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The Search for Mathematical Roots, 1870-1940

Book Description

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913).

This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI.

Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials.

Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Chapter 1 Explanations
    1. 1.1 Sallies
    2. 1.2 Scope and limits of the book
      1. 1.2.1 An outline history
      2. 1.2.2 Mathematical aspects
      3. 1.2.3 Historical presentation
      4. 1.2.4 Other logics, mathematics and philosophies
    3. 1.3 Citations, terminology and notations
      1. 1.3.1 References and the bibliography
      2. 1.3.2 Translations, quotations and notations
    4. 1.4 Permissions and acknowledgements
  6. Chapter 2 Preludes: Algebraic Logic and Mathematical Analysis up to 1870
    1. 2.1 Plan of the chapter
    2. 2.2 ‘Logique’ and algebras in French mathematics
      1. 2.2.1 The ‘logique’ and clarity of ‘idéologie’
      2. 2.2.2 Lagrange’s algebraic philosophy
      3. 2.2.3 The many senses of ‘analysis’
      4. 2.2.4 Two Lagrangian algebras: functional equations and differential operators
      5. 2.2.5 Autonomy for the new algebras
    3. 2.3 Some English algebraists and logicians
      1. 2.3.1 A Cambridge revival: the ‘Analytical Society’, Lacroix, and the professing of algebras
      2. 2.3.2 The advocacy of algebras by Babbage, Herschel and Peacock
      3. 2.3.3 An Oxford movement: Whately and the professing of logic
    4. 2.4 A London pioneer: De Morgan on algebras and logic
      1. 2.4.1 Summary of his life
      2. 2.4.2 De Morgan’s philosophies of algebra
      3. 2.4.3 De Morgan’s logical career
      4. 2.4.4 De Morgan’s contributions to the foundations of logic
      5. 2.4.5 Beyond the syllogism
      6. 2.4.6 Contretemps over ‘the quantification of the predicate’
      7. 2.4.7 The logic of two-place relations, 1860
      8. 2.4.8 Analogies between logic and mathematics
      9. 2.4.9 De Morgan’s theory of collections
    5. 2.5 A Lincoln outsider: Boole on logic as applied mathematics
      1. 2.5.1 Summary of his career
      2. 2.5.2 Boole’s ‘general method in analysis’, 1844
      3. 2.5.3 The mathematical analysis of logic, 1847: ‘elective symbols’ and laws
      4. 2.5.4 ‘Nothing’ and the ‘Universe’
      5. 2.5.5 Propositions, expansion theorems, and solutions
      6. 2.5.6 The laws of thought, 1854: modified principles and extended methods
      7. 2.5.7 Boole’s new theory of propositions
      8. 2.5.8 The character of Boole’s system
      9. 2.5.9 Boole’s search for mathematical roots
    6. 2.6 The semi-followers of Boole
      1. 2.6.1 Some initial reactions to Boole’s theory
      2. 2.6.2 The reformulation by Jevons
      3. 2.6.3 Jevons versus Boole
      4. 2.6.4 Followers of Boole and/or Jevons
    7. 2.7 Cauchy, Weierstrass and the rise of mathematical analysis
      1. 2.7.1 Different traditions in the calculus
      2. 2.7.2 Cauchy and the Ecole Polytechnique
