, AND SUSAN STEBBING ON INCOMPLETE SYMBOLS: THE HIDDEN INFLUENCE OF EARLY ANALYTIC FEMALE LOGICIANS

FREDERIQUE JANSSEN-LAURET, UNIVERSITY OF MANCHESTER, UK

1. The History of and the Legacy of Female Philosophers Conventional history: analytic philosophy: a logical, analytical endeavour founded by Russell, Moore, Wittgenstein based on ideas from Frege; no women until the 1950s. Usual hypothesis: Women stress the normative, the analytic project was systematic/. Historical record falsifies this: female systematic philosophers always around and were in fact responsible for several key theses of analytic philosophy: – A woman, Constance Jones, formulated the sense-reference distinction two years before Frege; Russell was aware of her but refused to give her credit [3]. – Early analytic philosophy had been strongly atomistic and considered holism muddled and Hegelian; middle analytic philosophy was holist or foundherentist (Quine, late Wittgenstein). Where did holism come from? Susan Stebbing diagnosed the flaws in atomism and proposed a moderate foundherentism in 1930-32 [2]. – Early-to-mid analytic philosophy was ardently extensionalist (Quine, Tarski, early Carnap) and considered extensional discourse unscientific; late analytic philosophy has modality everywhere. Where did modality come from? From the work of Ruth Barcan Marcus in the mid-40s [1]. Alternative history of analytic philosophy: Women’s contributions have been written out of history due to a variety of factors all of which come down primarily to sexism. Sexism and dismissiveness of peers; institutional discrimination and lack of support; sexism of ref- erees/appointment committees; sexism of historians unfairly finding women’s work derivative or odd; lack of funds and means; originality in female thinkers judged negatively.

2. Two Curious Cases of Neglected Contributions by Female Philosophers: Sense/Reference and Modality 1. Very Early Analytic Philosophy: Anti-Psychologism, Sense and Reference – Earliest analytic philosophy texts date from before anyone in the UK had read Frege. – Some key ideas of analytic philosophy traceable to their reading of Kant not Frege: e.g. prob- lematising the synthetic a priori category of substance and attribute. – Some key analytic philosophy of logic doctrines were known in Cambridge before: anti- psychologism, sense-reference distinction. Who proposed them?

2. Early Analytic Philosophy: Logical Atomism and Early Analytic Philosophy: Logical Atomism and Foundationalism – Russell and Moore rebelled against idealism, but also against Bradley’s extreme holism. 1 2 FREDERIQUE JANSSEN-LAURET, UNIVERSITY OF MANCHESTER, UK

– Bradley: language does not let us divide reality into individually cognisable chunks. All judge- ments leave something out and must be supplemented by other judgements. – V. early Russell/Moore: yes, we can know individual bits of reality. Foundationalism! – Objection: does every word stand for a thing? Problem of falsehood; Meinongianism. – Fix: not every word, but every sentence, stands for something. Incomplete symbols. – Extreme foundationalism, in the sense that we know the world via its individually knowable con- stituents. (Not in the sense that we know only the mental directly.) Nowadays: analytic holism/foundherentism almost everywhere. Where did they come from? How were they brought under the umbrella of analytic philosophy?

3. My Solutions: Neglected Contributions by Female Philosophers. My thesis (1): Anti-psychologism and the sense-reference distinction were known to the Cam- bridge early analytic philosophers via the works of Constance Jones, although Russell tried to minimise her contributions. Jones lacked Frege’s mathematical-logic sophistication, but her phi- losophy of logic pre-empts Frege’s sense-reference distinction, views on identity, anti-psychologism and sidesteps his problematic ‘third realm’. My thesis (2): Efforts to bring together the analytic approach to language, logical form, and ontology with more holist tendencies in are due to Quine but also to Susan Stebbing. She is an interesting, transitional figure with an original, proto-foundherentist view, not a logical atomism acolyte (as portrayed by male historians) [2].

