This electronic thesis or dissertation has been downloaded from the King’s Research Portal at https://kclpure.kcl.ac.uk/portal/ On the concept of experimental error. Hon, Giora The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without proper acknowledgement. END USER LICENCE AGREEMENT Unless another licence is stated on the immediately following page this work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ You are free to copy, distribute and transmit the work Under the following conditions: Attribution: You must attribute the work in the manner specified by the author (but not in any way that suggests that they endorse you or your use of the work). Non Commercial: You may not use this work for commercial purposes. No Derivative Works - You may not alter, transform, or build upon this work. Any of these conditions can be waived if you receive permission from the author. Your fair dealings and other rights are in no way affected by the above. Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 09. Oct. 2021 ON THE CONCEPT OF EXPERIMENTAL ERROR by Giora Hon Thesis submitted for the degree of Doctor of Philosophy Department of History and Philosophy of Science, Chelsea College, London University (April 1985) ACKNOWLEDGEMENTS I am grateful to Professor Heinz Post, my supervisor, for pointing out to me that the occurrences of experimental error constitute a philosophical problem. I have greatly benefited from his critical judgement and am indebted to him for constant encouragement. I should like to thank Professor A. Franklin for valuable discussions, and the staff and students of the Department of History and Philosophy of Science, Chelsea College, for commenting on my views. A special debt of gratitude is due to my parents. Thanks are also due to Y. Safran, Dr. G. Mandel, R. Judd, Dr. A. Simhony, A. Sharakiya, Dr. L. Archer, J. Kenaz and S. Arkley. Finally, I wish to acknowledge the financial assistance I have received from B'nai B'rith and the Humanitarian Trust. To Hannah Safran ABSTRACT This thesis is concerned with the concept of experimental error. It considers the occurrence of error an epistemological phenomenon which stands in the way of attaining knowledge. The concept of experimental error comprises intertwined elements of conceptual and physical origins. These elements form an obstacle that may obstruct the experimenter from reaching his goal, that is, the attainment of knowledge. The prime objective of the thesis is to throw light on such obstacles. It questions the con- clusiveness of experimental results by exposing the conceptual and physical difficulties which attend the execution of an experiment. However, the thesis underlines the positive feature of this concept, namely, that the comprehension of an error may contribute to knowledge. The thesis holds that the mathematical theory of error avoids conceptual discussions, and conceals the physical elements of experimental error under the mathematical cloak of abstractions. The mathematical theory of error is solely concerned with rendering the experimental error amenable to mathe- matical analysis and calculation. As the thesis seeks a comprehensive view of the concept of experimental error, it does not follow the mathematical approach. By way of introduction, the thesis juxtaposes several approaches towards the epistemological problem of error. It outlines the views of Aristotle, Bacon, Descartes, Spinoza and others, and concludes with Wittgenstein's instructive suggestion of distinguishing between the different ways in which something 'turns out wrong'. The thesis then focuses on the problem of experimental error by contrasting the approach of the Greek astronomers towards this problem with that of Kepler. An account of Kepler's explicit and comprehensive awareness of the problem of experimental error - an account which includes a study of his Astronomia Nova ath his work on optics - serves as a background against which the thesis introduces a classification of different types of experimental error. This classification consists of four categories: background theory; assumptions concerning the actual set-up and its working; observational reports; and theoretical conclusions. The thesis then proceeds to illustrate the classification with several case-studies of experiments. It deals mainly with the following: R.A. Millikan's and F. Ehrenhaft's measurements of the charge of the electron; H. Hertz's experiment on the deflection of cathode rays in an electric field; R. Blondlot's so-called discovery of N rays; and J. Franck's and G. Hertz's experiment on the quantized spectrum of the atom's energy levels. In the