      3. 2.7.3 The gradual adoption and adaptation of Cauchy’s new tradition
      4. 2.7.4 The refinements of Weierstrass and his followers
    8. 2.8 Judgement and supplement
      1. 2.8.1 Mathematical analysis versus algebraic logic
      2. 2.8.2 The places of Kant and Bolzano
  7. Chapter 3 Cantor: Mathematics as Mengenlehre
    1. 3.1 Prefaces
      1. 3.1.1 Plan of the chapter
      2. 3.1.2 Cantor’s career
    2. 3.2 The launching of the Mengenlehre, 1870–1883
      1. 3.2.1 Riemann’s thesis: the realm of discontinuous functions
      2. 3.2.2 Heine on trigonometric series and the real line, 1870–1872
      3. 3.2.3 Cantor’s extension of Heine’s findings, 1870–1872
      4. 3.2.4 Dedekind on irrational numbers, 1872
      5. 3.2.5 Cantor on line and plane, 1874–1877
      6. 3.2.6 Infinite numbers and the topology of linear sets, 1878–1883
      7. 3.2.7 The Grundlagen, 1883: the construction of number-classes
      8. 3.2.8 The Grundlagen: the definition of continuity
      9. 3.2.9 The successor to the Grundlagen, 1884
    3. 3.3 Cantor’s Acta mathematica phase, 1883–1885
      1. 3.3.1 Mittag-Leffler and the French translations, 1883
      2. 3.3.2 Unpublished and published ‘communications’, 1884–1885
      3. 3.3.3 Order-types and partial derivatives in the ‘communications’
      4. 3.3.4 Commentators on Cantor, 1883–1885
    4. 3.4 The extension of the Mengenlehre, 1886–1897
      1. 3.4.1 Dedekind’s developing set theory, 1888
      2. 3.4.2 Dedekind’s chains of integers
      3. 3.4.3 Dedekind’s philosophy of arithmetic
      4. 3.4.4 Cantor’s philosophy of the infinite, 1886–1888
      5. 3.4.5 Cantor’s new definitions of numbers
      6. 3.4.6 Cardinal exponentiation: Cantor’s diagonal argument, 1891
      7. 3.4.7 Transfinite cardinal arithmetic and simply ordered sets, 1895
      8. 3.4.8 Transfinite ordinal arithmetic and well-ordered sets, 1897
    5. 3.5 Open and hidden questions in Cantor’s Mengenlehre
      1. 3.5.1 Well-ordering and the axioms of choice
      2. 3.5.2 What was Cantor’s ‘Cantor’s continuum problem’?
      3. 3.5.3 “Paradoxes” and the absolute infinite
    6. 3.6 Cantor’s philosophy of mathematics
      1. 3.6.1 A mixed position
      2. 3.6.2 (No) logic and metamathematics
      3. 3.6.3 The supposed impossibility of infinitesimals
      4. 3.6.4 A contrast with Kronecker
    7. 3.7 Concluding comments: the character of Cantor’s achievements
  8. Chapter 4 Parallel Processes in Set Theory, Logics and Axiomatics, 1870s–1900s
    1. 4.1 Plans for the chapter
    2. 4.2 The splitting and selling of Cantor’s Mengenlehre
      1. 4.2.1 National and international support
      2. 4.2.2 French initiatives, especially from Borel
      3. 4.2.3 Couturat outlining the infinite, 1896
      4. 4.2.4 German initiatives from Klein
      5. 4.2.5 German proofs of the Schröder-Bernstein theorem
      6. 4.2.6 Publicity from Hilbert, 1900
      7. 4.2.7 Integral equations and functional analysis
      8. 4.2.8 Kempe on ‘mathematical form’
      9. 4.2.9 Kempe—who?
