1.1 Early Analytic Philosophy, Stebbing’s Role, and Historiography: Against the Great Men Narrative

Exactly when analytic philosophy began is a matter of dispute. Some historians argue it came into being as late as Wittgenstein’s arrival in Cambridge to study with Russell in 1911 (Reference Quinton and HonderichQuinton, 2005: 28). Others, who consider Frege a founder, might say it began as early as his Begriffsschrift (Reference FregeFrege, 1879). More commonly, historians consider Frege an ancestor rather than a founder of analytic philosophy (e.g. Reference BurgeBurge, 2005: 7–8). Historians of this school of thought generally take the first work of analytic philosophy to be ‘The Nature of Judgement’ (Reference MooreMoore, 1899), the paper which inaugurated the mini-movement of two research fellows, Moore and Russell, dubbed by them ‘The New Philosophy’. The New Philosophy was a fervently anti-idealist project. It went in search of a realist alternative to the idealism common in late nineteenth-century British universities, most pressingly to supplant the system of their key opponent, the British Hegelian F. H. Reference BradleyBradley (1883, Reference Bradley1897). The New Philosophers at first maintained that a view of judgement as a binary relation between a mind and something independent of and distinct from that mind meant that the logical form of true statements about judgement entailed the falsity of idealism (Reference MacBrideMacBride, 2018: 30–9). Moore and Russell’s early attempts (Reference MooreMoore, 1899; Reference RussellRussell, 1903), which boldly suggested that all words refer, led to a bloated ontology and difficulties explaining the difference between truth and falsity. Attempts to rectify these shortcomings led to the theory of descriptions and logical atomism. Moore, Russell, and, a few years later, Reference WittgensteinWittgenstein (1922), replaced the faulty view that all words refer with the more viable proposal that it is instead every true sentence which stands for something – namely, for a fact. Falsity is then readily explained as failure to correspond to a fact. But our ordinary-language sentences do not straightforwardly map onto one fact each. They admit of further, detailed analysis. Logical atomism presumed that our claims about everyday middle-sized objects – humans, dogs, cats, plants, houses, cities, mountains, tables, and so on – were, strictly speaking, claims about a complex plurality of micro-facts: their components in some arrangement. A statement about a wooden table is really about protons and electrons arranged into atoms, which are in turn arranged into molecules, arranged into cells, arranged into cellulose fibres, arranged into planks, and arranged into the familiar tabular shape. We analyse statements about organisms into their physical (and perhaps mental) atoms in a biological arrangement.

Stebbing’s most famous works were to focus on what exactly was involved in the process of analysis used in logical atomism and more generally in analytic philosophy. In several of her books and papers, she defended anti-idealism. It is readily apparent that her work concentrated on themes central to early analytic philosophy. Despite that fact, she has only rarely been considered a central figure in the analytic movement or a founder of analytic philosophy. Part of the explanation for her relative obscurity lies with gendered factors. Implicit and explicit sexist attitudes on the part of her contemporaries and of historians of analytic philosophy often led to a woman’s works being cited less often and taken less seriously (Reference Janssen-Lauret, Cook and YapJanssen-Lauret, in press-a). Institutional sexism meant that faculty at women’s colleges had less visibility in the profession and less often succeeded at placing their former students in jobs where those students might promote the work of their former supervisors.

