[FOM] Did Goedel's result come as a surprise to Bertrand Russell

Irving ianellis at iupui.edu
Fri Apr 2 13:24:34 EDT 2010

A number of questions and comments have been raised regarding the 
initial question and answers.

Most recently, for example, Charles Silver referred to BR's explanation 
for abandoning work in logic after completing Principia.

There are several accounts of this. In fact, Russell frequently excused 
himself from doing work in logic after work on the Principia was 
completed by saying that the effort of writing the Principia had 
exhausted him and left him incapable of doing any more mathematical 
work. John Edensor Littlewood, for example, recalled that Russell "said 
that Principia Mathematica 
 took so much out of him that he had never 
been quite the same again." (Littlewood's Miscellany (Bela Bollobas, 
editor; Cambridge/London/New York: Cambridge University Press; revised 
ed., 1986, first published in 1953 as A Mathematician’s Miscellany), p. 

Alfred Jules Ayer was accurately expressing Russell's explanation by 
stating (p. 27) that "after the years of labor which he expended on 
'Principia Mathematica', he became impatient with minutae." ("Bertrand 
Russell as a Philosopher", Proceedings of the British Academy LVIII 
(London: Oxford University Press, 1972), 3-27.

One more reaction which BR expressed on his goal of the PM to work out 
all of mathematics axiomatically on the basis of a small number of 
logical rules, as it relates to Goedel's incompleteness results, was 
reported by Daniel J. O'Leary on p. 52 of his "Principia Mathematica 
and the Development of Automated Theorem Proving", in Thomas Drucker 
(editor), Perspectives on the History of Mathematical Logic 
(Boston/Basel/Berlin: Birkhäuser, 1991), 47-53. There, O'Leary records 
that in a letter to Herbert Simon of 2 November 1956 when, upon being 
informed by Simon about early computerized proofs of theorems of 
propositional logic found in Principia, Russell replied: "I am 
delighted to know that Principia Mathematica can now be done by 
machinery. I wish Whitehead and I had know of this possibility before 
we wasted ten years doing it by hand."

We also have, related to this, that Russell told Alice Mary Hilton (in  
a letter of 9 June 1963, quoted on p. 250 in The Autobiography of 
Bertrand Russell: vol. III, 1944-1969 (New York: Simon and Schuster, 
1969), acknowledging receipt of her book Logic, Computing Machines and 
Automation (Washington [D.C.]: Spartan Books; Cleveland: World 
Publishing Co., 1963), that: "The followers of Goedel had almost 
persuaded me that the twenty man-years spent on the Principia had been 
wasted and that the book had better been forgotten."

If we want to attempt to account for Russell's apparently strange 
interpretation, in his letter to Henkin, that Goedel's results allow 2 
+ 2 = 4.001 in "school-boy arithmetic, we might resort to the 
possibility that, by the 1960s, if not earlier, Russell reverted to the 
neo-Hegelian philosophy of his college days and Cambridge Fellowship, 
such as we find in his Essay on the Foundations of Geometry (1897), 
before he discovered Peano in 1900. (In fact, Ivor Grattan-Guinness, in 
reconstructing the writing of chronology of The Principles of 
Mathematics (1903) ("How Did Russell Write 'The Principles of 
Mathematics' (1903)?", Russell (n.s.) 16 (1996-97), 101-127), strongly 
proposed that Russell did not adopt logicism until the last rewriting 
of PoM prior to taking it to press.) We know, for example, that one of 
the first logic books that Russell read, if not THE first, was Oxford 
neo-Hegelian Francis Herbert Bradley's 1883 Principles of Logic; 
Russell read it in September 1893 and again in January 1898, and there 
is also evidence that he read it again in 1905 and 1910 (see Melanie 
Chalmers & Nicholas Griffin, "Russell's Marginalia in His Copy of 
Bradley's Principles of Logic", Russell (n.s.) 17 (1997), 43-70; N. 
Griffin, "Bradley's Contribution to the Development of Logic", in James 
Bradley (editor), Philosophy after F. H. Bradley (Bristol: Thoemmes, 
1996), 197-202; C. N. Keen, "The Interaction of Russell and Bradley", 
Russell (o.s.) no. 3 (Autumn, 1971), 7-11. Russell's example to Henkin 
would sound rather familiar to readers of Bradley, and it would not be 
too surprising if Russell thought that Goedel's theorems might be in 
some way affirming Bradley's assertion in Principles of Logic (London: 
Kegan Paul, Trench, 1883), vol. II, Chapt. II, §7, 399, where Bradley 
wrote: "It is false that "one and one are two". They make two, but do 
not make it unless I happen to put them together; and I need not do so 
unless I happen to choose. The result is thus hypothetical and 

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
URL: http://www.irvinganellis.info

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