    3. 4.3 American algebraic logic: Peirce and his followers
      1. 4.3.1 Peirce, published and unpublished
      2. 4.3.2 Influences on Peirce’s logic: father’s algebras
      3. 4.3.3 Peirce’s first phase: Boolean logic and the categories, 1867–1868
      4. 4.3.4 Peirce’s virtuoso theory of relatives, 1870
      5. 4.3.5 Peirce’s second phase, 1880: the propositional calculus
      6. 4.3.6 Peirce’s second phase, 1881: finite and infinite
      7. 4.3.7 Peirce’s students, 1883: duality, and ‘Quantifying’ a proposition
      8. 4.3.8 Peirce on ‘icons’ and the order of ‘quantifiers’, 1885
      9. 4.3.9 The Peirceans in the 1890s
    4. 4.4 German algebraic logic: from the Grassmanns to Schröder
      1. 4.4.1 The Grassmanns on duality
      2. 4.4.2 Schröder’s Grassmannian phase
      3. 4.4.3 Schröder’s Peircean ‘lectures’on logic
      4. 4.4.4 Schröder’s first volume, 1890
      5. 4.4.5 Part of the second volume, 1891
      6. 4.4.6 Schröder’s third volume, 1895: the ‘logic of relatives’
      7. 4.4.7 Peirce on and against Schröder in The monist, 1896-1897
      8. 4.4.8 Schröder on Cantorian themes, 1898
      9. 4.4.9 The reception and publication of Schröder in the 1900s
    5. 4.5 Frege: arithmetic as logic
      1. 4.5.1 Frege and Frege′
      2. 4.5.2 The ‘concept-script’ calculus of Frege’s ‘pure thought’, 1879
      3. 4.5.3 Frege’s arguments for logicising arithmetic, 1884
      4. 4.5.4 Kerry’s conception of Fregean concepts in the mid 1880s
      5. 4.5.5 Important new distinctions in the early 1890s
      6. 4.5.6 The ‘fundamental laws’ of logicised arithmetic, 1893
      7. 4.5.7 Frege’s reactions to others in the later 1890s
      8. 4.5.8 More ‘fundamental laws’ of arithmetic, 1903
      9. 4.5.9 Frege, Korselt and Thomae on the foundations of arithmetic
    6. 4.6 Husserl: logic as phenomenology
      1. 4.6.1 A follower of Weierstrass and Cantor
      2. 4.6.2 The phenomenological ‘philosophy of arithmetic’, 1891
      3. 4.6.3 Reviews by Frege and others
      4. 4.6.4 Husserl’s ‘logical investigations’, 1900–1901
      5. 4.6.5 Husserl’s early talks in Göttingen, 1901
    7. 4.7 Hilbert: early proof and model theory, 1899–1905
      1. 4.7.1 Hilbert’s growing concern with axiomatics
      2. 4.7.2 Hilbert’s different axiom systems for Euclidean geometry, 1899–1902
      3. 4.7.3 From German completeness to American model theory
      4. 4.7.4 Frege, Hilbert and Korselt on the foundations of geometries
      5. 4.7.5 Hilbert’s logic and proof theory, 1904–1905
      6. 4.7.6 Zermelo’s logic and set theory, 1904–1909
  9. Chapter 5 Peano: the Formulary of Mathematics
    1. 5.1 Prefaces
      1. 5.1.1 Plan of the chapter
      2. 5.1.2 Peano’s career
    2. 5.2 Formalising mathematical analysis
      1. 5.2.1 Improving Genocchi, 1884
      2. 5.2.2 Developing Grassmann’s ‘geometricalcalculus’, 1888
      3. 5.2.3 The logistic of arithmetic, 1889
      4. 5.2.4 The logistic of geometry, 1889
      5. 5.2.5 The logistic of analysis, 1890
      6. 5.2.6 Bettazzi on magnitudes, 1890
    3. 5.3 The Rivista: Peano and his school, 1890–1895
      1. 5.3.1 The ‘society of mathematicians’
      2. 5.3.2 ‘Mathematicallogic’, 1891
      3. 5.3.3 Developing arithmetic, 1891
      4. 5.3.4 Infinitesimals and limits, 1892–1895
      5. 5.3.5 Notations and their range, 1894
      6. 5.3.6 Peano on definition by equivalence classes
      7. 5.3.7 Burali-Forti’s textbook, 1894
      8. 5.3.8 Burali-Forti’s research, 1896–1897
    4. 5.4 The Formulaire and the Rivista, 1895–1900
