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"A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth- andearly twentieth-century probability theory, mathematics and logicVerburgt, L.M.

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Citation for published version (APA):Verburgt, L. M. (2015). "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth-and early twentieth-century probability theory, mathematics and logic

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Download date: 14 Feb 2019

“A terrible piece of bad metaphysics”?

Towards a history of abstraction in nineteenth- and early twentieth-century

probability theory, mathematics and logic

Lukas M. Verburgt

If the true iswhat is grounded,then the groundis neither true nor false

l u d w i g w i t t g e n s t e i n

Whether all grow black,or all grow bright,or all remain grey,it is grey we need,to begin with,because of what it is,and of what it can do,made of bright and black,able to shed the former ,or the latter,and be the latteror the former alone.But perhaps I am the prey,on the subject of grey,in the grey, to delusions

s a m u e l b e c k e t t

“A terrible piece of bad metaphysics”?

Towards a history of abstraction in nineteenth- and early twentieth-century

probability theory, mathematics and logic

AC ADEM I S CH PROEF S CHR I F T

ter verkrijging van de graad van doctor

aan de Universiteit van Amsterdam

op gezag van de Rector Magnificus

prof. dr. D.C. van den Boom

ten overstaan van een door het College voor Promoties ingestelde commissie

in het openbaar te verdedigen in de Agnietenkapel

op donderdag 1 oktober 2015, te 10:00 uur

door

Lukas Mauve Verburgt

geboren te Amersfoort

Promotiecommissie

Promotor:Prof. dr. ir. G.H. de Vries Universiteit van Amsterdam

Overige leden:Prof. dr. M. Fisch Universitat Tel AvivDr. C.L. Kwa Universiteit van AmsterdamDr. F. Russo Universiteit van AmsterdamProf. dr. M.J.B. Stokhof Universiteit van AmsterdamProf. dr. A. Vogt Humboldt-Universität zu Berlin

Faculteit der Geesteswetenschappen

© 2015 Lukas M. Verburgt

Graphic design Aad van Dommelen (Witvorm)

Printing Lenoirschuring

Binding Atelier Kloosterman

Paper Biotop 3 Next 100 g/m²

Cover paper Les Naturals Safrangelb 325 g/m²

Typeface dtl Fleischmann

isbn 978-90-824198-0-1

6

acknowledgments — 8

Introduction — 10Structure of the book — 23

part 1 British probability theory, logic and mathematics — 25

sec tion 1 Logicist, idealist and quasi-empiricist probability — 26

chapter 1 The objective and the subjective in mid-nineteenth-century British probability theory — 28

chapter 2 Remarks on the idealist and empiricist interpretation of frequentism: Robert Leslie Ellis versus John Venn — 62

sec tion 2 Robert Leslie Ellis: probability theory and idealism — 80

chapter 3 Robert Leslie Ellis’s work on philosophy of science and the foundations of probability theory — 82

chapter 4 Robert Leslie Ellis, William Whewell and Kant: the role of Rev. H.F.C. Logan — 135

sec tion 3 John Venn: probability theory and induction — 142

chapter 5 John Venn’s hypothetical infinite frequentism and logic — 143

chapter 6 “A modified acceptance of Mr. Mill’s view”: John Venn on the nature of inductive logic and the syllogism — 184

sec tion 4 British symbolic logic and algebra: the limits of abstraction — 215

chapter 7 John Venn on the foundations of symbolic logic: a non-conceptualist Boole — 217

chapter 8 Duncan Farquharson Gregory and Robert Leslie Ellis: second generation reformers of British mathematics — 267

chapter 9 Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction — 305

table of contents

7

part 2 The axiomatization of probability theory and the foundations of modern mathematics — 357

sec tion 1 David Hilbert and Richard von Mises: the axiomatization

of probability theory as a natural science — 358

chapter 10 The place of probability in Hilbert’s axiomatization of physics, ca. 1900-1926 — 360

chapter 11 Richard von Mises’s philosophy of probability and mathematics: a historical reconstruction — 414

sec tion 2 Moscow mathematics: formalism, intuitionism

and the search for mathematical content — 469

chapter 12 On Aleksandr Iakovlevich Khinchin’s paper ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ — 471

chapter 12 ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926) — 512english translation, with olga hoppe-kondr ikova

sec tion 3 Moscow probability theory: toward the Grundbegrife — 527

chapter 13 On Aleksandr Iakovlevich Khinchin’s paper ‘Mises’ theory of probability and the principles of statistical physics’ — 529

chapter 13 ‘Mises’ theory of probability and the principles of statistical physics’ (1929) — 583english translation, with olga hoppe-kondr ikova