Stebbing has also been neglected because she has been given insufficient credit for originality. Ayer is typical in describing her as ‘very much a disciple of Moore’ (Reference AyerAyer, 1977: 71). Several recent commentators also describe Stebbing several times over as a ‘Moorean’ (Reference Milkov and StadlerMilkov, 2003: 355, 358; Reference Beaney and StadlerBeaney, 2016: 242, 245–6, 248–50, 253–4; Reference Beaney and ChapmanBeaney & Chapman, 2021: §§3–4). Although Stebbing certainly viewed Moore as a mentor figure, and regularly credited him with specific views she endorsed or with inspiring her to develop her own views on a given topic, she similarly gave credit to Russell and to Whitehead, on whose philosophy she wrote more papers than on Moore’s (Reference StebbingStebbing, 1924, Reference Stebbing1924–25, Reference Stebbing1926). What’s more, Stebbing’s expertise stretched to technical areas of philosophy of which Moore never made any serious study. Moore’s anti-idealism had originally grown out of rejecting the Kantianism he had found appealing as a young man and out of embracing the Platonism with which he had become familiar in his reading of the classics and his Moral Sciences degree. By contrast, Stebbing’s anti-idealism found expression especially in her philosophical work on the new physics with its theory of relativity and subatomic particles. Unlike many of her contemporaries, Stebbing argued that the new physics did not obviously tell in favour of idealist or panpsychist interpretations. Stebbing also differed from Moore (but resembled Russell and Whitehead) in taking an interest in the philosophy of set theory. She discussed how modern mathematics affects ordinary-language discourse about numbers and the no-class theory (Reference StebbingStebbing, 1930: 141). Where Stebbing staked out a line in which she acknowledged the influence of Moore, as in her work on metaphysical analysis, she often made advances on his views, such as her sharp distinction between grammatical and directional analysis and her solution to the paradox of analysis (see Section 4). Stebbing further differed from Moore in the amount of attention she paid to usage in ordinary language. Chapman has presented an interpretation of Stebbing as making moves which foreshadowed modern discourse analysis and argumentation theory (Reference ChapmanChapman, 2013: 172–86).

Stebbing, then, was also a clear representative of the branch of analytic philosophy which seeks to design a philosophy to fit the latest developments in mathematics and science. In this respect, she resembled Russell, Whitehead, or even W. V. Quine more than she resembled Moore. Stebbing is best seen as an original philosopher, a transitional figure who played a pivotal role in moving analytic philosophy on from its early phase, where (at least in the UK) it was dominated by logical atomism, towards a middle period typified by more focus on ordinary language and a more holist approach. To view her primarily as a Moorean is problematic because it denies her credit for originality, but also because it appears to fall prey to what I have called the Great Men narrative of analytic philosophy (Reference Janssen-Lauret, Elkind and KleinJanssen-Lauret, in press-b). According to this historiographical narrative, analytic philosophy is the work of three or four particular men, their followers, and their followers’ followers. Soames writes, ‘analytic philosophy … is a certain historical tradition in which the early work of G. E. Moore, Bertrand Russell, and Ludwig Wittgenstein set the agenda for later philosophers’ (Reference SoamesSoames, 2003: xiii) and Beaney describes analytic philosophy as ‘the tradition that originated in the work of Gottlob Frege (1848–1925), Bertrand Russell (1872–1970), G. E. Moore (1873–1958), and Ludwig Wittgenstein (1889–1951) and developed and ramified into the complex movement (or set of interconnected subtraditions) that we know today’ (Beaney, 2013: 9).

Soames and Beaney’s characterisations of analytic philosophy are formulated the way they are for a reason: to sidestep known issues with attempted definitions of ‘analytic philosophy’ which define it too narrowly, whether geographically as ‘Anglo-American’ philosophy, thematically as philosophy focussed on the analysis of language, or as ‘critical’ rather than speculative philosophy (Reference Katzav and VaesenKatzav & Vaesen, 2017). All of those candidate definitions leave out major figures in the history of analytic philosophy: German, Austrian, and Polish analytic philosophers, including Frege, Wittgenstein, Carnap, Tarski, Maria Kokoszynska, and Janina Hosiassion (Reference Janssen-Lauret, Uebel and Limbeck-LilienauJanssen-Lauret, 2022c); analytic metaphysicians like Russell, Stebbing, Moore, and Elizabeth Anscombe; and naturalistic system-builders such as Whitehead, Quine, Dorothy Emmet, and Mary Midgley.