      1. 5.4.1 The first edition of the Formulaire, 1895
      2. 5.4.2 Towards the second edition of the Formulaire, 1897
      3. 5.4.3 Peano on the eliminability of ‘the’
      4. 5.4.4 Frege versus Peano on logic and definitions
      5. 5.4.5 Schröder’s steamships versus Peano’s sailing boats
      6. 5.4.6 New presentations of arithmetic, 1898
      7. 5.4.7 Padoa on classhood, 1899
      8. 5.4.8 Peano’s new logical summary, 1900
    5. 5.5 Peanists in Paris, August 1900
      1. 5.5.1 An Italian Friday morning
      2. 5.5.2 Peano on definitions
      3. 5.5.3 Burali-Forti on definitions of numbers
      4. 5.5.4 Padoa on definability and independence
      5. 5.5.5 Pieri on the logic of geometry
    6. 5.6 Concluding comments: the character of Peano’s achievements
      1. 5.6.1 Peano’s little dictionary, 1901
      2. 5.6.2 Partly grasped opportunities
      3. 5.6.3 Logic without relations
  10. Chapter 6 Russell’s Way In: From Certainty to Paradoxes, 1895–1903
    1. 6.1 Prefaces
      1. 6.1.1 Plans for two chapters
      2. 6.1.2 Principal sources
      3. 6.1.3 Russell as a Cambridge undergraduate, 1891–1894
      4. 6.1.4 Cambridge philosophy in the 1890s
    2. 6.2 Three philosophical phases in the foundation of mathematics, 1895–1899
      1. 6.2.1 Russell’s idealist axiomatic geometries
      2. 6.2.2 The importance of axioms and relations
      3. 6.2.3 A pair of pas de deux with Paris: Couturat and Poincaré on geometries
      4. 6.2.4 The emergence of Whitehead, 1898
      5. 6.2.5 The impact of G. E. Moore, 1899
      6. 6.2.6 Three attempted books, 1898–1899
      7. 6.2.7 Russell’s progress with Cantor’s Mengenlehre, 1896-1899
    3. 6.3 From neo-Hegelianism towards ‘Principles’, 1899–1901
      1. 6.3.1 Changing relations
      2. 6.3.2 Space and time, absolutely
      3. 6.3.3 ‘Principles of Mathematics’, 1899–1900
    4. 6.4 The first impact of Peano
      1. 6.4.1 The Paris Congress of Philosophy, August 1900: Schröder versus Peano on ‘the’
      2. 6.4.2 Annotating and popularising in the autumn
      3. 6.4.3 Dating the origins of Russell’s logicism
      4. 6.4.4 Drafting the logic of relations, October 1900
      5. 6.4.5 Part 3 of The principles, November 1900: quantity and magnitude
      6. 6.4.6 Part 4, November 1900: order and ordinals
      7. 6.4.7 Part 5, November 1900: the transfinite and the continuous
      8. 6.4.8 Part 6, December 1900: geometries in space
      9. 6.4.9 Whitehead on ‘the algebra of symbolic logic’, 1900
    5. 6.5 Convoluting towards logicism, 1900–1901
      1. 6.5.1 Logicism as generalised metageometry, January 1901
      2. 6.5.2 The first paper for Peano, February 1901: relations and numbers
      3. 6.5.3 Cardinal arithmetic with Whitehead and Russell, June 1901
      4. 6.5.4 The second paper for Peano, March–August 1901: set theory with series
    6. 6.6 From ‘fallacy’ to ‘contradiction’, 1900–1901
      1. 6.6.1 Russell on Cantor’s ‘fallacy’, November 1900
      2. 6.6.2 Russell’s switch to a ‘contradiction’
      3. 6.6.3 Other paradoxes: three too large numbers
      4. 6.6.4 Three passions and three calamities, 1901–1902
    7. 6.7 Refining logicism, 1901–1902
      1. 6.7.1 Attempting Part 1 of The principles, May 1901
      2. 6.7.2 Part 2, June 1901: cardinals and classes
      3. 6.7.3 Part 1 again, April–May 1902: the implicational logicism
      4. 6.7.4 Part 1: discussing the indefinables
      5. 6.7.5 Part 7, June 1902: dynamics without statics; and within logic?
