Abstract
This essay addresses the historical role of women’s work in the foundations debate in mathematical logic at the University of Cambridge. Part I gives an overview of the philosophical culture of Cambridge in the interwar era, its significance for women post-graduates, and its vested interests in achievement. Part II assesses the contents of the American logician Alice Ambrose’s post-graduate publications on the foundations debate, her teacher Ludwig Wittgenstein’s denunciation of her work, and Bertrand Russell’s subsequent critique of Ambrose’s remarks on the grammar of mathematical expression. At the center of this investigation is a portrait of Ambrose’s contributions to the Cambridge school of analysis and the elite capture of her ingenuity in elaborating Wittgenstein’s later philosophy. In recovering the historical context of this moment, the essay highlights those oblong dimensions of sociality in the English ancient university that warped women’s position as students and commentators in mathematical logic, giving shape to their later perspectives as late-twentieth-century professional philosophers.
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Notes
- 1.
For the purposes of this article, I will follow Janssen-Lauret in characterizing philosophical analysis historically as “a logic-focused, heavily male-dominated enterprise.” Op cit., “Grandmothers of Analytic Philosophy: The Formal and Philosophical Logic of Christine Ladd-Franklin and Constance Jones” in Minnesota Studies in the Philosophy of Science (forthcoming), p. 1.
- 2.
Anonymous, “[Marginalia]: Letter of 16 March 1934” in The Cambridge Moral Sciences Faculty Board Minutes. MIN.IV.10b. University Library Manuscripts Archive. University of Cambridge, p. unmarked [197a].
- 3.
Cf. Alice Ambrose, “Alice Ambrose to E. B. McGilvary, 19 May 1933” The Papers of Alice Ambrose. GBR/0012/MS.Add.9938/3. University Library Manuscripts Archive, University of Cambridge, Folio 20.
- 4.
Personal correspondence with Louise Clarke, Reading Room Superintendent, University Library Manuscripts Archive, University of Cambridge.
- 5.
Ambrose, “Alice Ambrose to E. B. McGilvary, 16 October 1932,” The Papers of Alice Ambrose, Folio 3–4. This is exhibited again in Ambrose’s ongoing concern in her first academic year for receiving the necessary funds from Newnham College to continue research as a post-graduate student vis-à-vis Moore’s contention that funding typically went to men of Trinity. Alice Ambrose, “Alice Ambrose to E. B. McGilvary, 19 May 1933”, The Papers of Alice Ambrose, Folio 23.
- 6.
Alice Ambrose, ‘In Defense of An Extensional Logic’. AW AM18 (M1-A-5). The University of Wisconsin, 1932.
- 7.
“Scholarships and Fellowships” in ‘Wellesley College Bulletin: Calendar Number 1932–1933.’ Wellesley, MA, 1932, p. 175. https://repository.wellesley.edu/islandora/object/wellesley%/3A484/datastream/OBJ/download (accessed 30 April 2022).
- 8.
Ambrose, “Alice Ambrose to E. B. McGilvary, 16 October 1932,” The Papers of Alice Ambrose, Folio 3–4.
- 9.
Op cit., “Alice Ambrose to E. B. McGilvary, 26 June 1933,” The Papers of Alice Ambrose, Folio 24.
- 10.
On the study of finitism in Wittgenstein’s philosophy of mathematics and logic see Mathieu Marion, Wittgenstein, Finitism, and the Foundations of Mathematics (Oxford: The Clarendon Press, 1998).
- 11.
Cf. For the 1932–1933 academic year, the Board of the Faculty of Moral Sciences announced Wittgenstein’s course lectures, “Philosophy for Mathematicians,” as open to students reading for the Mathematical Tripos “on payment of the composition fee of their Faculty.” Cf. Cambridge University Reporter (1932–1933, pp. 2, 26, 486, 510, 774, 798).
- 12.
Ambrose defines a verbal form as expressing both the truth and falsity of a proposition, what Wittgenstein identifies as the rules or “grammar” of logical statements. Op cit., “Finitism in Mathematics [II]” in Mind (New Series) 44, no. 175 (July 1935): 317n3.
- 13.
This was in spite of the 1932 publication of Kurt Gödel’s incompletability theorems, which proved the system of Principia to be incomplete and the metatheory of its axioms inconsistent.
- 14.
Contrast this with Frank P. Ramsey’s report on the results of the Tractatus to the Society of Apostles see: Cheryl Misak, Frank Ramsey: A Sheer Excess of Powers. Oxford: Oxford University Press, 2020, pp. 137–140, 215–216.
- 15.
Ambrose, “Finitism in Mathematics [II],” 319n1. Ambrose is cautious in the second half of her 1935 essay to stress that “Any reader who finds mistakes or absurdities in my views must not suppose that [Wittgenstein] is responsible for them. Even where … I cite an example actually given by him, it must not be assumed that the use which I make of such an example is that which he intended to make.” Her clarification is the result of the upsetting ordeal she experienced shortly after publication of the first half of “Finitism in Mathematics,” which I detail below.
- 16.
