# Brixton Letter 36

## BR to C.D. Broad (via Frank Russell)

## July 11, 1918

- TL
- Trinity College
- Edited by

Kenneth Blackwell

Andrew G. Bone

Nicholas Griffin

Sheila Turcon

Cite*The Collected Letters of Bertrand Russell*, https://russell-letters.mcmaster.ca/brixton-letter-36
BRACERS 53925

<letterhead>1

57 GORDON SQUARE

LONDON, W.C. 1.

11 July 1918.

C.I. Broad2
Esq.

University

St. Andrews

Scotland.

Lord Russell is desired by Mr. Bertrand Russell to convey the following message to Mr. Broad: — “I have read him in this month’s *Mind* with much pleasure and approval, but I don’t altogether like shrieks3
upside-down. Tell him he should get into communication with Whitehead as to notation.”

- 1
**[document]**The letter was edited from a photocopy of the unsigned, typed letter is in Broad’s papers in Trinity College Library, Cambridge. BR’s message is not in the extant letters to his brother, and probably was communicated to Frank during a visit to Brixton. - 2
**C.I. Broad**Frank Russell got the second initial wrong. - 3
**in this month’s**Exclamation marks — known as “shrieks” — serve a number of purposes in the symbolism of*Mind*… shrieks*Principia Mathematica*, e.g. to indicate a predicative function or that a descriptive function is uniquely satisfied. In “A General Notation for the Logic of Relations”,*Mind*27 (1918): 284–303, C.D. Broad gave them additional roles, e.g. to distinguish relational propositions from relational complexes. The relevant one in this context is “*R*(!,**‘‘***β*)”, the class of things which have the relation*R*to some member of*β**.*(The*Principia*notation for this is*R***‘‘***β*[*PM*, *37.01].) Similarly, in Broad’s notation, “*R*(**‘‘***α*, !)” represents the class of things to which some member of*α*has the relation*R*. But also to be considered are the class of things which have the relation*R*to every member of*β**α*has the relation*R.*For these Broad turned the shriek upside-down: “*R*(¡,**‘‘***β*)” and “*R*(**‘‘***α,*¡)”, respectively. It’s not obvious why BR didn’t like the upside-down shriek notation, but perhaps it was because it might be confused with the other*Principia*notation. For example, “¡” is hard to distinguish in writing from “İ”, which, by the usual*PM*principles, would represent the product of two relations (except that in*PM*BR and Whitehead omitted the over-printed dot). Broad may, in fact, have had this in mind, for the situation he used “¡” to represent is a kind of product (albeit more properly of classes than relations), while that symbolized by “!” is a kind of sum. Alternatively, BR may have thought that using an upside-down shriek would be hard to distinguish in writing from an over-dotted “1”, which is needed in relation-arithmetic (*cf*.*PM*, *181).

Rather surprisingly, the formalism of*Principia*allows only for two-term (or dyadic) relations. In fact the class of relations, Rel, is defined for dyadic relations only. Broad’s main purpose in the paper was to extend the notation to allow for relations of greater adicity. This, he said, would be of especial importance in dealing with geometry. Indeed, he demonstrated the power of his symbolism by translating Hilbert’s four axioms of order for Euclidean geometry into it. (*Cf*. David Hilbert,*Foundations of Geometry*, trans. E.J. Townsend [Chicago: Open Court, 1902].) This, presumably, was why BR recommended that he get in touch with Whitehead, who was working (on his own) on the never-finished, fourth volume of*Principia*, which would have dealt with geometry.

Though the purpose of Broad’s paper was simply to propose a symbolism, and he explicitly avoided taking a stand on logical and philosophical issues, the fact that BR approved of the paper indicates the extent to which he was moving away from some of the doctrines in*Principia*. In particular, Broad’s notational distinction between relational propositions and relational complexes, which would be a very useful one in a more ordinary sort of system than*Principia*, has no role in*Principia,*where there are no propositions.

All that said, Broad’s notation never did catch on.

##### 57 Gordon Square

The London home of BR’s brother, Frank, 57 Gordon Square is in Bloomsbury. BR lived there, when he was in London, from August 1916 to April 1918, with the exception of January and part of February 1917.

##### A.N. Whitehead

Alfred North Whitehead (1861–1947), Cambridge-educated mathematician and philosopher. From 1884 to 1910 he was a Fellow of Trinity College, Cambridge, and lecturer in mathematics there; from 1911 to 1924 he taught in London, first at University College and then at the Imperial College of Science and Technology; in 1924 he took up a professorship in philosophy at Harvard and spent the rest of his life in America. BR took mathematics courses with him as an undergraduate, which led to a lifelong friendship. Whitehead’s first major work was *A Treatise on Universal Algebra* (1898), which treated selected mathematical theories as “systems of symbolic reasoning”. Like BR’s *The Principles of Mathematics* (1903), it was intended as the first of two volumes; but in 1900 he and BR discovered Giuseppe Peano’s work in symbolic logic, and each decided to set aside his projected second volume to work together on a more comprehensive treatment of mathematics using Peano’s methods. The result was the three volumes of *Principia Mathematica* (1910–13), which occupied the pair for over a decade. After *Principia *was published, Whitehead’s interests, like BR’s, turned to the empirical sciences and, finally, after his move to America, to pure metaphysics. See Victor Lowe, *Alfred North Whitehead: the Man and His Work*, 2 vols. (Baltimore and London: Johns Hopkins U. P., 1985–90).