      6. 6.7.6 Sort-of finishing the book
      7. 6.7.7 The first impact of Frege, 1902
      8. 6.7.8 Appendix A on Frege
      9. 6.7.9 Appendix B: Russell’s first attempt to solve the paradoxes
    8. 6.8 The roots of pure mathematics? Publishing The principles at last, 1903
      1. 6.8.1 Appearance and appraisal
      2. 6.8.2 A gradual collaboration with Whitehead
  11. Chapter 7 Russell and Whitehead Seek the Principia Mathematica, 1903–1913
    1. 7.1 Plan of the chapter
    2. 7.2 Paradoxes and axioms in set theory, 1903–1906
      1. 7.2.1 Uniting the paradoxes of sets and numbers
      2. 7.2.2 New paradoxes, mostly of naming
      3. 7.2.3 The paradox that got away: heterology
      4. 7.2.4 Russell as cataloguer of the paradoxes
      5. 7.2.5 Controversies over axioms of choice, 1904
      6. 7.2.6 Uncovering Russell’s ‘multiplicative axiom’, 1904
      7. 7.2.7 Keyser versus Russell over infinite classes, 1903–1905
    3. 7.3 The perplexities of denoting, 1903–1906
      1. 7.3.1 First attempts at a general system, 1903–1905
      2. 7.3.2 Propositional functions, reducible and identical
      3. 7.3.3 The mathematical importance of definite denoting functions
      4. 7.3.4 ‘On denoting’ and the complex, 1905
      5. 7.3.5 Denoting, quantification and the mysteries of existence
      6. 7.3.6 Russell versus MacColl on the possible, 1904–1908
    4. 7.4 From mathematical induction to logical substitution, 1905–1907
      1. 7.4.1 Couturat’s Russellian principles
      2. 7.4.2 A second pas de deux with Paris: Boutroux and Poincaré on logicism
      3. 7.4.3 Poincaré on the status of mathematical induction
      4. 7.4.4 Russell’s position paper, 1905
      5. 7.4.5 Poincaré and Russell on the vicious circle principle, 1906
      6. 7.4.6 The rise of the substitutional theory, 1905–1906
      7. 7.4.7 The fall of the substitutional theory, 1906–1907
      8. 7.4.8 Russell’s substitutional propositional calculus
    5. 7.5 Reactions to mathematical logic and logicism, 1904–1907
      1. 7.5.1 The International Congress of Philosophy, 1904
      2. 7.5.2 German philosophers and mathematicians, especially Schönflies
      3. 7.5.3 Activities among the Peanists
      4. 7.5.4 American philosophers: Royce and Dewey
      5. 7.5.5 American mathematicians on classes
      6. 7.5.6 Huntington on logic and orders
      7. 7.5.7 Judgements from Shearman
    6. 7.6 Whitehead’s role and activities, 1905–1907
      1. 7.6.1 Whitehead’s construal of the ‘material world’
      2. 7.6.2 The axioms of geometries
      3. 7.6.3 Whitehead’s lecture course, 1906–1907
    7. 7.7 The sad compromise: logic in tiers
      1. 7.7.1 Rehabilitating propositional functions, 1906–1907
      2. 7.7.2 Two reflective pieces in 1907
      3. 7.7.3 Russell’s outline of ‘mathematical logic’, 1908
    8. 7.8 The forming of Principia mathematica
      1. 7.8.1 Completing and funding Principia mathematica
      2. 7.8.2 The organisation of Principia mathematica
      3. 7.8.3 The propositional calculus, and logicism
      4. 7.8.4 The predicate calculus, and descriptions
      5. 7.8.5 Classes and relations, relative to propositional functions
      6. 7.8.6 The multiplicative axiom: some uses and avoidance
    9. 7.9 Types and the treatment of mathematics in Principia mathematica
      1. 7.9.1 Types in orders
      2. 7.9.2 Reducing the edifice
      3. 7.9.3 Individuals, their nature and number
      4. 7.9.4 Cardinals and their finite arithmetic
      5. 7.9.5 The generalised ordinals
      6. 7.9.6 The ordinals and the alephs
      7. 7.9.7 The odd small ordinals
      8. 7.9.8 Series and continuity
      9. 7.9.9 Quantity with ratios
  12. Chapter 8 The Influence and Place of Logicism, 1910–1930
    1. 8.1 Plans for two chapters
    2. 8.2 Whitehead’s and Russell’s transitions from logic to philosophy, 1910–1916
      1. 8.2.1 The educational concerns of Whitehead, 1910–1916
      2. 8.2.2 Whitehead on the principles of geometry in the 1910s
      3. 8.2.3 British reviews of Principia mathematica