But a definition of analytic philosophy as three or four men and their followers is overly narrow, too, not least because it misrepresents all women working on logic and philosophy of science in the early analytic period as either marginal figures who followed the Great Men or not analytic philosophers at all. The women whom I have dubbed ‘grandmothers of analytic philosophy’, including E. E. C. Jones and Christine Ladd-Franklin (Reference Janssen-Lauret, Cook and YapJanssen-Lauret, in press-a, in Reference Janssen-Lauret, Elkind and Kleinin press-c), Victoria Welby (Reference Connell and Janssen-LauretConnell & Janssen-Lauret, 2022), and Grace de Laguna (Reference Janssen-Lauret, Elkind and KleinJanssen-Lauret, in press-b) fall into the latter category. The ‘grandmothers’, similar in age to Frege or Whitehead rather than Russell or Wittgenstein, also resembled Frege in being originators of ideas – such as the sense-reference distinction (Reference JonesJones, 1890) and inferentialism in logic and language which became influential only many years after the very early analytic period in which they lived. In recent work, Beaney has added Stebbing to his list as a fifth founder of analytic philosophy. While Beaney’s solution is welcome in that it makes room for a female founder, it does not extend to grandparents of analytic philosophy other than Frege – notably, no grandmothers and no other candidate grandfathers like Whitehead or Stout (Reference MacBrideMacBride, 2018: 115–52) – nor for other analytic philosophers and logicians of similar stature to Stebbing, such as Carnap, Ramsey, and Tarski, who might lay equal claim to co-foundership.

My alternative proposal is to view analytic philosophy not as the works of some handful of individuals and their followers but rather as a broad and varied movement with a variety of strands, each with a range of central and more peripheral figures, each with doctrines in some respects allied, in some respects in tension with some of the others. There is no neat and tidy set of plausible necessary and sufficient conditions for who counts as an analytic philosopher or brief definition of ‘analytic philosophy’. My model for the genesis of analytic philosophy is not that of the United States of America, a government of founding fathers gradually taking over land belonging to Indigenous peoples, or that of an exclusive gentlemen’s club with a manifesto which sets the agenda for its followers. My models are, rather, those of wider intellectual, political, or artistic movements, a looser coalition of ideas, not all of which point in the same direction or are wholly mutually compatible. Among the strands making up the early analytic philosophy movement are empiricism, advances in formal and mathematical logic since the nineteenth-century revolution in rigour – not just Frege’s but the algebraic calculi, too – the analysis of language, and new developments in physics and psychology. On that alternative conception of analytic philosophy, it has multiple grandfathers and grandmothers besides Frege and multiple founding fathers and mothers, too. One way to restore female early analytic philosophers to their rightful place is to give up the hero narrative of the Great Men and embrace the ‘movement’ narrative of early analytic philosophy.

What I take to be most distinctive about early analytic philosophy is its quest to find a philosophy compatible with new developments in the sciences, especially the natural sciences and pure mathematics. Most narratives of the emergence of analytic philosophy to date have focussed more on early Russell and Moore’s opposition to idealism (e.g. Reference HyltonHylton, 1990; Reference CandlishCandlish, 2007). But Frege, Russell, Whitehead, and other early analytic philosophers were also driven by reflection on the mathematical revolution in rigour and general relativity. These results upset traditional philosophical certainties about the infinite, parts and wholes – for example, the intuition that no whole is the same size as any of its proper parts – and the nature of space and time. Analytic philosophers held that philosophy should accept these results as true, set out to clarify and interpret them, and fit philosophical enquiry around them (Reference MacBride and Janssen-LauretMacBride & Janssen-Lauret, 2015). For some lesser-known early or proto-analytic philosophers, such as Welby, Stout, Ladd-Franklin, and de Laguna, reflection on new findings in the emerging science of psychology was also a major driving force. A further concern for many early analytic philosophers was opposition to idealism, although later generations of analytic philosophers contained some idealists. Critical analysis of linguistic meaning, reference, and truth became crucial items in the analytic philosopher’s toolbox as she set out to investigate the logical form of scientific truths and their collective ontological commitments. Stebbing, as we shall see, was an exemplar of analytic philosophy in her careful analysis of the logical forms of both physics and ordinary language. She was also typical of early analytic philosophy in her anti-idealism, although she, initially inspired by idealist philosophy as a student, was a reasonably sympathetic reader of idealism and anxious to represent idealist solutions fairly in her philosophy of physics. Lastly, Stebbing, sensitive to ordinary language and always clear that analytic philosophers must analyse sentences, can be seen as a transitional figure in the shift from logical atomism – which speaks of analysing propositions and tends to treat language as a ‘transparent’ (Reference RussellRussell, 1926: 118) medium to which we need not pay attention – towards the middle phase of analytic philosophy with its increasing focus on ordinary language.

