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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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