final section, the thesis presents Kaufmann's experiment in its historical setting and contrasts some of the principal responses it received. The varied responses illustrate how the detection of an experimental error and its characterization depend on the philosophical outlook one holds. TABLE OF CONTENTS Pace Acknowledgement 2 Abstract 3 Preface 0 CHAPTER I Introduction 11 CHAPTER II On the Concept of Experimental Error in Greek Science 48 CHAPTER III Kepler's View of the Concept of Experimental Error 80 CHAPTER IV A Classification of Types of Experimental Error 4.1 General discussion 144 4.2 'Background theory' 164 4.3 'Assumptions concerning the actual set-up and its working' 172 4.4 'Observational reports' 175 4.5 'Theoretical conclusions' 181 CHAPTER V Case-studies of Experiments R.A. Millikan's and F. Ehrenhaft's measurements 5.1 of the charge of the electron 191 5.2 H. Hertz's experiment on the deflection of cathode rays in an electric field 210 5.3 R. Blondlot's so-called discovery of N rays 226 J. Franck's and G. Hertz's experiment on the 5.4 quantized spectrum of the atom's energy levels 253 CHAPTER VI Kaufmann's Experiment and Its Reception 279 6.1 The experiment 281 6.2 Poincar's reaction 313 6.3 Einstein's reaction 323 6.4 Lorentz's reaction 332 Conclusion 350 Bibliography 357 5 Once (errors of measurement and other forms of experimental error]... have been discounted, our attention can turn to the logic o-mathematical structure.1 W. Sellars There is no such thing as a classification of the ways in which men may arrive at an error; it is much to be doubted whether there ever can be..2 A. de Morgan Knowledge and error flow from the same mental sources, only success can tell the one from the other. A clearly recognized error, by way of corrective, can benefit knowledge just as a positive piece of knowledge can.3 E. Mach The history of science is not restricted to the enumeration of successful investigations. It has to tell of unsuccessful inquiries, and to explain why some of the ablest men have failed to find the key of knowledge, and how the reputation of others has only given a firmer footing to the errors into which they fell.4 J.C. Maxwell 1. Sellars, 1961, p. 73; quoted by Mellor, 1965, p.106. 2. De Morgan, 1847, p.237. 3. Mach, 1976, p.84. 4. Maxwell, 1890, p.251. 6 PREFACE In his book, Discovering Plato, Alexandre Koyr (1892-1964) explicates, inter alia, the philosophical arguments which Plato employs in the Theaetetus to reveal the nature of knowledge and, for that matter, science.' The characters of the dialogue are ideal interlocutors for a scientific discussion: Theodorus is a good mathematician and astronomer, and Theaetetus is a teacher in the Academy and one of the leading geometers of his time. Having stated that wisdom and knowledge are the same, Socrates admits that he is not quite clear as to what knowledge really is. 'Herein lies the difficulty which I can never solve to my satisfaction,' Socrates confesses and proceeds to question Theaetetus: 'What is knowledge? Can we answer that question?'2 Needless to say, the great expertise of the interlocutors does not stand them in good stead, and they fail at the end of the dialogue to arrive at a satisfactory solution. 'And so, Theaetetus,' Socrates rhetorically asks, 'knowledge is neither sensation nor true opinion, nor yet definition and explanation accompanying and added to true opinion?' 3 A view with which Theaetetus has no choice but to agree. And thus another of Plato's dialogues comes to an end in a Socratic manner, that is, as Socrates himself concludes, 'if...you should ever conceive afresh, you will be all the better for the present investigation, and if not, you will be soberer and humbler and gentler to other men, and will be too modest to fancy that you know what you do not know'.4 In the course of explaining the second thesis of Theaetetus, namely, that knowledge is true opinion, Koyr, following Socrates, points out that 1. Koyr, 1945, pp.33-52. 2. Plato, 1949, p.5. 3. Ibid., p.84. 4. Ibid. 7 it amounts to the claim that errors are impossible. Having said that, he relegates the following sentence to a footnote: 'The problem of error,' Koyr& states, 'is one of philosophy's very serious and crucial problems.'1 This emphatic statement of Koyr,which stresses the importance of the problem of error in a rather incidental way, may serve as the departure point of this thesis. Indeed, Koyr's remark epitomizes the state of the problem of error: it is 'very serious and crucial', yet the treatments it has received have generally been scanty and peripheral, that is, metaphori- cally they amount to a footnote.