4. Case Study 1: Constance Jones’ Philosophy of Logic 4.1. Life and Works. Born into a strict Victorian family in 1848, E.E.C. Jones had only an intermittent education and was not allowed to go to university until her brothers had all finished. Yet she became trilingual living in South Africa in her teens, and had an ardent love of books, languages, and sound reasoning which saw her through, combined with some money provided by a supportive aunt. In her mid-twenties, she finally made it to the newly founded and very financially precarious Girton College for women. As Jones knew little Latin compared to the men, she took Moral Sciences, and was the first Girton student to achieve a First in it. (Although women sat examinations alongside men, they would not be allowed to graduate from Cambridge University until 1948.) Jones got on well with Sidgwick, whose posthumous works she edited and Stout, a big fan of her philosophy of logic, and stayed on as Librarian, Lecturer in Logic, and finally Mistress of Girton, publishing four logic books and two dozen articles. Jones brought renewed academic vigour and raised substantial funds, saving the college from financial ruin through sound management, all the while introducing female students to the joys of logic. 4.2. Jones’ Philosophy of Logic. ‘any Subject of Predication is an identity of denotation in diversity of intension’ [7, p. 167]; also [4, 5] – By ‘identity of denotation’, she means identity of reference, and by ‘diversity of intension’, she means difference of sense or meaning. Traditional logicians claimed that logic had three laws: non- contradiction (not both A and not-A), excluded middle (either A or not-A), and identity (A is A). But Jones thought this trio unsatisfactory: non-contradiction and excluded middle do not apply only to identities. The general form of propositions used in logic is actually ’S is P’, where Ostertag incorrectly treat ‘S is P’ as a contemporary-style schematic law in which any subject term may be substituted for ‘S’ and any predicate for ‘P’. Such schemata were unknown to Aris- totelian logicians, and were not strictly adhered to by mathematical logicians until Tarski and CONSTANCE JONES, BERTRAND RUSSELL AND SUSAN STEBBING ON INCOMPLETE SYMBOLS: THE HIDDEN INFLUENCE OF EARLY ANALYTIC FEMALE LOGICIANS3

Quine. E.g. ‘A’ typically occurs ambiguously in ‘either A or not-A’ and ‘A is A’. I propose a different reading of Jones’s law. It is significant that her formulation specifies that any subject of predication ‘is an identity of denotation in diversity of intension’: the ‘is’ and ‘in’ should be read as factive, not syntactic: there is an identical subject denoted and it is in two intensions. Jones is not formulating a law of grammatical form, but one of truth conditions for subject-predicate sentences. Thus interpreted, Jones’s law translates as ‘a subject-predicate sentence is true just in case one identical referent belongs to two diverse intentions, and the subject and the predicate each express an intension to which the thing denoted belongs’. All sentences which do so are true, and all subject-predicate sentences which fail to do so – which single out an identical referent or attribute to that referent an intension to which the referent does not belong – are false.

4.3. Reception. ‘[The] post-Hegelian doctrine which treats all predication as the statement of an Identity in Difference ... has been strikingly illustrated by a theory expressed first by Miss Constance Jones as long ago as 1890, and, a little later, by Prof. Frege’ [8, p. 521]. J.N. Keynes, citing her discussion in her second book [5, pp. 20 ff.] also credited her with its discovery (Keynes 1906: 190). Russell’s friend Jourdain had apparently tried to make Russell acknowledge a debt to her in a letter of 1909 which is now lost. Sadly, his efforts were in vain, and Russell continued to refuse to attribute the distinction to Jones: ‘[You say] that Miss Jones’s distinction of signification and denotation must be much the same as Frege’s Sinn and Bedeutung. But of course some such distinction is a commonplace of logic’ (Grattan-Guinness 1977, 119). In an exchange with Russell on the roles of names and descriptions at the the following year Jones politely but pointedly drew attention to Russell’s lack of proper attribution: ‘If it had not been . . . for the fact that I had recently become aware that Professor Frege’s Analysis of Categoricals seemed to be really the same as mine, and had been approved by Mr. Bertrand Russell in his Principles of Mathematics, I should not at this time have returned [Russell’s] attack’ [7, p. 167]. (Russell also thought Dewey ‘a good man but not a very clever one’ (CP 6: 258, 1914; quoted in Misak p. 104). There is no justification for the judgement of her one twenty-first century commentator, Gary Ostertag, who uses this judgement as an excuse for Russell’s attempts to avoid admitting ‘that he was influenced by Jones, or that she anticipated him in some small way [because it] would detract from Russell’s own contribution’. Rather than letting this statement serve as the indictment of Russell which it clearly is to the reasonable observer, Ostertag blithely continues, ‘It is one thing to acknowledge a debt to a Frege or to a Peano [but] Jones was manifestly not of their caliber’. Ostertag claims that she was ‘philosophically quite retrograde’ (Ostertag 2011 §4). But even Jones’s formal logic was by no means retrograde, but up-to-date with the latest formal methods of Victorian logic, such as Venn diagrams (e.g. [4, pp. 47-8], [5, pp. 35-48]. And her philosophy certainly wasn’t.

