion of imaginary properties which may be employed for establishing certain theorems in pure mathematics in a way more intelligible to many minds and more applicable to physical problems than that in which algebraic sym­ bols alone are used." 34 Similarly, he concluded the first section of the paper with the assertion, "my aim has been to present the mathematical ideas to the mind in an embodied form, as systems of lines or surfaces, and not as mere symbols, which neither convey the same ideas nor readily adapt themselves to the phenomena to be explained." 35 This notion that "embodied" mathematics provides greater insight into physical problems than do analytic formulas was repeated in Maxwell's reply to a letter from Faraday querying him about the possible application of a lines-of-force approach to gravitational problems. Max­ well responsed: "I do not think gravitation a dangerous subject to apply your methods to,... it may be possible to throw light on it also by the embodiment of the same ideas, which are expressed mathematically in the func­ tions of Laplace and Sir William R. Hamilton . . ." 36 Maxwell's concern with the geometrical, or spatial, and physical content and implications of mathematical ideas received its clearest and most fascinating formulations in his 1872 paper "On the Mathematical Classification of Physical Quantities"; 37 in the subsequent development 34 Scientific

Papers, Vol. 1, p. 160. Emphasis mine. p. 187. Emphasis mine. 36 Campbell and Gamett, The Life of James Clerk Maxwell with selec­ tions from his correspondence and occasional writings. New edition, abridged and revised, London, 1884, p. 204. This letter was not included in the first edition of The Life of James ClerkMaxwell. Emphasis mine. 37 Scientific Papers, Vol. 2, pp. 257-266. 35 Ibid.,

COMxMON SENSE AND T H E EXACT SCIENCES

and exploitation of the ideas presented there; throughout his Treatise on Electricity and Magnetism;38 and in his note "On the Proof of the Equations of Motion of a Connected System" presented to the Cambridge Philosophical Society in 1876. 39 In all these writings Maxwell sought to point out the value of—and to amplify and extend—the new ideas presented by William Rowan Hamilton's Calculus of Quaternions. Maxwell acknowledged the tremendous value to pure mathematics of Descartes' introduction of coordinate axes in geometry, for this allowed mathematicians to reduce all their methods to calculations performed on numerical quantities. But, he argued, for many purposes of physical reasoning, as distinguished from calculation, it is desirable to avoid explicitly introducing the Cartesian coordinates, and to fix the mind at once on a point of space instead of its three coordinates, and on the magnitude and direction of a force instead of its three components. This mode of contemplating geometrical and physical quantities is more primitive and natural than the other, although the ideas connected with it did not receive their full development till Hamilton made the next great step in dealing with space by the invention of his Calculus of Quaternions. 4 0 Just as the primary value of geometrical as opposed to algebraic mathematics lay in the fact that geometry kept attention focused on meaningful entities, the principal value of W. Rowan Hamilton's approach to mathematics, according to Maxwell, was that it suggested meaningful physical interpretations of mathematical quantities. Thus, for example, Maxwell emphasized Hamilton's discussion of the scalar product of two vectors in connection with the interpretation of energy. Energy is a scalar quantity with the dimensions ML2ZT2, where M, L, and T represent 38

James Clerk Maxwell, A Treatise on Electricity and especially Vol. 1, pp. 1-31, and Vol. 2, pp. 199-210. ^Scientific Papers, Vol. 2, pp. 308-309. 40 A Treatise on Electricity and Magnetism, Vol. 1, p. 9.

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units of length, mass, and time. Traditionally, energy had been considered as the product of mass and the square of the velocity of a moving body; in this case, the square of the velocity has no distinct physical meaning. In the language of Quaternions, on the other hand, energy is a scalar func­ tion of two vectors, one of which is a force and one a displacement (or one a momentum and one a velocity), so the Quaternion formulation continually reminds one of the physical concepts underlying the definition of work and energy. 4 1 In much the same way, other operations on vectors also suggest their physical interpretation. Max­ well continued: Vectors which are referred to a unit of length I shall call forces, using the word in a somewhat generalized sense, as we shall see. T h e operation of taking the in­ tegral of the resolved part of a force in the direction of a line for every element of that line, has always a physical meaning [i.e., the "work" done by the force]. In certain cases the result of the integration is i n d e p e n d e n t of the path of the line between its extremities. The result is then called a potential. Vectors which are referred to a unit of area I shall call fluxes. The operation of taking the integral of the re­ solved part of a flux perpendicular to a surface for every element of the surface has always a physical meaning. In certain cases the result of the integration over a closed surface is independent, with certain restrictions, of the position of the surface. The result then, expresses the quantity of some kind of matter, either existing within the surface, or flowing out of it, according to the physical nature of the flux. 42 Finally, Maxwell even gave a physical interpretation of the Hamiltonian operator, V \ 41

t ~r ^ J ι—*~ k — , pointax ay dzl

James Clerk Maxwell, "On the Mathematical Classification of Phys­ ical Quantities," Scientific Papers, Vol. 2, pp. 259-260. «Ibid., p. 261.

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ing out that V applied to a scalar, P gives the direction and rate of maximum decrease of the quantity P, while the scalar portion of V applied to any vector, a, gives what he called the "convergence" of σ (since if σ is a flux, ff a • dS = fff V odV), and the vector portion of V applied to a gives what he called the " c u r l " of σ) since it repre­ sents the direction and magnitude of the rotation of the matter carried by the vector σ). 4 3 Because the interpretation of Hamiltonian mathematics seemed to provide special insight into the geometrical characteristics of physical problems, Maxwell hoped to be able to discover some similar technique to obtain addi­ tional "dynamical" insights. In " O n the Mathematical Classification of Physical Quantities" he wrote: As our conceptions of physical science are rendered more vivid by substituting for the mere numerical ideas of Cartesian mathematics t h e geometrical ideas of Hamiltonian mathematics, so in the higher sciences the ideas might receive a still higher development if they could be expressed in language as appropriate to dynamics as Hamilton's is to geometry. 4 4 Maxwell attempted such a formulation of appropriate dynamical conceptions in chapter five of the fourth part of his Treatise on Electricity and Magnetism. Beginning with Lagrange's formulation of the equations of motion of a connected system in terms of generalized coordinates and momenta (a formulation consciously designed to eliminate all physical and geometrical concepts from mechanics in order to simplify the analytic process), Maxwell sought to reinterpret Lagrange's symbols in terms of velocity, momentum, impulse, and the newly formulated concept of energy. 4 5 Such a formulation was n e c e s s a r y , h e a r g u e d , b e c a u s e t h e i m p o r t a n c e of Lagrange's equations "does not d e p e n d on their being useful in solving problems in dynamics. A higher function 43

Ibid., p. 264-265. «ibid., p. 259. A Treatise on Electricity and Magnetism, Vol. 2, pp. 199-210.

45

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which they must discharge is that of presenting to the mind in the clearest and most general form the fundamental principles of dynamical reasoning." 4 6 Maxwell exploited his dynamical interpretation of Lagrange's equations in the mature form of his dynamical theory of electromagnetism throughout the remainder of the Treatise, and it clearly determined the form of his theory. But he did not remain completely satisfied with this presentation of dynamical ideas, and in 1876 he still argued that "it is therefore very desirable that men of science should invent some method of statement by which ideas, precise so far as they go, may be conveyed to the mind, and yet sufficiently general to avoid the introduction of unwarrantable details." 4 7 M a x w e l l ' s d i v e r g e n c e from t h e p u r e l y a n a l y t i c mathematical style of physics characterized most clearly by Lagrange and Fourier depended to a large extent on his conscious adoption of the old Common Sense demand that one should constantly keep the objects of one's investigation before the mind both because this allows one to avoid error and because it leads to increased insight. But Maxwell also took exception to a second Continental tradition of mathematical physics—the molecularist tradition of Laplace and his followers—which did emphasize the physical content of mathematical theories. Most Continental electrical theorists of the nineteenth century, including Ampere and M. W. Weber, adopted the approach of this school, emphasizing action-at-a-distance forces acting between particles or "molecules" of matter, so Maxwell's opposition demands some explanation. To some extent, Maxwell rejected the molecularist approach because of his preference for field theories over actionat-a-distance theories, and this preference seems clearly 46 James Clerk Maxwell, "On the Proof of the Equations of Motion of a Connected System," Scientific Papers, Vol. 2, p. 309. The same sentiment appears in a slightly less elegant form in the Treatise on Electricity and Magnetism, Vol. 2, p. 210. ^Scientific Papers, p. 309.

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related to his Hamiltonian training in philosophy. But there were other important concerns, also derived from Common Sense Philosophy, which led Maxwell to es­ chew the methods of the Continental molecularist school and to formulate his theories in another manner. The French molecularist school and all those who fol­ lowed variants of its methods began by assuming the existence of configurations of particles and of specified forces between them; then they deduced testable conse­ quences from their hypothetical systems and claimed con­ firmation of their hypotheses when experimental evi­ dence accorded with their theoretical deductions. This method violated at least one critical Common Sense re­ quirement: that any assumed entities or mechanisms have some independent evidence of existence, preferably di­ rect, but at least in an analogous situation. One should generally introduce only assumptions which are sug­ gested directly by experience, but if one is to postulate specific mechanisms, they ought to be independently jus­ tified. Maxwell's accord with these sentiments appears not only in his specific criticisms of the molecularist ap­ proach but also in the formulation of his own scientific work. In "On the Proof of the Equations of Motion of a Con­ nected System," for instance, Maxwell struck out at the molecularists' assumptions and emphasized the phenom­ enal approach to physical reasoning: In forming dynamical theories of the physical sci­ ences, it has been a too frequent practice to invent a particular dynamical hypothesis and then by means of the equation of motion to deduce certain results. The agreement of these results with real phenomena has been supposed to furnish a certain amount of evidence in favour of the hypothesis. The true method of physical reasoning is to begin with the phenomena and to deduce forces from them by a direct application of the equations of motion. 48 48 Ibid.,

p. 309.