1.2 Susan Stebbing: Life, Works, and Historical Context

Born in London in 1885 and orphaned in her teens, Susan Stebbing’s pre-university education consisted largely of intermittent homeschooling. Stebbing was not merely a Victorian girl-child – already at a disadvantage with respect to educational opportunities – but also significantly disabled by Ménière’s disease, an inner-ear disorder which causes attacks of dizziness and nausea and was not, at the time, treatable. Stebbing’s disability, and probably her lack of rigorous training in the exact sciences and the classics, limited her choice of subjects at Girton College, where the logician E. E. Constance Jones, one of the grandmothers of analytic philosophy, had recently been appointed Mistress. Stebbing began by reading History. According to different sources (Reference WisdomWisdom, 1944: 283; Reference ChapmanChapman, 2013: 11) she might have preferred either Classics or Natural Sciences. Perhaps her disability was incompatible with work in a laboratory. But there may also have been gendered pressures nudging her away from natural sciences and classics, which were, in the 1900s, among the most strongly male-coded fields in the academy.

The Victorian and Edwardian doctrine of gendered ‘separate spheres’ relegated women to the home, leaving the public sphere to men (this will be explored more in Section 2). Belief in separate spheres led many Victorians to oppose higher education for women altogether but disposed others to allow for higher education which did not require worldly knowledge potentially affecting women’s moral respectability. As a result, late Victorian and Edwardian culture did not classify all of mathematics as strongly masculine. Applied mathematics, used in the physical sciences and engineering, fields associated with economic gain and the public sphere, was highly male-coded. But those who didn’t wholly disapprove of women’s education often considered pure mathematics, such as mathematical logic, algebra, and set theory, which did not draw on worldly knowledge, suitable for a woman to study. For example, Grace Chisholm’s mathematics lecturers advised her to leave the very applied department in Cambridge to pursue her PhD in pure geometry in Germany (Reference JonesJones, 2000). Christine Ladd-Franklin was encouraged to give up trying to persuade reluctant male physics professors to admit her to their research laboratories and instead pursue pure mathematics, which she could study at home (Reference Janssen-Lauret, Cook and YapJanssen-Lauret, in press-a). Limited instruction in the classics was another frequent obstacle for the early generations of female academics. Educated parents immersed their sons in Greek and Latin from early childhood but only rarely did the same for their daughters. Constance Jones recounted in her autobiography that the women of her family learnt only enough Latin to teach their sons until the boys went to school (Reference JonesJones, 1922: 11). Even in the early 1940s, Mary Warnock and her fellow female classics students found ‘what a struggle it was for girls to keep their heads above water in Mods, an examination based on the assumption that boys had been learning Latin and Greek almost as soon as their education had started’ (Reference WarnockWarnock, 2000: 39).

Towards the end of her history degree, Stebbing happened at random upon Bradley’s Appearance and Reality while browsing in the library. She was immediately gripped. Stebbing decided to stay at Girton for another year to read for the Moral Sciences Tripos, as Cambridge called its exams in philosophy. She studied philosophy with the logician W. E. Johnson, who introduced her to Aristotelian logic. But Cambridge did not allow women who passed their Tripos exams to graduate with their degrees and would not begin to do so until 1948, after Stebbing’s death. Stebbing accordingly moved to the University of London, which did award degrees to women.

