[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.
128.
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
arbitrary."
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
USA
URL: http://www.irvinganellis.info
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