JAMES MAXWELL

As Robert Kargon has pointed out, 49 Maxwell's first physical paper, "On the Equilibrium of Elastic Solids," of 1850, directly contrasted his own phenomenalist approach to the molecularist approach of Navier, Poisson, Lame, and Clapeyron. Maxwell began this paper by stating the molecularist assumptions underlying theories of elastic solids and by pointing out that these assumptions led to incorrect predictions. Then he offered his own approach: I have therefore substituted for the assumptions of N a v i e r the following axioms as the results of experiments. If three pressures in three rectangular axes be applied at a point in an elastic solid,— 1. The sum of the three pressures is proportional to the sum of the compressions which they produce. 2. The differences between two of the pressures is proportional to the difference of the compressions which they produce. 5 0 From these axioms he developed a set of equations of motion for elastic solid media which conformed to all laws of elasticity induced from experiment. Similarly, Maxwell e m p h a s i z e d the i n d e p e n d e n t existence criterion for hypothetical mechanisms both in his critical and in his synthetic writings. In his 1870 address to the mathematical and physical sections of the British Association, Maxwell praised William Thomson's vortex-ring theory of the properties of molecules because a close approximation to such rings did clearly exist in the smoke-rings formed by experienced pipe-smokers and because the laws of motion of such rings were fully known from hydrodynamics. T h e s e circumstances made the status of such a theory far more secure than had the speculations of the French molecularists. 49 Robert Kargon, "Model and Analogy in Victorian Science: Maxwell's Critique of the French Physicists," Journal of the History of Ideas, 30 (1969), p. 431. ^Scientific Papers, Vol. 1, p. 31. Emphasis mine.

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If a theory of this kind should be found, after conquer­ ing the enormous mathematical difficulties of the sub­ ject, to represent in any degree the actual properties of molecules, it will stand in a very different scientific position from those theories of molecular action which are formed by investing the molecule with an arbitrary system of central forces invented expressly to account for the observed phenomena. 51 That Maxwell applied the demand for independent evidence of the existence of elements of proposed hypotheses to his own work is especially clear in both "On Physical Lines of Force" and "A Dynamical Theoryofthe Electromagnetic Field." In the first of these two articles Maxwelljustified his assumption of the elastic-solid-like properties of an electromagnetic medium by arguing that the wave theory of light led independently to a similar assumption about the luminiferous ether: "The undulatory theory of light requires us to admit this kind of elastic­ ity in the luminiferous medium, in order to account for transverse vibrations. We need not then be surprised if the magneto-electric medium possess the same property." 52 Since this passage was written before the luminiferous ether and the "magneto-electric medium" had been identified with one another, the accepted prop­ erties of the first could be called upon to justify assigning similar properties to the second. The appeal to an independent-existence criterion to justify the assumed characteristics of a hypothetical magneto-electric medium is even clearer in "A Dynami­ cal Theory." Here again Maxwell appealed to evidence for the existence and properties of an etherial medium from studies of heat and light. He continued: We may therefore receive, as a datum derived from a branch of science independent of that which we have to 51 Scientific 52 Scientific

Papers, Vol. 2, p. 223. Emphasis mine. Papers, Vol. 1, p. 489.

JAMES MAXWELL

deal, the existence of a pervading medium, of small but real density, capable of being set in motion, and of transmitting motion from one part to another with great, but not infinite velocity. 53 Such a medium, of course, provided the basis for all the e x p l a n a t i o n s of e l e c t r o m a g n e t i c p h e n o m e n a in "A Dynamical Theory of the Electromagnetic Field" and in the subsequent Treatise on Electricity and Magnetism. It is true that Maxwell apparently ignored or relaxed the independent-existence requirement with regard to the assumptions of his papers on the kinetic theory of gases. But the circumstances surrounding his initial development of kinetic theory were quite unusual, and his first recorded ideas on the subject—in a letter to Sir George Gabrial Stokes, dated 30 May, 1859—indicate his deep unease overbasingatheory of gases on assumptions about entities which had not yet been shown to exist. Maxwell confided to Stokes that he had been struck by Rudolph Clausius' Philosophical Magazine paper of February 1859, and had thus been stimulated to draw up a theory of the motions of free particles acting only by impact. In fact, Maxwell was convinced that Clausius' theory was inadequate, but, he wrote: As I found myself able and willing to deduce the laws of motion of systems of particles acting on each other only by impact, I have done so as an exercise in mechanics. Now do you think there is any so complete a refutation of this theory of gases as would make it absurd to investigate it further so as to found arguments upon measurements of strictly "molecular" quantities before we know whether there be any molecules? One curious result is that [the coefficient of viscosity] is independent of the density. This is certainly very unexpected, that the friction should be as great in a rare as in a dense gas. . . . 53

Ibid., p. 528. Emphasis mine.

311

COMMON SENSE AND THE EXACT SCIENCES Have you the means of refuting this result of the hypotheses? 54 This statement makes it quite clear that Maxwell's ini­ tial attitude toward the dynamical theory of gases, based upon arbitrary assumptions, was highly skeptical. But after Maxwell discovered that his theoretically derived density-independence of viscosity was confirmed by ex­ periment and that other important transport properties of gases could be accounted for by his kinetic theory, it was clear that the fruitfulness of the theory outweighed his qualms about the soundness of its methodology. His epistemological and methodological beliefs account for ten­ dencies in his work. They did not hold absolute sway over his judgment, nor could they have cancelled out his in­ volvement with such an apparently successful theory as the dynamical theory of gases. MAXWELL AND "CONSISTENT REPRESENTATIONS" In addition to the frequent demand of independent existence which Maxwell applied to hypothetical con­ structs, there was a second demand which he universally applied to physical or dynamical hypotheses or theories. This was the demand that any acceptable hypothesis or theory must afford a consistent representation of the phenomenon to be accounted for, meaning that it must not only be self-consistent and in accord with the particular phenomena needing explanation but also that it must not contradict principles established by other sciences. 55 54 Quotedby Stephen G. Brush mKineticTheory,Vol.1: TheNature of Gases and of Heat (Oxford: Pergamon Press, 1965), p. 27, from Memoir and Scientific Correspondence of the Late Sir George Gabriel Stokes, Bart. (Cambridge, 1909), II, pp. 8-11. Emphasis mine. 55 Joseph Turner's "Maxwellon the Logic of Dynamical Explanation," Philosophy of Science, 23 (1956), pp. 36-47, deals very nicely with Maxwell's emphasis on consistent representation, although he does not, as I hope to, connect Maxwell's use of the motion of consistency with William Hamilton's writings.

JAMES MAXWELL

We can best understand Maxwell's emphasis on consistency as a prime consideration in evaluating scientific hypotheses and theories by recalling the emphasis on the relativity of knowledge which he shared with Hamilton, and by remembering some of the implications this had for Hamilton's evaluation of hypotheses and theories. Since we can never have apodictic certainty about the absolute correspondence of any system of explanation with the reality u n d e r l y i n g the p h e n o m e n a to be explained, Hamilton argued that one of the most fundamental grounds for evaluating the possible truth of such a system was to analyze it for internal consistency and for its consistency with other unquestionable principles or facts of consciousness. "Are the principles which a particular system involved convicted of contradiction; or are these principles proved repugnant to others, which, as facts of consciousness, every positive philosophy must admit; there is established a relative skepticism, or the conclusion, the philosophy, insofar as it is realized in this system, is groundless." 5 6 Several passages in Maxwell's writings make it clear that he shared this basic point of view—Sir Joseph Larmor called it the "agnostic attitude" toward physics 57 —with his philosophical mentor. For instance, Maxwell stressed the internal consistency criterion in his Encyclopedia Britannica article, "Atom." Here he wrote, "All that is necessary to form a correct mathematical theory of a material system is that its properties shall be clearly defined and shall be consistent with each other." 5 8 Of course he went on to acknowledge that the utility of the theory depends upon the real existence of the chosen system, but the major emphasis was on choosing only self-consistent systems to investigate. That self-consistency and consistency with a set of phenomena are sufficient as well as m

Discussions on Philosophy, p. 87. Sir Joseph Larmor, Aether and Matter (Cambridge: Cambridge University Press, 1900), p. 28. ^Scientific Papers, Vol. 2, p. 467. 57

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necessary conditions to warrant consideration of a theory already known to conform with the results of established science is evident from Maxwell's introduction to his first paper on kinetic theory, "Illustrations of the Dynamical Theory of Gases." In this paper, Maxwell used the laws of mechanics to determine the properties of an aggregation of perfectly elastic spheres acting on one another during impact. "If the properties of such a system of bodies are found to correspond to those gases," he then argued, "an important physical analogy will be established, which may lead to more accurate knowledge of the properties of matter. If experiments on gases are inconsistent with the hypotheses of these propositions, then our theory, though consistent with itself, is proved to be incapable of ex­ plaining the phenomenon of gases." 59 Whether the molecules of a gas really are elastic spheres or not was, for Maxwell, an unanswerable question given the evidence available. The elastic-sphere model, however, was nonetheless of immense value because it seemed to pro­ vide a representation of gases which was consistent with everything known about gases and about the mechanics of elastic bodies. Maxwell soon abandoned his elastic-sphere theory be­ cause he found that it predicted a relationship between the temperature and viscosity of gases which was not confirmed by experiment; he replaced the elastic-sphere model with one in which molecules were assumed to be centers of forces varying inversely as the fifth power of the distance. 60 This assumption was made purely to simplify certain computational procedures of the theory and the 59 Scientific

Papers, Vol.1, p. 378. Papers, Vol. 2, pp. 32-33. In my attempt to focus on aspects of Maxwell's work related to Common Sense Philosophy, I have cer­ tainly not done justice to a variety of interesting problems connected with the dynamical theory of gases. See P. M. Heimann, "Molecular Forces, Statistical Representation, and Maxwell's Demon," Studies in the History and Philosophy of Science, I (1970) pp. 189-211, for an excellent introduction to Maxwell's central concern with molecular forces, a concern which I have completely ignored. so Scientific