Ambrose’s use of the term of art ‘verification’ is peculiar; she seemingly ignores prevalent literatures on giving a verification in a system of logical empiricism and her commentary on verification is sui generis, excluding the obvious influence of Wittgenstein. Cf. Ambrose (1935b, p. 318).
- 17.
The other three being Martha Hurst’s essay article, “Implication in the Fourth Century B.C.” and Susan Stebbing’s critical notice on Carnap’s Logische Syntax der Sprache, published together in the third issue of the 1935 volume, along with Helen Knight’s piece, “Stout on Universals,” published in the fourth issue. On Mind as a new forum for women philosophers see: Thomas W. Staley, “The Journal Mind in its Early Years: 1876–1920: An Introduction” in The Journal of the History of Ideas 70, no. 2 (Apr., 2009): 261.
- 18.
Alice Ambrose, “Alice Ambrose to Dorothy Moore 16 February 1936”. The Correspondence of G. E. Moore. GBR/0012/MS Add.8830 8 L/8. University Library Manuscripts Archive, University of Cambridge, Folio 4.
- 19.
Russell in nearly all instances addressed recipients of his letters with the formal titles “Mr.,” “Mrs.” and “Miss.” His use of the title “Miss” in addressing Ambrose, then, evidences an intergenerational dispute over the way in which to publicly address a woman title holder in print. As I show, this etiquette was itself predicated on a culture of learning wherein women were not guaranteed the same access to education or certification as men. Russell’s elision of Ambrose’s formal title of doctor can therefore not be extricated from the world of elite masculinity and bias at Cambridge and should not be passed over without proper historicization. For more on Russell, sexism and historiography see: Connell and Janssen-Lauret (2022). Cf. Bertrand Russell, My thanks to Landon Elkind and Sophia Connell and Frederique Janssen-Lauret for illuminating aspects of this topic for me.
- 20.
R. B. Braithwaite, in his 1970 tribute to Russell made the point this way: “In his later writings [Russell] regarded the general problem as that of establishing an identity of the relational structure between the realm of perception and that of the physical world, without always realising that to say that two realms have the same structure is to say very little unless the ordering relations in both realms are given.” R. B. Braithwaite, “Bertrand Russell as Philosopher of Science,” The Journal for the Philosophy of Science 21, no. 2 (May 1970): 130.
- 21.
To make this even more plain to the intended audience, Ambrose in this section of her piece cites a “Dr. M. Lazerowitz,” her partner and a fellow Wittgensteinian, as concurring with her “that Russell and I both agree on the important point regarding the existence of an infinite expansion and disagree on the relatively trivial point as to what kind of impossibility is involved in the supposition that one runs through π.” Ambrose, “‘Finitism’ and the Limits of Empiricism,” “Mind (New Series) 46, no. 183 (Jul., 1937): 383.
- 22.
Ambrose, “Alice Ambrose to Dorothy Moore, 16 February 1936”. The Correspondence of G.E. Moore, Folio 3–5.
- 23.
Janssen-Lauret and Connell (2022) have noted the common assumption in the historiography of analytic philosophy that Lazerowitz, and not Ambrose, was the source of philosophical insight in their partnership. My forthcoming research on Ambrose and Lazerowitz and Smith College’s Department of Philosophy shows this to, indeed, be incorrect—the result of the continued prevalence of implicit bias in disciplinary philosophy after 1945. In point of fact, it was Ambrose, not Lazerowitz, who was responsible for the logic-focused heavy-lifting in their partnership. See: David Loner, “Alice Ambrose and Morris Lazerowitz and the Later Wittgenstein in Postwar US Women’s College Education, 1938–1972” (forthcoming). On claims of Lazerowitz’s supposed intellectual leadership over Ambrose and bias in historiography see also Connell (2022).
- 24.
Alice Ambrose, “Recollections of Wittgenstein.” CA-MS-00101. Alice Ambrose Lazerowitz and Morris Lazerowitz Papers, Smith College Archives, Smith College, Box 895, Folder, 19, Folio 2.
- 25.
Selections quoted herein from The Papers of Alice Ambrose, The Correspondence of G. E. Moore and the Minutes of the Board of the Cambridge Moral Sciences Faculty and the Cambridge University Reporter appear courtesy of the Syndics of Cambridge University Press. Selections quoted herein from The Alice Ambrose Lazerowitz and Morris Lazerowitz Papers appear courtesy of Smith College Archive. Excerpts from Frederique Janssen-Lauret’s forthcoming articles appear courtesy of the author. My thanks to Landon Elkind and Alex Klein for their editorial guidance and to Michael Beaney for his kind invitation to contribute to this volume. My thanks also to Frank Bowles and Nanci Young for their expert knowledge in securing access to archival materials. Portions of this article were first presented to the Bertrand Russell Society’s March 5–6, 2021, conference, “Feminism and Philosophical Women in Russell’s Circle,” hosted online by McMaster University’s Bertrand Russell Research Centre.
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Loner, D. (2024). Alice Ambrose and Women’s Work in the Foundations Debate at the University of Cambridge, 1932–1937. In: Elkind, L.D.C., Klein, A.M. (eds) Bertrand Russell, Feminism, and Women Philosophers in his Circle. History of Analytic Philosophy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-33026-1_5
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