      4. 8.2.4 Russell and Peano on logic, 1911–1913
      5. 8.2.5 Russell’s initial problems with epistemology, 1911–1912
      6. 8.2.6 Russell’s first interactions with Wittgenstein, 1911–1913
      7. 8.2.7 Russell’s confrontation with Wiener, 1913
    3. 8.3 Logicism and epistemology in America and with Russell, 1914–1921
      1. 8.3.1 Russell on logic and epistemology at Harvard, 1914
      2. 8.3.2 Two long American reviews
      3. 8.3.3 Reactions from Royce students: Sheffer and Lewis
      4. 8.3.4 Reactions to logicism in New York
      5. 8.3.5 Other American estimations
      6. 8.3.6 Russell’s ‘logical atomism’ and psychology, 1917–1921
      7. 8.3.7 Russell’s ‘introduction’ to logicism, 1918–1919
    4. 8.4 Revising logic and logicism at Cambridge, 1917–1925
      1. 8.4.1 New Cambridge authors, 1917–1921
      2. 8.4.2 Wittgenstein’s ‘Abhandlung’ and Tractatus, 1921–1922
      3. 8.4.3 The limitations of Wittgenstein’s logic
      4. 8.4.4 Towards extensional logicism: Russell’s revision of Principia mathematica, 1923–1924
      5. 8.4.5 Ramsey’s entry into logic and philosophy, 1920–1923
      6. 8.4.6 Ramsey’s recasting of the theory of types, 1926
      7. 8.4.7 Ramsey on identity and comprehensive extensionality
    5. 8.5 Logicism and epistemology in Britain and America, 1921–1930
      1. 8.5.1 Johnson on logic, 1921–1924
      2. 8.5.2 Other Cambridge authors, 1923–1929
      3. 8.5.3 American reactions to logicism in mid decade
      4. 8.5.4 Groping towards metalogic
      5. 8.5.5 Reactions in and around Columbia
    6. 8.6 Peripherals: Italy and France
      1. 8.6.1 The occasional Italian survey
      2. 8.6.2 New French attitudes in the Revue
      3. 8.6.3 Commentaries in French, 1918–1930
    7. 8.7 German-speaking reactions to logicism, 1910–1928
      1. 8.7.1 (Neo-)Kantians in the 1910s
      2. 8.7.2 Phenomenologists in the 1910s
      3. 8.7.3 Frege’s positive and then negative thoughts
      4. 8.7.4 Hilbert’s definitive ‘metamathematics’, 1917–1930
      5. 8.7.5 Orders of logic and models of set theory: Lowenheim and Skolem, 1915–1923
      6. 8.7.6 Set theory and Mengenlehre in various forms
      7. 8.7.7 Intuitionistic set theory and logic: Brouwer and Weyl, 1910–1928
      8. 8.7.8 (Neo-)Kantians in the 1920s
      9. 8.7.9 Phenomenologists in the 1920s
    8. 8.8 The rise of Poland in the 1920s: the Lvóv-Warsaw school
      1. 8.8.1 From Lvóv to Warsaw: students of Twardowski
      2. 8.8.2 Logics with Łukasiewicz and Tarski
      3. 8.8.3 Russell’s paradox and Leśniewski’s three systems
      4. 8.8.4 Pole apart: Chwistek’s ‘semantic’ logicism at Cracov
    9. 8.9 The rise of Austria in the 1920s: the Schlick circle
      1. 8.9.1 Formation and influence
      2. 8.9.2 The impact of Russell, especially upon Carnap
      3. 8.9.3 ‘Logicism’ in Carnap’s Abriss, 1929
      4. 8.9.4 Epistemology in Carnap’s Aufbau, 1928
      5. 8.9.5 Intuitionism and proof theory: Brouwer and Gödel, 1928–1930
  13. Chapter 9 Postludes: Mathematical Logic and Logicism in the 1930s
    1. 9.1 Plan of the chapter
    2. 9.2 Gödel’s incompletability theorem and its immediate reception
      1. 9.2.1 The consolidation of Schlick’s ‘Vienna’ Circle
      2. 9.2.2 News from Gödel: the Konigsberg lectures, September 1930
      3. 9.2.3 Godel’s incompletability theorem, 1931
      4. 9.2.4 Effects and reviews of Gödel’s theorem
      5. 9.2.5 Zermelo against Gödel: the Bad Elster lectures, September 1931
    3. 9.3 Logic(ism) and epistemology in and around Vienna
      1. 9.3.1 Carnap for ‘metalogic’ and against metaphysics
      2. 9.3.2 Carnap’s transformed metalogic: the ‘logical syntax of language’, 1934
      3. 9.3.3 Carnap on incompleteness and truth in mathematical theories, 1934–1935
      4. 9.3.4 Dubislav on definitions and the competing philosophies of mathematics
      5. 9.3.5 Behmann’s new diagnosis of the paradoxes
      6. 9.3.6 Kaufmann and Waismann on the philosophy of mathematics
    4. 9.4 Logic(ism) in the U.S.A.