JAMES MAXWELL

principle criterion of its validity or value remained its capacity to prove consistent with experimental results. Finally, Maxwell's concern that his theoretical discus­ sions of one science be consistent with other unquestion­ able scientific results was expressed in the Treatise on Electricity and Magnetism. Speaking of his attempt to develop an acceptable theory of electricity he wrote: In forming the ideas and words relating to any science, which, like electricity, deals with forces and their ef­ fects, we must keep constantly in mind the ideas ap­ propriate to the fundamental science of dynamics, so that we may, during the first development of the sci­ ence, avoid inconsistency with what is already estab­ lished. 61 P. M. Heimann has cogently argued that the phrase "consistent representation" as used by Maxwell in the closing sections of A Treatise on Electricity and Magnetism., 62 carries more than the mere demand for the three forms of consistency we have mentioned so far. In this context Maxwell seems to have been translating Carl Freidrich Gauss's call for a "construirbar vorstelling" of the propagation of electromagnetic forces as a call for a "consistent representation" of that propagation. Here, then, "consistent representation" implies a completeness of knowledge about intermediate mechanisms not con­ tained in Maxwell's other discussions of consistency. 63 In a sense Heimann is correct. But if we keep in mind Maxwell's "agnostic attitude" toward the possibility of discovering the real mechanism of propagation, and his consequent emphasis on criteria of consistency for all hypotheses and theories, we can understand why Maxwell should have chosen to interpret Gauss's phrase as "consis61A

Treatise on Electricity and Magnetism, Vol. 2, p. 210. p. 290-493. 63See P. M. Heimann, "Maxwell and the Modes of Consistent Rep­ resentation," Archive for the History of Exact Science, 6 (1970), pp. 171-213. 62Ibid.,

COMMON SENSE AND THE EXACT SCIENCES

tent representation" rather than "concrete representation" as J. J. Thompson did or "working representation" as Sir Joseph Larmor did. The German term "construirbar" did not by itself carry any connotation to suggest the English term "consistent"; it is a geometrical term implying the constructability of a given figure, and its connotations probably come closer to Thompson's notion ofconcreteness as opposed to abstract than to either Maxwell's or Larmor's notions. Maxwell almost certainly translated "construirbar vorstelling" as "consistent representation" to reinforce his own belief that the sole criterion for judging the value of any model or representation of the mechanism sought must be its consistency with itself, with phenomena, and with the known principles of dynamics.

T H E SPECIAL CHARACTER O F G E N E R A L DYNAMICAL T H E O R I E S

So far we have used a series of Maxwell's phrases, including "physical analogy," "physical hypothesis," "physical theory," "dynamical hypothesis," and "dynamical theory," without clearly distinguishing among them. This has been justifiable because none of the issues discussed has depended upon making these distinctions. When the distinctions were not crucial, Maxwell himself was somewhat casual about the way he used the phrases. Thus, in his "Illustrations of a Dynamical Theory of Gases" he used the terms "hypothesis," "theory," and "physical analogy" all to refer to aspects of one methodological approach to explaining the behavior of gases. 64 Within his general relationalist framework, however, Maxwell did occasionally wish to distinguish between explanatory schemes which depended upon exploiting specific mechanical or geometrical analogies and schemes 6i

Scientiflc Papers, Vol 1, p. 378.

316

JAMES MAXWELL

which involved only considerations of greater generality and certainty (which he called dynamical theories). Robert Kargon has discussed the relationship between Maxwell's physical modeling and his dynamical theories in the following way: A significant point to bear in mind is that both "On Faraday's Lines of Force" and "On Physical Lines of Force," are steps toward a dynamical theory; the analogies and models are heuristic devices and not rep­ resentations of nature. It is, therefore, beside the point to observe, as one commentator has done, that Maxwell "quietly abandoned" the earlier model of the 1861-62 paper. He did not abandon the model; he transcended it. His next paper in this area, "A Dynamical Theory of the Electromagnetic Field," was no longer an inter­ mediate investigation requiring analogies to aid the mind. It was rather a dynamical theory, assuming only the existence of matter in motion by which observed electromagnetic phenomena are produced. Analogies are omitted, not because Maxwell has forsaken them, but because the method of physical analogies was in­ troduced for a prior stage of development of physical theory. 85 Just as Rankine formulated his abstractive method to supplement the method of hypotheses and to give greater generality and certainty to his science of energetics, Maxwell sought to formulate dynamical theories inde­ pendent of any specific hypotheses; like Rankine's ab­ stractive theories, Maxwell's dynamical theories were supposed to be founded only upon experimental evi­ dence and not upon assumptions about intermediate mechanisms. In "A Dynamical Theory of the Electromag­ netic Field," for example, Maxwell asserted that: 65 Robert Kargon, "Model and Analogy in Victorian Science: Max­ well's Critique of the French Physicist,"Journal oftheHistory of Ideas,

30, (1969), p. 434.

COMMON SENSE AND THE EXACT SCIENCES

the conclusions arrived at in the present paper are ind e p e n d e n t of this hypothesis [i.e., respecting the stresses and strains of a physical medium like that assumed in "Physical Lines of Force"], being deduced from experimental facts of three kinds: 1. The induction of electric currents by the increase to the changes in the lines of force passing through the circuit. 2. The distribution of magnetic intensity according to the variations of a magnetic potential. 3. The induction (or influence) of statical electricity through dielectrics. 6 6 Maxwell's intention to avoid the uncertainties of hypothetical models in connection with forming dynamical theories was specifically reiterated in 1876 in "On the Proof of the Equations of Motion of a Connected System." In forming dynamical theories of the physical sciences it has been a too frequent practice to invent a particular dynamical hypothesis and then by means of the equations of motion to deduce certain results. . . . The true method of physical reasoning is to begin with the phenomena and to deduce forces from them by a direct application of the equations of motion. 67 In spite of Maxwell's emphasis on the phenomenal basis of dynamical theories, Kargon has vastly overemphasized the independence of dynamical theory from the notion of physical analogy. In fact, in two places Maxwell demonstrated his belief that dynamical theories merely involved the exploitation of a particularly general physical analogy or "Scientific Metaphor." In 1870 he wrote: The figure of speech or of thought by which we transfer the language and ideas of a familiar science to one with which we are less acquanted may be called Scientific Metaphor. ^Scientific Papers, Vol. 1, p. 564. ^Scientific Papers, Vol. 2, p. 309.

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JAMES MAXWELL

Thus, the words velocity, momentum, force, etc., have acquired certain precise meanings in Elementary Dynamics. They are also employed in the Dynamics of a Connected System in a sense which, though perfectly analogous to the elementary sense, is wider and more general. These generalized forms of elementary ideas may be called metaphorical terms in the sense in which every abstract term is metaphorical. The characteristic of a truly scientific system of metaphors is that each term in its metaphorical use retains all the formal relations to the other terms of the system which it had in its original use. The method is then truly scientific—that is, not only a legitimate product of science, but capable of generating science in its turn. There are certain electrical phenomena again which are connected together by relations of the same form as those which connect dynamical phenomena. To apply to these the phrases of dynamics with proper distinc­ tions and provisional reservations is an example of a metaphor of a bolder kind; but it is a legitimate metaphor if it conveys a true idea of the electrical rela­ tions to those who have already been trained in dynamics. 68 The last paragraph here is a precise description of what Maxwell did in forming his dynamical theory of the elec­ tromagnetic field. Whether we call the process one of establishing scientific metaphors or physical analogies seems to make little difference. How then, do we connect this view of dynamical theory with the view that dynami­ cal theories are somehow different and more directly rooted in phenomena than theories dependent upon specific mechanical models? The answer to this question was eloquently stated in Maxwell's review of Thompson and Tait. Here again he emphasized that the practical interest of dynamical explanations arises out of "the 68Ibid.,

p. 227.

COMMON SENSE AND THE EXACT SCIENCES

fact that real bodies do behave in a manner strikingly analogous to that in which we have proved that the masssystems of abstract dynamics must behave." 69 But more important, the generalized Lagrangian formulation of dynamics purports to contain in its equations only terms corresponding to observable variables and to be indepen­ dent of any assumptions about "hidden" or "inter­ mediate" variables. Thus, a theory based on generalized dynamics which also satisfied Maxwell's consistency criterion automatically satisfies a second extremely im­ portant condition. In Hamilton's terms, it satisfies the law of parsimony. No other theory could account for (be con­ sistent with) the phenomena while making fewer assump­ tions. Maxwell stated this principle in a different but equivalent form: ... when we have reason to believe thatthe phenomena which fall under our observation form but a very small part of what is really going on in the system, the ques­ tion is not—what phenomena will result from the hypothesis that the system is of a certain specified kind? But—what is the mostgeneral specification of a material system consistent with the condition that the motions of those parts of the system which we can observe are what we find them to be? 70 In other words, what are the minimal assumptions needed to generate a fully consistent theory? These will automat­ ically be given by a dynamical theory since such a theory makes no assumptions beyond those necessary to stipu­ late the minimum number of independent variables needed to specify the observable properties of the system. Dynamical theory thus plays for Maxwell almost the same role that abstractive theory does for Rankine. It is that form of theory which contains the greatest degree of cer­ tainty and generality attainable in science. It does so be69 Ibid., 70 Ibid.,

p. 781. p. 781. Emphasis mine.

JAMES MAXWELL

cause it does not go beyond the realm of experience in its assumptions. At the same time, however, this form of theory lacks the suggestiveness of theories which depend upon specific hypotheses or models. Hence, the continued advance of science depends upon exploiting the fruitful suggestions of particular analogies as well as consolidating our gains by encompassing newly discovered phenomena within general dynamical theories.

