 Author
 Title
 "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth and early twentiethcentury probability theory, mathematics and logic
 Supervisors
 Award date
 1 October 2015
 Number of pages
 624
 ISBN
 9789082419801
 Document type
 PhD thesis
 Faculty
 Faculty of Humanities (FGw)
 Institute
 Amsterdam School for Cultural Analysis (ASCA)
 Abstract

This dissertation provides a contribution to a new history of exact thought in which the existence of a break between "nonmodern" and "modern" abstraction is put forward to account for the possibility of the "modernization" of probability theory, mathematics and logic during the 19th and early 20thcentury. The articles that make up the dissertation are all concerned not with the "modern" idea of a formal axiomatic system as such, but with what allowed it to become conceivable and they understand the way in which this came about not from the perspective of the "modern" but from that of the "nonmodern".
The articles can be read on four different levels  the first two of which form the main body of the text. Firstly, as detailed historical studies of the work of "nonmodern" probabilists, mathematicians and logicians (ca. 18301930). Secondly, as an elaboration of a general view of "nonmodern" conceptions of probability theory, mathematics and logic  a negative characterization which suggests that the later modifications of some of the ideas of "nonmoderns" were unthinkable for them given the foundations of their position. Thirdly, as a contribution to a postKuhnian history of "modernization" in these realms of exact thought which evokes, fourthly, a theoretization of the philosophical "break" in abstraction that underlies the "modernist transformation."
 Permalink
 http://hdl.handle.net/11245/1.492352
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Thesis (complete)

Front matter

Introduction

Part 1, Section 1: Logicist, idealist and quasiempiricist probability

Chapter 1: The objective and the subjective in midnineteenthcentury British probability theory

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

Part 1, Section 2: Robert Leslie Ellis: probability theory and idealism

Chapter 3: Robert Leslie Ellis’s work on philosophy of science and the foundations of probability theory

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

Part 1, Section 3: John Venn: probability theory and induction

Chapter 5: John Venn’s hypothetical infinite frequentism and logic

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

Part 1, Section 4: British symbolic logic and algebra: the limits of abstraction

Chapter 7: John Venn on the foundations of symbolic logic: a nonconceptualist Boole

Chapter 8: Duncan Farquharson Gregory and Robert Leslie Ellis: second generation reformers of British mathematics

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

Part 2, Section 1: David Hilbert and Richard von Mises: the axiomatization of probability theory as a natural science

Chapter 10: The place of probability in Hilbert’s axiomatization of physics, ca. 19001926

Chapter 11: Richard von Mises’s philosophy of probability and mathematics: a historical reconstruction

Part 2, Section 2: Moscow mathematics: formalism, intuitionism and the search for mathematical content

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

Chapter 12  Appendix: ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926)

Part 2, Section 3: Moscow probability theory: toward the Grundbegriffe

Chapter 13: On Aleksandr Iakovlevich Khinchin’s paper ‘Mises’ theory of probability and the principles of statistical physics’

Chapter 13  Appendix: ‘Mises’ theory of probability and the principles of statistical physics’ (1929)

Concluding remarks

Back matter

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