Concluding remarks — 605

samenvatting — 613

summary — 618

note on funding and co-translatorship — 623

– appendix

– appendix

8

acknowledgments

Paul Valéry once wrote that ‘the whole question comes down to this: can the human mind master what the human mind has made?’. This seems to assume that the human mind either makes things which it can master or makes things which it cannot master. I think that there are at least two other possibilities: there are things which the mind can make that destroy its ability to master and there are things which the human mind cannot make because they are destroyed when they are mastered. It is to the future exploration of these possibilities that this book is dedicated.

I will always be grateful to Gerard de Vries, whose willingness to mistake my ignorance for the possibility of insight and to allow me to take the risk of thinking as someone who does not know implicitly what it means to think must make him a real master.

There are many people whom I have never met, but who have contributed much to this book: the anonymous referees, the editors Tom Archibald, Niccoló Guicciardini, Tony Mann, David Miller and Volker Peckhaus, and Jeremy Gray, Adrian Rice, Reinhard Siegmund-Schultze, and, especially, Tilmann Sauer. The articles on Russian mathematics could not have been written without Jan Von Plato, who sent me the copies of Khinchin’s papers and shared with me many bibliographical details about Khinchin, Kolmogorov and Heyting. I am indebted to Berna Kiliç, David Vere-Jones and Sandy Zabell for providing me with some of their valuable articles and to Stephen Stigler and Menachem Fisch, whose appreciation of two of my articles I consider as a great honor.

I am thankful to Lorraine Daston not only for hosting me in Department II at the Max Planck Institute for the History of Science (MPIWG) in Berlin – where I was a Pre-Doctoral Visiting Fellow from September until December 2014 –, but also for critically reading two of the articles. At the MPIWG, Donatella Germanese helped me with the translation of several passages from the work of Richard von Mises, Elena Aronova was so kind to bring me into contact with some of her colleagues in Moscow, Ellen Garske managed to obtain several documents from the Hilbert Nachlass in Göttingen, and Regina

9

Held assisted me with the many practicalities of my stay. I would like to express my gratitude to Annette Vogt whose encouragement, advice and deep knowl-edge of the history of German and Russian mathematics have been of invalua-ble importance to me. Jessica, Marco and Pim allowed me to live and work in Dahlem as a worldly monk.

I thank Rob and my (former) fellow PhD-candidates Berend, Floortje, Guus, Martin, Pim and, of course, Willemine for introducing me into academic life, my new colleagues Federica, Franz, Jacques, Michiel and, of course, Huub for welcoming me to the department, Olga Kondrikova for her help in translating Khinchin’s papers and Aad van Dommelen for his design of the book. I also want to thank, for many diferent reasons, Andries, Jattie, Jan Bouwe, Judith, Ludo, Mathijs, Robby, Sander, Simone, Tess, Vera and Wout, the saviors of pop-music Bowie, Julien and Thijs, my long-lost friend Bart and my family; Ad, Jana, Jantien, Niek, Julia, Geraldine, Elizabeth, Oek, Jeanne, Imar, Danny, Teuntje and my grandmother and two grandfathers who passed away in recent years, Dies, Ton and Klaas. Then there are Floris, Guido, Maite and Mees – who have taught me that what goes for thinking also goes for friendship; that when you do it ‘you should burn yourself completely, like a good bonfire, leaving no trace of yourself’.

I started writing the articles for this book while living with the love of my young life, Imke. My love goes to her and to my parents Hannet and Peter.