321

EPILOGUE

WHEN Pierre Duhem characterized nineteenth-century scientific styles in La Theorie Physique: Son Objet, Sa Structure, he isolated at least seven dominant traits which distinguished British physics from the work done in France. He observed that (1) mechanical models employing pulleys, cams, gears, ball bearings, etc., filled the pages of Victorian works in theoretical physics; 1 that (2) some British physicists asserted that producing a model to immitate natural phenomena was equivalent to having a complete understanding of the phenomena; 2 that (3) the models used were frequently chosen without apparent metaphysical concern or justification; 3 and that (4) these models were not even assigned a physical reality. 4 D u h e m added that (5) one could find several alternative and mutually exclusive models applied to the same phenomenon in one theoretical paper, in seeming violation of all canons of logical coherence. 5 H e even thought that (6) the mathematics used by British theoreticians took on the characteristics of their models, imitating "more or less faithfully, the laws of the phenomena under study, as an apparatus of different bodies moving in accordance with the laws of mechanics would imitate the laws of phenomena," 6 and that (7) British theoretical physics therefore depended on a vastly more extensive use of geometrical techniques and vector analysis. 7 To the extent that Duhem's characterization of Victorian style cor'Pierre Duhem, The Aim and Structure of Physical Theory, translated from the second (1914) French edition by Philip P. Wiener (New York: Atheneum Press, 1962, from the Princeton University Press edition of 1954), p. 71. 2 Ibid., p. 72. 3 Ibid., pp. 73-74. "Ibid., p. 75. 5 Ibid., pp. 81-86. e Ibid., p. 79. 'Ibid., p. 77.

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responds with dominant aspects of the exact sciences in Britain during the nineteenth century, it can be largely accounted for by recognizing the role played by Scottish Common Sense Philosophy in providing methodological guides. Duhem's interpretation demands at least some modification, however, and the directions of modification are also suggested by a study of the interaction between Common Sense methodological writings and the scien­ tific work of such men as Rankine and Maxwell. What are we to say regarding Duhem's contention that mechanical models dominated British physics? It is true that the writings of William Thompson (Lord Kelvin) and Oliver Lodge are dominated by models containing springs, pulleys, gyroscopes, gears, etc., and that such artifacts frequently appear in the models used by virtually all Victorian physicists, including those of Rankine, Max­ well, J. H. Poynting (1852-1914), Joseph Larmor (1857— 1942), and J. J. Thomson (1856-1940). But Duhem's ex­ clusive emphasis on the mechanical content of British sci­ entific models hides more of the story than it illuminates. Not only does it fail to take into account geometrical mod­ els, but it also ignores the connection between specifi­ cally mechanical models and the rise of modeling in gen­ eral as an accepted method in the exact sciences. Duhem's critique of British modeling procedures seems particularly misguided; for though he explicitly acknowledges that "the history of physics shows us that the search for analogies between two distinct categories of phenomena has perhaps been the surest and mostfruitful method of all the procedures put in play in the construc­ tion of physical theories," 8 he does not seem to see that the use of mechanical models is a direct outgrowth of this general awareness of the power of analogy. In fact, Duhem argues that we should not confuse the appeal to physical analogy with the use of models. 9 If we are to understand the growth of a pattern of mechanical model­ ing in British physics, however, we must see it as a final 8Ibid.,

pp. 95-96.

9Ibid.,

p. 97.

EPILOGUE

stage in the development of a growing methodological emphasis on analogy which originated among eighteenthcentury Scottish philosophers and scientists. Starting with Dugald Stewart's methodological discussions, there was a great emphasis in the Scottish tradition on the ex­ ploitation of analogies to suggest hypotheses and theories. This emphasis was taken up almost immediately by Scot­ tish scientists like John Playfair and John Leslie, and made into a guiding principle of scientific method by James David Forbes and his student, James Clerk Maxwell. Initially, the principal emphasis within the tradition (following Stewart and Boscovich) was on the exploitation of analogies between sets of natural phenomena or sys­ tems of thought to suggest hypotheses for testing. There was no conscious attempt to think of one set of phenomena or one theory as a "model" for another. Thus Leslie exploited the analogies between heat and electricity to suggest the hypothesis that the flow of electricity from a charged body might follow a pattern similar to Newton's law of cooling. Similarly, he exploited the phenomenal analogies between heat convection and electrical dis­ charge to justify a convection theory of electrical transfer in gases. One of the main justifications for an emphasis on analogical processes at this stage came from Newton's dictum, emphasized by Reid and Stewart, that no more causes of phenomena should be called for than are neces­ sary so that similar phenomena should be explained by the same or similar mechanisms. Gradually it became common to place increasing em­ phasis in scientific arguments on investigating the proper­ ties of the analogue to be exploited. Thus J. J. Waterston's great paper on kinetic theory was predominantly a study of the properties of an ensemble of perfectly elastic collid­ ing spheres. Whether gases were composed of such spheres was not at issue. Waterston merely attempted to develop in detail the properties of the hypothetical sys­ tem and to see the extent to which these properties cor­ responded with those of gaseous media. Much the same approach was used by Maxwell in his papers on kinetic

EPILOGUE

theory and in his early papers on electromagnetic theory, and by Rankine in his papers on the molecular vortex theory. In all these cases, the system whose theory was developed was expected only to provide analogies with important natural phenomena. The systems were being used as models of mechanisms underlying phenomena. F ew of the models used by British physicists during the first t\yo-thirds of the nineteenth century were mechani­ cal models in the sense apparently meant by Pierre Duhem. In fact, only Maxwell's vortex model of an elec­ tromagnetic medium in "On Physical Lines of Force," among those mentioned so far, would fall into such a classification, because of its use of "idle wheels" between vortexes. Nearly all the models were mechanical in a more general sense, however. They were based upon consider­ ations of matter in motion. To understand why such gen­ erally dynamical models had particular appeal is rela­ tively easy. Among phenomena available to be used as models or analogues, none but dynamical phenomena were capable of satisfying a host of explicit demands made by Rankine and Maxwell but initially suggested and codified by Common Sense philosophers. All Common Sense philosophers from Reidto Hamilton had joined in insisting that any hypothetical entity posited to account for phenomena must 1) have its existence es­ tablished independent of the phenomena for which it is being used to account, 2) be fully understood in itself, and 3) be simpler than the phenomena for which it is expected to provide an explanation. These criteria were initially established, of course, to limit candidates for reality, and there is no α-priori reason that they should have been retained as demands upon models not intended to have any ontological significance. Butthe discussions of Max­ well and Rankine make it very clear that their models were intended to satisfy these conditions. Maxwell, in particular, emphasized the independent-existence criter­ ion. Rankine emphasized both the simplicity argument and the demand that the explanatory model should be

EPILOGUE

understood in full. Furthermore, for Rankine and Max­ well, as well as for Thomas Brown and the immensely influential John Herschel, the phenomena of dynamics (of matter in motion) alone satisfied all of these criteria. The existence of material bodies was unquestioned among scientists, the laws of dynamical systems were fully worked out, and they seemed to have a suitable simplicity. Thus, dynamical models, hypotheses, or theories, became the natural source of analogies in virtu­ ally all other fields. Particular mechanical hypotheses or models (in Duhem's sense) are, of course, one type of dynamical model—a type whose special psychological appeal to Vic­ torian Britons can certainly be understood, as Thomas Brown pointed out, because of the cultural importance of mechanical artifacts in their rapidly industrializing and modernizing society. Hence, for both epistemological and psychosocial reasons, the use of mechanical models was legitimized in the works of Maxwell and Rankine. Neither of these men was satisfied with the exclusive use of particular mechanical hypotheses or models, how­ ever. Each saw such models as appropriate to one stage in physical theory construction but hoped to get beyond that stage to one of greater certainty and generality. Their search for greater generality was again consciously con­ nected to general methodological considerations which had been discussed among Common Sense philosophers and by Sir John Herschel. Particular models or hypoth­ eses served a primarily suggestive function and provided a kind of "scaffolding" for the erection of theories grounded solidly in inductive generalization. This idea had been nascent in the writings of Stewart and Brown, who kept insisting that suggestive analogies formed only the starting-point for thoroughly grounded theories, and it was fully developed by both Herschel and Rankine. Turning from the importance of the mechanical model tradition in British physics, letus assess Duhem's related assertion that British physicists believed that to under-

EPILOGUE

stand a phenomenon and to produce a mechanical model of the phenomenon were equivalent acts. There is no doubt that William Thomson's assertion, "It seems to me that the test of'do we or do we not understand a particular subject in physics?' is 'can we make a mechanical model of it?' " 10 is strong support for Duhem's contention. Al­ though few other late Victorian physicists would have gone so far, many, including M. H. Poynting, Joseph Larmor, Oliver Lodge, and J. J. Thomson, certainly felt that an important element of physical understanding was an ability to form a mental picture or mental image of the physical phenomena being considered. 11 But the em­ phasis on mental images among most Victorian physicists is not quite the same as Kelvin's emphasis on mechanical models as interpreted by Duhem, and again the distinc­ tion can be understood in historical terms. One of the most frequent loci of appeals to the need for mental images in physical-theory construction was the annual address of the president of the mathematical and physical section of the British Association, for which Maxwell's address of 1870 set the precedent. Thus, there is good reason to see Maxwell as the central figure in propagating the British emphasis on pictorial imagery. 12 Furthermore, when we look at Maxwell's reasons for em­ phasizing the role of visualizable or physically interpretable elements in scientific theory, we come face to face 10 Ibid., p. 71. Quoted from W. Thomson, Lectures on Molecular Dy­ namics (Baltimore, 1884), pp. 131-132. 11 The terms "mental picture" and "mental image" were widely used by Victorian physicists. See, for example, J. H. Poynting, Report of the BritishAssociationfortheAdvancementofScience (1899), pp. 618-620; J. J. Thomson, Electricity and Matter (Westminster, 1904), p. 16, and "Tendencies of Recent Investigations in the Field of Physics," Broad­ cast National Lectures (London, 1930), pp. 15-16; Joseph Larmor, Re­ port of the British Associationfor the Advancement of Science (1900), p. 627; Oliver Lodge, My Philosophy (London, 1933), p. 110. 12 I share the emphasis on Maxwell as the central figure in Victorian physics with Robert Kargon (see "Model and Analogy in Victorian Sci­ ence . . ,"Journal of the History of Ideas, 30 [1969], pp. 435-436.) in opposition to Duhem's emphasis on William Thompson (Lord Kelvin).