4.4. Jones’s Reply to Russell. ‘But unless it has a meaning, how can we interpret it into “Some one wrote Waverley and no one else did,” and how could we say, as Mr. Russell does on p. 125 (foot), that the meanings of “the author of Waverley” and ”the author of Marmion” are not identical ? How can we know that their meanings are not identical unless (1) they both have meanings, and (2) we know what those meanings are?’ [7, p. 181] – Jones is claiming that we need to distinguish meanings (senses). ‘If Scott is the author of Waverley signifies that Scott and the author of Waverley are one and the same person, the two terms Scott and the author of Waverley both refer to one identical object, and the assertion may be not trivial and may be worth making because, owing to diversity of intension, it may convey information.’ [7, p. 177] ‘ But I agree with Mr. Russell that even Proper Names 4 FREDERIQUE JANSSEN-LAURET, UNIVERSITY OF MANCHESTER, UK really stand for descriptions-as a rule, he says-always, I think, except when first actually attached as a label. A name would be of no use, and therefore would not continue to be used, even as a label, if it did not carry with it some intensional implication.’ ’ [7, p. 183] – Jones agrees that what we ordinarily call ‘proper names’ in general carry descriptive meanings. ‘But if it is a fact that so-called Proper Names (e.g., Scott) are to some extent descriptive, I feel that a refutation of my identity-in-diversity analysis founded on the assumption that Scott is merely “a noise or shape” and entirely without intension, cannot, so far, be regarded as very conclusive.’ – Russell thinks definite descriptions have no meaning in isolation, but can only be given contextual definitions. Jones raises the worry that without acquaintance – which she has doubts about this leads to an infinite regress: unless we have some sense to give to the description, we cannot know what it means. We might be able to build up meanings from the ground if we had acquaintance with things denoted, but in practice we always build some meaning into our name-statements: they are never just mere noise.

5. Case Study 1: Susan Stebbing on Incomplete Symbols, Epistemology, and Ontology 5.1. Life and Works. A woman with a disability, Stebbing missed out on early education due to M´eni`ere’sdisease. At Girton, she read History until 1907 and then Moral Sciences (philosophy) after stumbling upon F.H. Bradley’s work in the library. She is thanked by Jones for reading the proofs of [6]. Master’s thesis on , London (1912). Her main logic tutor was W.E. Johnson. Lectureship at King’s College London from 1913 to 1915. Part-time lectureship at Bedford College (1915-1920) whilst running a girls’ school in Hampstead with her sister and two friends. Met Moore, Russell, and Whitehead in London around 1917, discussed logic, science, analytic philosophy. She gradually went over to analytic philosophy and abandoned idealism. Full-time lecturer at Bedford College in 1920, Reader in 1927, and Professor in 1933. Stebbing was the first female philosophy professor in the UK. Popularised Vienna Circle and Carnap. Wrote four books, including first accessible text on polyadic logic and its philosophy.

5.2. Stebbing’s Objections to Logical Atomism. What is the analysis of analytic philosophy? – Analysis of language (‘same-level analysis’), or facts (directional analysis) [10, p. 92] ? – Must analysis be analytic or a priori? Same-level analysis: yes, directional analysis: no. – That casts further doubt on Russell’s ideas that incomplete symbols are definitions in the math- ematical sense, and clarify what we meant all along [9, p. 441]. – Must every analysis terminate in simples with which we are acquainted? Can we be acquainted with plausible candidate simples, e.g. particles? Mental states? Universals?

