A short timeline for Whitehead and Russell as logicians I. Grattan-Guinness

? = date approximate + = from then onwards

1890–1894 Russell at Trinity College Cambridge, studying mathematics and philosophy 1895+ Russell Fellowship for six years, on the philosophy of mathematics 1896+ Russell engages with Cantor’s set theory 1897 Russell An essay on the foundations of geometry 1898 Whitehead Universal algebra, including some Boolean algebra 1899+ Russell changes philosophy from neo-Hegelianism to a form of positivism 3 August 1900 Russell and Whitehead hear Peano in Paris; Russell quickly converted September 1900+ Russell learns Peano’s mathematical logic, adds logic of relations January 1901? Russell conceives of logicism May 1901? Russell finds a paradox in set theory 1901+ Whitehead’s interaction with Russell gradually becomes a collaboration on the logicism project May 1902 Russell sends the manuscript of The principles of mathematics to Cambridge University Press June 1902?+ Russell begins to read Frege in detail; adds appendix to book May 1903 Russell The principles of mathematics August 1904 Russell discovers the need for the axiom of choice in set theory July 1905 Russell's theory of definite descriptions provides ground for mathematical functions in logicism 1905-1906 Whitehead produces important work on geometry, with consequences for logicism and for theories of space Early 1907 Russell decides on the vicious circle principle as the ground for solving the paradoxes; he and Whitehead exegete logicism October 1909 first three volumes of Principia mathematica literally carted to Cambridge University Press; book approved by Johnson November 1909? Press requests financial support for publication; Whitehead and Russell secure it from the Royal Society of London December 1910 volume 1 of Principia mathematica published January–May Whitehead notices conceptual error in handling cardinals in volume 2; 1911 printing delayed, some rewriting for Whitehead, some extra printing costs for Russell 1912, 1913 volumes 2 and 3 of Principia mathematica published 1910–1918? Whitehead works on volume 4 of Principia mathematica, on aspects of geometry, but then abandons it 1911–1913 first interactions between Russell and Wittgenstein, over logic and philosophy; invention of the truth-table method for evaluating compound propositions 1914 Russell's first major book in its philosophical style: Our knowledge of the external world as a field for scientific method in philosophy March-May 1914 lecture courses by Russell at Harvard University and the Lowell Institute on Principia mathematica and on Our knowledge; extensive notes taken by T. S. Eliot 1910-1916 Russell logic teaching at Cambridge, and private teaching of Nicod and Wrinch May-September 41/2 months for Russell in Brixton prison for anti-war activities; writes 1918 popular account of logicism, helped by Wrinch, who brings him books from libraries 1919 Russell An introduction to mathematical philosophy 1921+ Wittgenstein resuems contact with a long manuscript on logic; Wrinch secures possibility of publication in a German philosophical journal as long as Russell writes an introduction 1921 in this introduction Russell proposes a hierarchy of languages, but never realises the significance of his own suggestion 1921–22 Cambridge offers new edition of Principia mathematica 1923, 1924 Russell writes new material for edition, but no hierarches 1925-1926? Press resets volumes 1 and 2; Russell reads proofs with Ramsey 1925, 1927, 1927 second edition of Principia mathematica published; volume 3 lithographed 1927 Russell The analysis of matter carries out logical constructionism in the context of the new physics 1934 Whitehead sketches a new version of logicism, but with a social core; not influential 1935+ Russell returns somewhat to logic: technical paper, long new preface to reprint of The principles 1938–41 Russell contacts with new generation of logicians: Tarski, Gödel, Quine (and Carnap already); some impact on An enquiry into meaning and truth (1940) 1942–44 some involvement with logic when dealing with the Schilpp volume The philosophy of Bertrand Russell (1944) 1948 some use of logic by Russell in Human knowledge –1965 continuing nemesis for Russell: failing to understand the significance of Gödel’s first incompletability theorem, or even state it properly

Logicism in the context of the development of set theory I. Grattan-Guinness

Set theory began to be developed on a large scale from the late 1890s onwards; for example, it was part of the mathematical logic that grounded logicism, and for convenience much of Principia mathematica was elaborated in its terms. Several different parts and features of set theory became prominent, and logicism was supposed to embrace all of them. In practice, though, how many did it tackle?

The lecture will consist of a series of shorts discourses on a selection of the following topics: 1. State of set theory around 1895 2. Applications of descriptive set theory to modern mathematical analysis: functional analysis, integral equations, measure theory 3. Order-types 4. Transfinite arithmetic 5. Paradoxes and their solutions 6. Axiomatic set theory as a solution? 7. The axioms of choice in logic 8. Relationship of set theory to model theory 9. The inescapable inadequacy of set theory to ground mathematics 10. Moments and set theory 11. Zero, and our misreading of counting

Synoptic table of the historical context of Principia mathematica.

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