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with epistemological and pedagogical arguments from Common Sense Philosophy. From the earliest writings of Reid and Stewart, Common Sense philosophers had insisted that any term supposed to apply to the material world would have a clearly determined sensory referent. Moreover, they argued that abstractions for which the sensory referents did not appear evident were susceptible of misinterpretation, and that reasoning which involved such abstractions failed to provide the mental training and strengthening which was a desideratum of all thought. William Hamilton, Maxwell's mentor in logic and metaphysics, was particularly adamant on this last point, and Maxwell referred explicitly to the mental-training argument when he emphasized the desirability of being able to form a mental construct of all entities of both physics and mathematics. Even if we acknowledge that it was out of Common Sense Philosophy by way of the writings of James Clerk Maxwell that the British emphasis on pictorial imagery (and also on embodied mathematics, like vector analysis) was originally generated, we are still left with the question of whether the construction of a mechanical model or a self-consistent mental image was widely accepted as both a necessary and a sufficient condition for extablishing an "understanding" of a physical phenomenon. This study, of course, has offered nothing to justify any inferences about the beliefs of those who followed Maxwell's lead on this topic. But we can say something about Maxwell's opinions and those of his near contemporary, William Rankine. Rankine certainly did not see model construction as necessary in the formulation of scientific knowledge, and his discussion of abstractive theories makes this very clear. Even though much of his best work involved the exploitation of the molecular vortex model or hypothesis, he followed the long line of Common Sense philosophers and John Herschel in granting highest status to general theories which were hypothesis- and modelindependent. Because such abstractive theories were in 329

EPILOGUE

some sense "better" than hypothetical ones, it is also true that for Rankine the creation of a model of any kind could not in itself be sufficient to establish scientific knowledge of the highest kind. Maxwell's views were slightly different. Though by training and preference he sought to establish a model or a "consistent representation" of the mechanisms supposed to underlie any phenomenon of interest, he was willing to admit the validity—if not the psychological appeal—of alternative approaches. In this sense, model-building was not a necessary step in the formulation of scientific knowledge. On the other hand, because of his belief—again engendered primarily in connection with his Hamiltonian philosophical position—that one could never know more than relations among phenomena, Maxwell did seem willing to accept the establishment of a "physical analogy" between one set of phenomena (which we might call the model) and another set—that to be explained—as constituting scientific knowledge. In this sense he did see the construction of a model of a phenomenon as sufficient to the understanding of it. Duhem's assertion that the models chosen by British physicists were often generated without care to ensure their conformity to any accepted scheme of metaphysics, and that the models were not encompassed within a tightly knit logical system of great generality, is to some extent true of the models used by the scientists discussed in this study. J. J. Waterston's elastic-sphere model of gases, for instance, was apparently developed with full realization of the philosophical critique of impact explanations. And Maxwell used first an impact model and then a center-of-force model in his papers on kinetic theory even though he had previously established his philosophical preference for field theoretical models in "On Faraday's Lines of Force." Though in some cases the failure of British scientists to provide a broad, metaphysically justified context for a given model grew out of a more or less ignorant and 330

EPILOGUE

disdainful attitude toward metaphysics, this was not true of Maxwell. Maxwell was fully cognizant of and concerned with metaphysical questions about the nature of matter and reality. Furthermore, the emphasis on field theory in his work on electromagnetism was, as we have seen, consciously related to metaphysical and epistemological arguments derived from Hamilton about the primacy of the whole in perception and the derivative nature of the notion of isolated parts. How then are we to understand Maxwell's willingness to use models in kinetic theory which presumed a metaphysics which was uncongenial to him? A large part of the answer to this question lies in his realization that certain metaphysical questions were unanswerable in our present—and probably even in any future—state of knowledge. Thus, the adoption of action-at-a-distance or fieldtheory approaches to physical questions was to some extent merely a matter of preference, assuming, of course, that either stance was capable of producing a theory in conformity with phenomena. This realization is most fully apparent in Maxwell's emphasis (again following Hamilton) on internal consistency, correspondence with phenomena, and consistency with other established scientific (i.e., phenomenal) knowledge as the sole criteria for the acceptability of a scientific theory. A second consideration probably played some role in Maxwell's willingness to use models with quite varied metaphysical implications in his work, as it played an even greater role in the concerns of such men as David Brewster. If the value of a model or hypothesis depends more upon its suggestiveness than upon its "truth," then we need not be deeply concerned about the metaphysical pedigree of the model. Of all the points made by Duhem, this is perhaps most crucial in understanding the radical divergence of nineteenth-century British physics from the earlier Newtonian tradition and from Continental Positivist and Idealist traditions. And one of the prime spurs to the acceptance of hypothesis and models which 331

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were not expected to provide the true unfolding and exposition of the mechanisms of nature arose in connection with Common Sense considerations. Although Francis Bacon had asserted that the truth emerges sooner from error than from ignorance, Dugald Stewart was the first British philosopher to emphasize strongly that even erroneous hypotheses could be tremendously fruitful in guiding research and in leading to their own correction. John Leslie and Henry Brougham used arguments very much like Stewart's to justify the use of hypotheses and theories which they personally felt to be incorrect in fundamental ways. But David Brewster presented the argument in its most unequivocal form when he argued in favor of using an undulatory theory of light based on the assumption of a luminiferous ether, even through as a physical hypothesis (i.e., as a statement of what nature is rather than of what it might possible resemble) such a theory was insupportable. This emphasis on fruitfulness rather than on reality or truth, combined with the Common Sense emphasis on the importance of analogy, provided great impetus to the transformation of concerns with the problems of hypotheses as potentially true statements of natural circumstances into concerns with the value of models as suggestive statements about natural relationships. By the time Maxwell and Rankine began to write, there was general agreement—at least in the Scottish philosophical and scientific community—about the immense heuristic value of models and hypotheses as long as they were acknowledged as suggesting only what nature is like, not what nature is. The suggestive or heuristic use of models discussed here also bears on two other characteristics of British physics enunciated by Duhem. As Duhem pointed out, it was quite possible, given this interpretation of the use of models and analogies, to have several alternative acceptable models or theories of the same phenomena. Stewart had pointed out that exploiting diverse sources of analogical insight strengthens rather than weakens our 332

EPILOGUE

understanding of phenomena, and Maxwell quite consciously argued for the desirability of having alternative theoretical approaches to a phenomenon. In many cases, the existence of alternative models in one theoretical discussion did give the impression that British scientists were not concerned about logical coherence. To the extent that logical coherence demands that every single statement of a discussion is logically tied to every other statement, Duhem was correct: the multiplicity of models used by many British physicists does violence to coherence. But, as we have seen with Maxwell, this does not mean that the discussion of each model could be carried on without careful attention to the coherence of the argument regarding its properties. Nor does the fact that a variety of provisional models was used in the hypothetical stage of developing scientific knowledge mean that logical closure was not a crucial concern in what Rankine would call the abstractive stage or in what Maxwell saw as the dynamical (as opposed to mechanical) theory stage of scientific explanation. Finally, let us turn to Duhem's contention that British scientists tended to use less Classical analysis and more geometry and vector analysis than did their Continental counterparts, and that they expected their mathematical treatments to act as models, imitating the laws of the phenomena under study. Maxwell's writings, Rankine's famous paper "On the Geometrical Representation of the Expansive Action of Heat and the Theory of Thermodynamic Engines," and P. G. Tait's fascination with quaternions, culminating in his Elementary Theory of Quaternions of 1867, all give credibility to Duhem's assertion. All three of these men began learning their mathematics in the Scottish geometrical tradition, and all were exposed to Common Sense interpretations of the nature of mathematics, the relation of mathematical entities to tactile experience, and the value of keeping the entities being considered before the imagination while one is reasoning in mathematics. Maxwell, moreover, 333

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used Common Sense arguments to justify his preference for geometry and such "pictorial" schemes as vector analysis; and his philosophical attitude can be seen as firmly within a tradition of Scottish mathematics with clear precedents in the works of such men as Robert Simpson, John Playfair, and John Leslie. Later Cambridge-trained physicists like George Cayley and Oliver Heaviside did not have the same early geometrical training or the same philosophical reasons for undertaking investigations of vectorial analysis that Maxwell and Tait did. But to the extent that Tait's and Maxwell's writings were important in introducing the ideas of quaternions and the associated vector analysis into British physics and in promoting the value of "embodied mathematics" among British scientists, their philosophical biases were extremely important. The study of the interaction between Common Sense Philosophy and the exact sciences in Britain discloses a number of interesting phenomena not associated with Duhem's characterization of British scientific sytle. By bringing to light the prominence of the methodological criterion of independent existence for acceptable hypotheses, it helps to account for an important tradition of opposition to etherial explanations. Thus, we can understand the motivation underlying critical arguments of John Playfair against a variety of gravitational theories, of John Robison and John Leslie against fluid theories of electricity, and, most importantly, of Henry Brougham, David Brewster, and W. J. M. Rankine against the dominant interpretation of the wave theory of light with its implicit assumption of a luminiferous ether. Additionally, the intimate connection between Common Sense epistemological and methodological discussions and the writings of Roger J. Boscovich helps to account for the vogue of Boscovichian natural philosophy in early nineteenth-century Scotland which is associated with John Robison, John Leslie, Henry Brougham, and 334

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Thomas Thomson. And the qualified endorsement of speculative theorizing by Common Sense philosophers also helps to explain why John Dalton's atomistic theories recieved their earliest support from Edinburgh-trained chemists like Thomas Thomson and William Henry.