5.3. Stebbing’s Solutions/Replies to Russell. Distinguish clearly between cases of ‘same-level’ analysis of language—a relation between symbols, such as mathematical definitions, which are analytic—and directional analysis of facts, identifying their underlying constituents: e.g. a com- mittee is composed of people, who are composed of mental and bodily states — this need not be analytic [12, pp. 35-36]. Clarify what exactly the connection is between knowledge by acquaintance and direct reference, knowledge by description and logical constructions: how do we know simples? Give up extreme foundationalism, allow some interdependence between statements of our lan- guage back in; meaning does not come only from acquaintance plus logical constructions. CONSTANCE JONES, BERTRAND RUSSELL AND SUSAN STEBBING ON INCOMPLETE SYMBOLS: THE HIDDEN INFLUENCE OF EARLY ANALYTIC FEMALE LOGICIANS5

5.4. Comparison of Stebbing’s and Jones’s Regress Arguments. ‘Ordinary language is essentially descriptive. It is for this reason that no non-general fact can be expressed. If we attempted to use a sentence not containing any descriptive symbol, we should be reduced to a set of pointings. In such a case, we could say nothing; we could only point’ [11, p. 341]. A kind of proto-foundherentism, in between holism and foundationalism. We need direct reference of objects of acquaintance in our language, but we have no statements which consist of nothing but such demonstrative content. Some descriptive content must always be involved. Use of demonstratives depends on background theory. ‘Pure demonstration is a limit of approximation.’ [11, p. 342] In my [2], I attributed Stebbing’s ontological ‘foundherentism’ to her being influenced by Bradley. Although this influence is there, the argument above may also have come from Jones.

6. Conclusion The historical record clearly reflects that these women influenced the debate and made substan- tial, original contributions which shaped the field. But historical narratives do not reflect these facts. They tend to neglect these towering female figures altogether or present them either as hand- maidens to the ‘great men’ or as proposing defective precursors of ideas so much improved by the ‘great men’ that their versions were not worth mentioning. But as we have seen, these women’s ideas were well worked out and interesting, possibly preferable to the more familiar doctrines of orthodox analytic philosophy.

References [1] Frederique Janssen-Lauret. Meta-ontology, naturalism, and the Quine-Barcan Marcus debate. In Frederique Janssen-Lauret and Gary Kemp, editors, Quine and His Place in History, pages 146–167. Palgrave Macmillan, Basingstoke, 2015. [2] Frederique Janssen-Lauret. Susan Stebbing, incomplete symbols, and foundherentist meta-ontology. Journal for the History of Analytical Philosophy, 5(2):6–17, 2017. [3] Frederique Janssen-Lauret. Grandmothers of analytic philosophy. In Minnesota Studies in Philosophy of Science XX. University of Minnesota Press, Minneapolis, 2021. [4] E.E.C. Jones. Elements of Logic as a Science of Propositions. T. and T. Clark, Edinburgh, 1890. [5] E.E.C. Jones. An Introduction to General Logic. Longmans, Green, and Co, London, 1892. [6] E.E.C. Jones. A Primer of Logic. E.P. Dutton, New York, 1905. [7] E.E.C. Jones. A new law of thought. Proceedings of the Aristotelian Society, 11:166–186, 1910. [8] Augusta Klein. Negation considered as a statement of difference in identity. , 20:521–529, 1911. [9] L.S. Stebbing. A Modern Introduction to Logic. Methuen, London, 1930. First Edition. [10] L.S. Stebbing. The method of analysis in metaphysics. Proceedings of the Aristotelian Society, 33:65–94, 1932. [11] L.S. Stebbing. Mr. Joseph’s defence of free thinking in logistics. Mind, 42(167):338–351, 1933. [12] L.S. Stebbing. Directional analysis and basic facts. Analysis, 2(3):33–36, 1934.