##### Brixton Prison

Located in southwest London Brixton is the capital’s oldest prison. It opened in 1820 as the Surrey House of Correction for minor offenders of both sexes, but became a women-only convict prison in the 1850s. Brixton was a military prison from 1882 until 1898, after which it served as a “local” prison for male offenders sentenced to two years or less, and as London’s main remand centre for those in custody awaiting trial. The prison could hold up to 800 inmates. Originally under local authority jurisdiction, local prisons were transferred to Home Office control in 1878 in an attempt to establish uniform conditions of confinement. These facilities were distinct from “convict” prisons reserved for more serious or repeat offenders sentenced to longer terms of penal servitude.

##### C.D. Broad

Charlie Dunbar Broad (1887–1971), British philosopher, studied at Trinity College, Cambridge (1906–10), where he came in contact with BR, whose work had the greatest influence on him, though he was taught primarily by W.E. Johnson and J.M.E. McTaggart. (He wrote the definitive refutation of McTaggart’s philosophy after the latter’s death.) In 1911 BR examined Broad’s fellowship dissertation, which was published as *Perception, Physics, and Reality* (1914) and which BR reviewed in *Mind *in 1918 (**15** in *Papers* 8). BR reviewed more books by Broad in the 1920s, and Broad returned the favour over the decades. Outstanding among his reviews was that of the first volume of BR’s *Autobiography* in *The Philosophical Review* 77 (1968): 455–73. From 1911 to 1920 Broad taught at St. Andrews University; in 1920 he moved to Bristol as Professor of Philosophy before returning to Trinity in 1923, where, as Knightbridge Professor of Moral Philosophy, he remained for the rest of his life. He wrote extensively on a wide range of philosophical topics, including ethics, philosophy of mind, philosophy of science, and psychical research. His philosophical writings are marked by the impartiality and clarity with which he stated, revised, and assessed the arguments and theories with which he was dealing, rather than by originality in his own position. BR and Moore were the two philosophers with whose views his were most closely aligned. Broad was evidently devoted to BR. One of the current editors was introduced to Broad upon visiting Trinity College Library in 1966. He was keen to hear about BR from someone who had recently talked with him. Following BR’s death Broad introduced a reprint of G.H. Hardy’s *Bertrand Russell and Trinity: a College Controversy of the Last War* (Cambridge U. P., 1944; 1970).

##### Frank Russell

John Francis (“Frank”) Stanley Russell (1865–1931; 2nd Earl Russell from 1878), BR’s older brother. Author of *Lay Sermons* (1902), *Divorce* (1912), and *My Life and Adventures* (1923). BR remembered Frank bullying him as a child and as having the character and appearance of a Stanley, but also as giving him his first geometry lessons (*Auto*. 1: 26, 36). He was accomplished in many fields: sailor, electrician, house builder, pioneer motorist, local politician, lawyer, businessman and company director, and (later) constructive junior member of the second Labour Government. Frank was married three times. The first marriage involved serious legal actions by and against his wife and her mother, but a previous scandal, which ended his career at Oxford, had an overshadowing effect on his life (see Ruth Derham, “‘A Very Improper Friend’: the Influence of Jowett and Oxford on Frank Russell”, *Russell* 37 [2017]: 271–87). The second marriage was to Mollie Sommerville (see Ian Watson, “Mollie, Countess Russell”, *Russell* 23 [2003]: 65–8). The third was to Elizabeth, Countess von Arnim. Despite difficulties with him, BR declared from prison: “No prisoner can ever have had such a helpful brother” (**Letter 20**).

##### Principia Mathematica

*Principia Mathematica*, the monumental, three-volume work coauthored with Alfred North Whitehead and published in 1910–13, was the culmination of BR’s work on the foundations of mathematics. Conceived around 1901 as a replacement for the projected second volumes of BR’s *Principles of Mathematics* (1903) and of Whitehead’s *Universal Algebra* (1898), *PM* was intended to show how classical mathematics could be derived from purely logical principles. For a large swath of arithmetic this was done by actually producing the derivations. A fourth volume on geometry, to be written by Whitehead alone, was never finished. In 1925–27 BR, on his own, produced a second edition, adding a long introduction, three appendices and a list of definitions to the first volume and corrections to all three. (See B. Linsky, *The Evolution of Principia Mathematica* [Cambridge U. P., 2011].) In this edition, under the influence of Wittgenstein, he attempted to extensionalize the underlying intensional logic of the first edition.