335

I N D E X

Aberdeen Philosophical Society, 27,49 Abstract ideas (see Mathematics, objects of) sciences, 257-258, 282-283 terms, most certain, 92-93 terms, subject to misinterpretation, 89-90, 329 Abstraction basis for classification, 74-75 defined, 75 in mathematics, 67, 73-77, 87, 89, 92, 329 opposed to "field" approach, 293-294 Abstractive theory, 281-286, 317, 320, 329, 333 Academy of Physics, 11, 125 Action-at-a-distance, 99, 159, 162, 197, 243, 278, 296, 307, 330, 331 Aepinus, Franz, 160,195,196,203, 209 Agassiz, Louis, 229 Air as agent of electrical conduction, 202-207 as agent of heat transmission, 201, 215 Alembert, Jean, d', 62, 92-93, 118, 160 Algebra (see Analysis) Analogical reasoning ,(see Analogy)

Analogy attitudes toward, of R. J. Boscovich, 108, 119 attitudes toward, of Thomas Brown, 95, 96 attitudes toward, of P. Duhem, 324 attitudes toward, of J. D. Forbes, 226-228 attitudes toward, of Wm. Hamilton, 146-149, 152, 290 attitudes toward, of J. Leslie, 211 attitudes toward, of J. C. Maxwell, 288-293, 299, 302, 320-321 attitudes toward, of T. Reid, 34, 48-53 attitudes toward, of D. Stewart, 96, 106, 114-121 passim between circular and hyperbolic functions, 165-167, 189 between gases and media composed of perfectly elastic bodies, 246-249 between glaciers and rivers, 226, 230-232 between gravitation and other phenomena, 239-240 between heat and electricity, 196, 200-201, 207-209, 325 between heat and light, 226-228 between heat and sound, 215 between laws of molecular phenomena and laws of motion, 281

337

INDEX Analogy —Continued between reflection and refraction, 220, 223 implication of in doctrine of ideas, 48-52 mentioned, 3, 4, 6, 17, 26, 167', 219-220, 232, 240, 325-327, 330 physical, 6, 235, 250, 251, 290, 292, 299^300, 302, 314, 3 1 6 319, 324, 330 real, in nature, 289-292 strictures on use of, 116-119 variation of, desirable, 118, 292, 293, 295, 296 Analysis criticized by Stewart, 84, 90 compared to geometry, 20, 21, 22, 89-91, 160, 164-169, 188192, 298, 302-303, 304, 333 lauded by D'Alembert, 92-93 lauded by Lagrange, 92-93 prized by continental scientists, 3, 91-93 shunned by British scientists, 4, 6, 332-333 Anatomists, 39, 114-115, 116 Apostles Club, 289, 290, 292, 299 Aristotle, 58, 121, 132, 139, 272 Atheism, 28, 3 1 , 70, 160 Atomism Boscovichian, 6, 99-106, 2 1 1 213, 221 Brown's, 129 Daltonian, 185-186, 233, 248, 277, 280, 335 Rankine's, 274-275 J. J. Waterston's, 243 Axioms (see "First Principles")

Bacon, Sir Francis, 6, 15, 32, 34, 43, 94, 96, 120, 161, 226-228, 238, 255, 265, 332

Beattie, James, 6, 27-33 passim, 49,58-59,62-65 passim, 71,132, 161, 178 Berkeley, George, 81, 84-85, 88, 188, 259-260 Black, Joseph, 157, 159, 161 Boscovich, Roger Joseph 6, 98 -105,108-109, 114, 116, 159, 163, 170, 196-197, 210214, 221, 325, 334 Brewster, David, 6, 178-187 passim, 224, 237, 238, 246, 250, 251, 331, 332, 334 British Association for the Advancement of Science, 178, 236, 297, 309, 328 British Scientific Style (see Scientific Styles) Brougham, Henry, 6, 11, 125, 191, 192, 332, 334 and Herschel's Preliminary Discourse, 253-254, 258 reviews by 172-177, 180, 186189 work in optics, 219-224 Brown, Thomas central doctrines of, 62-65, 9 4 98, 111-114, 125-130 mentioned, 3, 26, 35, 71, 117, 125, 131, 134, 142, 149, 152, 157, 180, 225, 242, 243, 289, 290, 293, 327 relationships to work of Hamilton, 133, 136, 137 relationship to work of Herschel, 253, 257, 261-269 passim relationship to work of Playfair, 164-168 relationship to work of Rankine, 277-278

Cajori, Florian, 22, n. 20 Cambridge University, 12,66,289

338

INDEX Campbell, George, 27, 31, 49, 60, 74, 77, 89, 117-118, 132, 255 Cantor, Geoffrey, 174 Causal Principle justified by Hamilton, 133-141 passim justified by Kant, 137 justified by Reid, 42 Causation (see Cause) Cause Brown on, 125 efficient, 42, 44, 95, 106, 258259 essential, 47, 94-95 Herschel on, 252, 258-264, 266 Humian notion of, 16,42^7, 94, 106, 125, 180, 197, 260-264 independent existence of, 4142, 140, 176, 180, 209, 286 physical, 43, 260-261 proper, 43, 258-259 Reid on, 41—46 Cavendish, Henry, 183-184, 195 Certainty available only in non-hypotheti­ cal sciences, 46, 286 in mathematics, 56, 61-65, 81 sought, 38-39, 47, 53, 131, 185, 313, 317, 320, 327 Cipher (see Cypher) Clarke, Samuel, 49-50 Clausius, Rudolph, 250, 272, 311 Cognitive Faculties (see Human Understanding) Coherence as criterion for selecting hypoth­ eses and theories, 111, 143145, 151, 153, 199, 313-316, 320 fundamental psychological need, 122, 323 lack of concern for, 331-333 Combe, George, 150 Common Sense philosophy

aims of, 28 anti-intellectualism of, 30-31 defined, 29-30 origins of, 27 scientific method as key to, 34 principles of, 29-30, 46, 57-62, 141-142 Comte, Auguste, 179-182 passim, 289 Conditioned, Law of (see Law of the Conditioned) Conduction (see Heat) Conjectures (see Hypotheses) Consistent Representation, 312316, 330 Contact Action (see Impact) Continuity, Law of, 99-100, 202203, 212 Convection (see Heat) Copernicus, 120 Corpuscular theory of light, 102, 120 Criteria forjudging value of hypotheses (see Hypotheses, criteria for accepting) Cullen, William, 148-149 Cypher, 109-110, 163

Dalton, John, 185, 247, 335 his atomic theory, 6, 185-186, 233, 247-248 Darwin, Erasmus, 35 Davie, George Elder, 3, 20, n. 16, 235 Davy, Humphry, 185 Definitions (see "First Principles") Descartes, Rene, 37, 40, 53, 241, 304 Description as primary goal of natural philos­ ophy, 43,44,95,105, 106, 284

INDEX Determinism avoided by Hamilton's causal principle, 140-141 Maxwell on, 289 opposed, 29-30, 117, 160 related to materialism, 105 related to mathematics, 70 Dewey, John, 14 Duhem, Pierre, 3,4,5,7,251,297, 323-334 passim Dynamical Theories, 295, 297, 306, 307, 308, 310, 312, 314, 316-θ21, 326-327, 333

mentioned, 42, 159, 160, 162164, 169-176, 180, 196, 245, 269, 296, 310, 311, 334 Etherial Media (see Ether) Euclid, 57, 64, 86 Euler, Leonhard, 160, 176, 192 Explanation as function distinct from gen­ eralization, 265-266,282,284, 316-317 d e m a n d for leads to hypotheses, 266 Extension tangible vs. visible, 84-88

Edinburgh Review, 66, 125, 173, 196, 174 Edinburgh, University of, 7, 67, 125,131,157,158,172,178,225, 235-236, 271, 287 Electric Fluid, 160, 171-172, 196, 198-200,206,209,278-279,334 Electricity Leslie's studies of, 195-210 electrostatics, 195-207 conduction, 207-210 Morgan's view on, refuted, 171— 172 Electricity and Magnetism Maxwell's work on, 290, 294, 295, 296, 297, 299, 302, 304, 306, 307, 308, 310-311, 315, 317, 318, 319, 326, 331 Embodied Mathematics, 301,302,

Falsification, 112-113, 143, 151, 152, 188, 286 Faraday, Michael, 290, 295, 296, 302, 303, 317 Field Theories development of encouraged by Scottish philosophy, 5 Maxwell's preference for, 294, 295, 307, 330-331 "First Principles" mathematics demonstrates im­ portance of, 56-62 passive acceptance of, 68 role of, emphasized by Reid, 34, 56-57 Forbes, James David, 6, 225-236 passim, 238, 272, 287, 291, 325 Fourier, Joseph, 7, 307 Franklin, Benjamin, 196,203,209 Free Will (see Determinism)

303, 329, 334 " E n e r g e t i c s " (see Thermody­ namics) Error, Avoidance of (see Certainty) Ether gravitational, 112,162-164,172, 197, 242-243, 278 luminiferous, 6, 160, 173-182, 184-185, 275, 279, 310, 334 medulary, 38-39, 47, 140, 170172

Galileo, 44, 106-107 Gall, Franz Joseph, 150, 152 Gases, Kinetic Theory of (see Kinetic Theory) Gassendi, Pierre, 120 Gay-Lussac, Joseph Louis, 247249 General Education (see Liberal Education)