      1. 9.4.1 Mainly Eaton and Lewis
      2. 9.4.2 Mainly Weiss and Langer
      3. 9.4.3 Whitehead’s new attempt to ground logicism, 1934
      4. 9.4.4 The début of Quine
      5. 9.4.5 Two journals and an encyclopaedia, 1934–1938
      6. 9.4.6 Carnap’s acceptance of the autonomy of semantics
    5. 9.5 The battle of Britain
      1. 9.5.1 The campaign of Stebbing for Russell and Carnap
      2. 9.5.2 Commentary from Black and Ayer
      3. 9.5.3 Mathematicians—and biologists
      4. 9.5.4 Retiring into philosophy: Russell’s return, 1936–1937
    6. 9.6 European, mostly northern
      1. 9.6.1 Dingler and Burkamp again
      2. 9.6.2 German proof theory after Gödel
      3. 9.6.3 Scholz’s little circle at Munster
      4. 9.6.4 Historical studies, especially by Jørgensen
      5. 9.6.5 History-philosophy, especially Cavaillès
      6. 9.6.6 Other Francophone figures, especially Herbrand
      7. 9.6.7 Polish logicians, especially Tarski
      8. 9.6.8 Southern Europe and its former colonies
  14. Chapter 10 The Fate of the Search
    1. 10.1 Influences on Russell, negative and positive
      1. 10.1.1 Symbolic logics: living together and living apart
      2. 10.1.2 The timing and origins of Russell’s logicism
      3. 10.1.3 (Why) was Frege (so) little read in his lifetime?
    2. 10.2 The content and impact of logicism
      1. 10.2.1 Russell’s obsession with reductionist logic and epistemology
      2. 10.2.2 The logic and its metalogic
      3. 10.2.3 The fate of logicism
      4. 10.2.4 Educational aspects, especially Piaget
      5. 10.2.5 The role of the U.SA.: judgements in the Schilpp series
    3. 10.3 The panoply of foundations
    4. 10.4 Sallies
  15. Chapter 11 Transcription of Manuscripts
    1. 11.1 Couturat to Russell, 18 December 1904
    2. 11.2 Veblen to Russell, 13 May 1906
    3. 11.3 Russell to Hawtrey, 22 January 1907 (or 1909?)
    4. 11.4 Jourdain’s notes on Wittgenstein’s first views on Russell’s paradox, April 1909
    5. 11.5 The application of Whitehead and Russell to the Royal Society, late 1909
    6. 11.6 Whitehead to Russell, 19 January 1911
    7. 11.7 Oliver Strachey to Russell, 4 January 1912
    8. 11.8 Quine and Russell, June–July 1935
      1. 11.8.1 Russell to Quine, 6 June 1935
      2. 11.8.2 Quine to Russell, 4 July 1935
    9. 11.9 Russell to Henkin, 1 April 1963
  16. Bibliography
  17. Index