340

INDEX Generality demand for, 4 5 - 4 6 , 4 8 , 1 0 7 , 1 3 3 134, 164, 232, 265, 267, 284, 286, 327, 329 excessive, 90-91 satisfaction of demand for, function of abstractive theory, 282 dynamical theory, 317-320 Genius role of in philosophy criticized by Reid, 37 Geometrical Techniques (see also Geometry) distinguished from analytic, 67, 89-91, 160-161, 300-304 J. C. Maxwell on, 295, 297-298, 302-307, 334 role of in British scientific style, 3, 4, 6, 333-334 role of in Scottish mathematical education, 20, 236 Geometry (see also Geometrical Techniques) epistemic superiority to analysis, 89-91, 164-167, 188-192 mind training character of, 2 1 22, 24, 67, 68, 254-257, 329 non-Euclidean, 84, 86-87 pedagogic superiority to analysis, 21, 24, 161 role of in liberal education, 20, 23-24, 67, 254-257 tactile foundations of, 84-88 geometry of visibles, 87 Glaciers early theories of motion of, 230 Forbes' viscous theory of, 2 3 0 232 Hopkin's theory of, 233-234 God belief in justified by analogy, 147-148, 290 omnipresence and omnipotence of, 50, 105, 122

ensures regularity of world, 45, 52 Reid on wisdom of, 39 Goethe, 67 Graham, Thomas, 248 Grave, S. A., 34 Gravity (see also Ether, gravitational) causes of, 36,106,162-164,210212, 213, 244 relation of to other phenomena, 239-240 Gregory, James, 72, 82, 83, 125 Gregory, John, 27-30, 32, 35, 45, 47, 48, 110, 226, 265

Hamilton, Sir William, Bart, central philosophical doctrines of, 131-149 passim mentioned, 3, 6, 26, 35, 46, 51, 55,87,111,113,117,119,225, 235-236, 270, 326, 329, 331 on mathematics, 21-22, 62-71 passim on phrenology, 149-152 relationship to work of Thomas Brown, 126, 130 relationship to work of James Clark Maxwell, 271, 287-294 passim, 301, 308, 313, 320 relationship to work of Adam Smith, 121-123 Hamilton, William Rowan, 303, 304, 306 Hartley, David, 8, 28, 34-40 passim, 47, 54, 109-111, 161, 170, 209 Heat conduction of, 218-219 convection of, 215, 216, 219 fluid theory of, 213-214 J. Hutton's theory of, 215 J. Leslie's studies of, 200-201, 205, 210-219

341

INDEX Heat—Continued radiation of, 215, 217-219, 227, 229, 275 Rankine's theory of, 274, 276, 277 specific (see Specific Heats) Waterston's theory of, 245 wave theory of, 213 Henry, William, 185, 335 Herschel, Sir John central philosophical doctrines of, 252-270 passim mentioned, 6, 7, 66, 235, 327, 329 on mathematics, 254-258 relationship to work of Brougham, 253-254 relationship to work of Brown, 253, 255, 257, 261 relationship to work of Rankine, 273, 278-285 passim Hopkins, William, 233-234, 302 Horner, Jeffery, 125 Human Understanding knowledge of underlies all sciences, 13-14, 36, 126-127 science of urged, 11, 28, 33-34 Hume, David causal principle, 42-43, 106107, 125, 162, 180, 182, 197 mentioned, 31,34-36,38,44,47, 59, 75, 76, 81, 94, 150, 212, 260, 272 principal opponent of early Common Sense Philosophy, 28 science of human nature as key to all studies, 11, 13, 32, 126 Hume Papers, 75-76 Hutcheson, Francis, 32, 54, 82 Hutton, James, 19, 20, 161, 214215 Hypothesis attitudes toward on the part of, Boscovich, 108, 114, 212

attitudes toward on the part of, Brewster, 178, 180, 184, 238 attitudes toward on the part of, Brougham, 175, 186-187 attitudes toward on the part of, Brown, 95, 108 attitudes toward on the part of, Comte, 179 attitudes toward on the part of, Gregory, 110 attitudes toward on the part of, Hartley, 38-40 attitudes toward on the part of, Herschel, 253, 266-270 attitudes toward on the part of, Kames, 40 attitudes toward on the part of, Leslie, 187 attitudes toward on the part of, Maxwell, 296-297, 299-300, 308-312, 314-316, 318 attitudes toward on the part of, Rankine, 277-281, 284, 286 attitudes toward on the part of, Reid, 34, 36-42, 47, 114 attitudes toward on the part of, Stewart, 95,108-111,114,188 attitudes toward on the part of, Whewell, 182-184 criteria for accepting (see also Coherence, Independent Existence, Simplicity), 109, 111, 120, 124, 138-141, 149, 151-152, 176-177, 180, 203, 267-268, 278-281, 312-315 distinguished from theory, 112, 124, 168, 174 French molecularist, 308 mathematical, 64, 72 mentioned, 6,26,42,47,98,316, 331-332 of molecular vortices explained, 273-277 justified, 277-281

INDEX Hypothesis—Continued mentioned, 285, 326, 329 transcended, 282 physical, 296, 299, 316 self-correcting, 118, 216-219, 332 simplicity of, 120,268-269,278279 used by Leslie, 196, 200, 203, 205, 208, 211, 216-219 Hypothetical Realism, 144-146

Invisible Entities assumed by Waterston, 243 Jefferey, Francis, 195 Joule, James P., 248, 276, 277

Idealism, 30, 5 1 , 105, 142, 185 Ideas doctrine of, 36-37,42,48-52,54, 103, 117 as intermediate variables, 42,50 Images (see Ideas) Imaginary Quantities, 89-91,164167, 188-192 passim Imagination role of in theorizing, 5, 37, 122123, 238, 333 Impact theories of interaction of matter, 99, 103, 162, 196-197, 212213, 330 criticized, 100-103, 162 Maxwell's attitudes toward, 295 used by Waterston, 243-249 Impenetrability of matter, 100 Impossible Quantities (see Imaginary Quantities) Independent Existence Criteria for Causes, Hypotheses, etc., 41-42, 140, 176, 180, 209, 286, 308-312, 326, 334 Induction method of, 11,27, 34, 94, 97, 99, 226, 232, 266, 269, 282, 285, 286 principle of, 46-47, 60, 113, 134 Intermediate variables or causes, 42,171,212, 320

Kames, Lord, 40, 130 Kant, Immanuel, 5, 8, 14, 32, 135, 142, 144, 239, 288 Kantian Philosophy analyzed by Thomas Brown, 125 causal principle in, 137 mentioned, 5, 64, 121 relationship to work of Hamilton, 131, 135, 137 similarities to Common Sense Philosophy, 32 Kargon, Robert, 309, 317, 318 Kellard, Phillip, 236, 287 Kelvin, Lord (see Thomson, William) Kinetic Theory of Gases Clausius papers on, 249, 273, 311 Maxwell's, 295, 297, 311-312, 314, 326, 330, 331 Waterston's, 243-249 passim response to, 249-251, 325 Kuhn, Thomas, 209 Lagrange, Louis, 93,160,188,192, 306, 307, 320 Language analogical use of, 49, 171 Campbell's theory of, 74-75, 117-118 mathematical vs. philosophical, 55, 61-62, 68-69 Laplace, Pierre S., 90, 192, 303, 307 Larmor, Sir Joseph, 313, 316, 324, 328 Lavoisier, Antoine, 187, 216 Law of Continuity (see Continuity, Law of)

343

INDEX Law of the Conditioned, 137-138 Law of Nature descriptive, equivalent to cause, 43, 44, 105, 260-261, 263 general, goal of natural philosophy, 44, 163, 264-265 imposed upon nature by man, 135 mentioned, 98, 113 non-mathematical, 54 Law of Parsimony Hamilton, 138-141 Maxwell, 320 Newton's version, 41 Leibniz, Gottfried Wilhelm von, 98, 99, 105 Le Sage, George Louis, 163 Leslie, John attitudes toward etherial media, 171-172, 195197 Lavoisier's system, 187 mathematics, 23-24, 190-193 his electrical studies, 195-209 passim his heat studies, 210-219 passim mentioned, 6, 16, 186, 223, 225, 227, 236, 243, 278, 325, 332, 334 relationship to works of R. J. Boscovich, 210-216 passim relationship to works of James Hutton, 214-216 Liberal Education decline of after J. D. Forbes, 235 emphasis on in Scotland, 13, 18 role of mathematics in (see Mathematics) role of natural philosophy in, 19 Light Brougham's studies of, 219-224 particulate theory of, 221 Rankine's molecular vibration theory of, 274-275

wave theory of accepted, 267, 310 analyzed, 177-182, 184-187 attacked, 5,173,179-180,220, 223-224 mentioned, 174, 176, 227, 228, 277, 334 Limitations of Human Capacities as goad to science, 45, 128-130, 133 and Law of Conditioned, 139140 Maxwell's concern with, 2 8 8 290 Locke, John, 15, 38, 80, 103, 272 Logic vs. mathematics, 66-71 passim Mach, Ernst, 107 Malbranche, Nicolas, 62, 91-92 Materialism, 28-30, 40-42, 102105, 142 Mathematics analytic (see Analysis) attitudes toward character of expressed by Brougham, 188-189 attitudes toward character of expressed by Forbes, 232235 attitudes toward character of expressed by Herschel, 257-258 attitudes toward character of expressed by Leslie, 190193 attitudes toward character of expressed by Maxwell, 297-298, 300-307 axioms of, 57-62 desensitizing character of, 6 7 68, 70 distinguished from philosophy, 55, 61-72 passim, 80-83, 254-258

344

INDEX Mathematics—Continued geometrical (see Geometrical and Geometry) Embodied (see Embodied Mathematics) in liberal education, 23-25, 6671, 254-256 as model for Common Sense philosophers, 33, 55-62 passim necessary aspects of, 59, 63-64, 69 objects of, 54, 62-65, 69, 72, 75-77, 79-81, 84-88, 92 pedagogical theory of, 20-25 proper quantities of, 82, 88 relation to experience of, 72-88 passim, 257-258, 297, 301, 303-304, 329, 333 Maxwell, James Clark as archetypal Victorian physi­ cist 7, 324-334 passim attitudes toward analogies, real in nature, 289-293 analogies, physical, 290, 299, 316, 317, 330 analogies, variation of, 297298 consistent representations, 312-316 dynamical theories, 307-311, 316-321 embodied mathematics, 301306 independent existence cri­ teria, 310-312 kinetic theory, 311-312, 314 mentioned, 4, 6, 35, 91, 116, 118, 177, 185, 235, 236, 250251, 270-271, 320 relationship to work of Hamil­ ton, 271, 287-294 passim, 301, 308, 313

scientific work of, 287-321 passim Melloni, Marcello, 227 Measurability defines mathematical objects, 79-80 Metaphors, 97 scientific, 318-319 Mind (see Human Understanding) Models contradictory, 5, 323, 332-333 heuristic value of, 4, 332 mechanical, 323-329 mentioned, 272, 277, 279, 296, 314, 317, 318, 323, 325, 326 Molecular Vortex Theory (see Hypothesis of Molecular Vorti­ ces) Molecularist Tradition French, 307-310 Momentum, 240-242 Moral Philosophy class, 13 core of Scottish University Edu­ cation, 26 importance for British physics, 12, 158 Morgan, G. C., 171 Morrell, J. B., 13, n. 4

National Styles in Science (see Scientific Styles) Natural Philosophy adopts ideas from moral philos­ ophy, 12, 12, n. 3, 15, 26 first principles of, 58-62 passim as model for moral philosophy, 32, 33,34 role of in liberal education, 19 Natural Realism, 51 Nature's Laws (see Laws of Nature) Necessitarianism (see Deter­ minism)

INDEX Newton, Sir Isaac mentioned, 34, 44, 53, 78, 94, 106-107,120,173-176 passim, 220, 223 quoted on hypotheses, 36 quoted on true and sufficient causes, 40-41, 325 Newtonian fluids, 196, 209 philosophy, 11, 32, 71, 123, 331 Newton's Law of cooling, 207, 217-219, 325 rules of reasoning in philosophy, 34, 40-41, 139 Nollet, Jean Antoine, 209 Non-Euclidean Geometry {see Geometry) Oersted, Hans, 239 Ohm, G. S., 208 Ohm's Law, 207-208 Oswald, James, 6, 30-31 Oxford University early specialization at, 12 Hamilton at, 131 Parsimony, Law of {see Law of Parsimony) Philosophical Magazine, 234,238, 250, 251, 311 Philosophical Society of Aberdeen, 27, 49 Philosophical Society of Glasgow, 273 Phrenology, 149-152 Physical Analogy {see Analogy, physical) Physical Hypotheses (see Hypothesis, physical) Physical Theory opposed to abstract science, 282 Pierce, Benjamin, 63

Playfair, John, 6, 157, 158, 1 6 1 168 passim, 186-187, 189, 197, 226, 243, 278, 325, 334 Popper, Karl, 113 Positivism, 42, 107, 182, 185, 302, 331 Potential defined in alternative ways by Maxwell, 294-295 Pragmatism (see Utilitarian) Prevost, Pierre, 7 Priestly, Joseph attitudes toward Common Sense philosophy, 31 ethers, 170 hypotheses, 37 mentioned, 8 , 2 8 , 3 4 , 3 6 , 3 9 , 4 0 , 105, 161, 183-184, 209 relationship to works of R. J. Boscovich, 98, 102 relationship to works of John Robison, 159-160 Primary Qualities the objects of mathematics, 8 0 81, 85, 89 Principle of Simplicity (see Simplicity) Principles of Common Sense (see Common Sense) Quaternions, 304-306, 334 Radiation (see Heat) Rankine, William J. M. central doctrines of, 271-286 passim and the hypothesis of molecular vortices, 274-281 passim and the luminiferous ether, 279 mentioned, 4, 6, 45, 91, 185, 236, 250, 251, 270, 317, 320, 324, 326, 327, 329, 332, 333 relationship to the works of Thomas Brown, 277, 278

INDEX Rankine—Continued relationship to the works of John Herschel, 273, 278, 279, 281-285 Reid, Thomas attitudes toward analogy, 48-52 causes, 41-44, 137 ethers, 162 genius, 37 hypotheses, 34-39, 40, 42, 109-110, 114, 175 "ideas", 49-52 inductive principle, 46-47, 115 mathematics, 55-61, 71-88, 165, 198 non-Euclidean geometry, 8 5 87 scientific method, 32, 34 simplicity, 52-54, 134 founder of Common Sense Philosophy, 27 mentioned, 3, 26, 28, 35, 67, 69, 94, 96, 97, 116, 121, 131, 132, 140, 141, 148, 157, 161, 171, 178, 212, 283, 325, 326, 329 relationship to works of Boscovich, 104 relationship to works of Brougham, 175 relationship to works of Herschel, 259-261, 265, 266 relationship to works of Hume, 31 relationship to works of Robison, 159-160 relationship to works of Waterston, 237, 243 Relational nature of scientific knowledge (seealso Relativism), 290,291 292-293, 316, 330 Relativism of scientific knowledge

to human characteristics Brown on, 126-130 passim, 131 Hamilton on, 137-138, 139 Maxwell on, 288-290, 313 Relativity (see Relativism) Robertson, William, 161-162 Robison, John central doctrines of, 157-161 mentioned, 6, 16, 21, 102, 172, 186, 195, 197, 243, 334 Royal Society of Edinburgh, 75, 157, 195, 274, 276, 287 Rules of Right Reasoning (see Newton's) Saint Andrews, University of, 161 Schofield, Robert, 195 Science of Man (see Human Understanding) Science of Mind (see Human Understanding) Scientific Styles, 3-4, 7, 323-334 passim Second Law of Thermodynamics (see Thermodynamics) Secondary Qualities (see Primary Qualities) Self-Consistent (see Coherence) Self-Contradiction (see Coherence) Simplicity criterion for accepting hypotheses, 120, 268-269, 279, 286 criticized, 52-54 demands for, 53, 97-98, 106, 119-121, 134-135, 164, 211, 214, 299-300, 314, 326 Simson, Robert, 22, 31, 57, 334 Skepticism Hume's, 13, 38, 59, 67, 69-70 mentioned, 55, 104, 142, 144, 313 opposed by Common Sense philosophers, 28-30, 37, 131

347

INDEX Skepticism—Continued source of in "ideas", 36-37 Smith, Adam, 17-18, 121-123, 130, 161 Specialization based upon liberal education, 14 based upon epistemology, 1415 early, at Cambridge and Oxford, 12 opposed in Scottish education, 17 Specific Heats, 248, 276 Speculations (see Hypotheses) Stewart, Dugald central philosophical doctrines of, 71-91 passim, 94-111 passim, 114-124 passim mentioned, 3 , 6 , 7 , 2 6 , 4 7 , 5 1 , 6 1 , 67, 69, 131, 137, 147, 149, 152, 157-159, 161, 167, 168, 171, 172, 177, 180, 185, 188, 225, 226, 243, 246, 265, 267, 268, 325, 327, 329, 332 on aims of science, 45-46 on analogy, 114-118 on hypotheses, 109, 216 on liberal education 14-18 passim, 35 on nature of mathematics, 22,55, 71-91 passim on simplicity, 118-121, 134 relationship to work of R. J. Boscovich, 98-106, 108, 159 relationship to work of D. Brewster, 178 relationship to work of J. Herschel, 256 relationship to work of J. Leslie, 171, 197-199, 212-213 relationship to work of J. C. Maxwell, 292, 300 relationship to work of W. J. M. Rankine, 272, 277, 279, 2 8 0 281, 283

Subtle Fluids (see Ether, Electric Fluid) Systems, 96, 107-108, 185 Tactile Experience basis for Euclidean geometry, 83-88 relation to primary qualities, 81 Tait, Peter Guthrie, 235, 300-301, 319-320, 333-334 Tangible Extension (see Extension) Theory distinguished from hypothesis, 112-113, 124, 168 legitimate, 112, 124, 313 need to vary (see Variation) Thermal Phenomena (see Heat) Thermodynamics classical, 273, 282 Rankine's formulation in "Science of Energetics", 273, 282, 285-286 second law of, 272-273,276-277 Thomson, Thomas, 185, 335 ,Thomson, William (Lord Kelvin), 4, 6, 7, 273, 300-301, 309, 319320, 324, 328 Touch (see Tactile) True and Sufficient Causes (see Cause) Undulatory Theory (see Light, Wave Theory) Unity demand for, 133-136, 152, 164, 239, 250 Unversal Laws (see Unity) Universal Terms, 55, 74 Utilitarian Demands, 96, 97, 132, 178, 253 Variation of Theory (see also Analogy, variation of), 118, 2 9 2 298 passim, 332-333

348

INDEX Vectors, 304-305, 306, 323, 329, 334 Verifiability of physical hypothesis, 111, 113, 188 Vibratory Theory {see Light, wave theory of) Victorian Scientific Style (see Scientific Styles) Viscous Theory of Glacial Motion (see Glacial) Visible Extension (see Extension) Vortex Ring Theory, 309

Waterston, John J., 4, 6, 185,236251 passim, 325, 330 Watt, James, 183, 185 Whewell, William, 66-67, 179186 passim, 234-235 Wilson, George, 225, 226, 236, 237, 287 Wise Club, 27 Wood, James, 173-174 Woodhouse, Robert, 188 Young, Thomas, 169, 174-177, 181, 220, 223-224, 228

Water composition of, 183-184

349

LIBRARY OF CONGRESS CATALOGING IN PUBLICATION DATA

Olson, Richard, 1940Seottish philosophy and British physics, 1750-1880. Bibliography: p. Includes index. 1. Physics—Philosophy. 2. Physics—History— Great Britain. 3. Philosophy, Scottish. I. Title. QC6.048 530'.01 74-34328 ISBN 0-691-08142-5