In London, she completed a master’s thesis on truth, pragmatism, and the French voluntarism of Bergson, later published in the Girton series by Cambridge University Press (Reference StebbingStebbing, 1914). After her move to London in the early 1910s, Stebbing continued to teach for Girton on a casual basis, as well as for Newnham, another Cambridge women’s college. She also held visiting lectureships in London, at King’s College for Women, and Homerton, a teacher training college. Stebbing regularly spoke at the Aristotelian Society and published papers in its Proceedings. Several of these earliest publications of hers were sympathetic to idealism. In one meeting of the Society, Stebbing criticised Russell’s views on relations and, though also disinclined to follow Bradley all the way down the road to monism, defended the idealist doctrine of concrete unity (Reference StebbingStebbing, 1916–17). Some twenty-five years later, Stebbing recounted that, having presented her paper, she was confronted about the ‘muddles’ (a favourite word of hers) inherent in her claims by a man she later discovered to be G. E. Moore. Stebbing described feeling ‘alarmed’ at first at Moore’s ‘thumping the table’ as he asked, repeatedly, ‘What on earth do you mean by that?’, but being soon drawn into the substance of the discussion to such an extent that she forgot to feel alarmed or apprehensive: ‘[N]othing mattered except trying to find out what I did mean’, she wrote (Reference Stebbing and SchilppStebbing, 1942: 530).

Although Stebbing commentators often make much of her labelling her first encounter with Moore as a ‘conversion’ (Reference ChapmanChapman, 2013: 34; Reference Beaney and StadlerBeaney, 2016: 242; Reference Beaney and ChapmanBeaney & Chapman, 2021: §3), it should be borne in mind that its context is a paper which is both explicitly intended as a homage to Moore and written by Stebbing in a retrospective mood, as her own health was failing. A closer look at the historical evidence reveals that Stebbing’s ‘conversion’ appears to have been both more gradual than the quotation suggests and a conversion to analytic philosophy generally rather than a conversion to ‘Moorean’ philosophy. First, Stebbing wrote and presented a second paper critical of Moore soon afterwards, accusing him of a ‘misuse of terms’ and of making ‘a serious mistake, viz. … the identification of reality with existence’ (Reference StebbingStebbing, 1917–18: 583). Chapman notes that Stebbing and Moore engaged in a frank exchange of views in correspondence afterwards (Reference ChapmanChapman, 2013: 34–5). Stebbing then published few original philosophical papers for a few years. Her philosophical thought was possibly in flux, but it is also known that she was busy with other professional activities. She was searching for an academic job, while at the same time setting up a girls’ school, Kingsley Lodge, with her sister Helen and her friends Hilda Gavin and Vivian Shepherd, as well as engaging in anti-war activism in the form of lectures on behalf of the League of Nations Union, advocating disarmament (Reference ChapmanChapman, 2013: 37–8). In 1920, Stebbing finally secured one of the few and far between academic posts open to women, a lectureship at Bedford College, a women’s college in London. From 1924 to 1929, Stebbing published a flurry of serious, original journal papers clearly belonging to the tradition of analytic philosophy. But these were not works of Moorean common-sense philosophy. Stebbing spent most of the 1920s publishing extensively on philosophy of physics, a topic which had been of interest to her since at least her master’s thesis, which includes detailed discussions of the question of whether physical laws are necessary (Reference StebbingStebbing, 1914: 3, 28–35, 70–1). Her main interlocutors were the analytic philosopher and logician A. N. Whitehead, the idealist physicist Arthur Eddington, and to a lesser extent other analytic figures such as Bertrand Russell, C. D. Broad, and C. E. M. Joad and other idealist physicists such as James Jeans. Moore, immersed in the classics to an extraordinary degree from his schooldays, and whose early philosophy had been inspired by Plato, with Kant and Bradley as foils, never made any serious venture into the philosophy of physics. We will examine Stebbing’s philosophy of physics in Section 3. Stebbing clearly regarded Moore as a mentor figure and mentioned him regularly in her work on incomplete symbols and analysis, which dates mostly from the early 1930s. Stebbing was generous with acknowledgements where she took her views to originate with others, a trait typical of early analytic female philosophers (Reference Connell and Janssen-LauretConnell & Janssen-Lauret, 2022). Although this trait is, in general, admirable, Stebbing at times gave herself insufficient credit for originality. In Section 4, I will argue that her theory of analysis in fact makes a significant advance on Moore’s, despite Stebbing’s modesty about her own achievements relative to his.

Stebbing enjoyed great success in her career at Bedford College. She was promoted to the position of being the UK’s first female professor of philosophy in 1933. She published primarily on philosophy of science, formal and philosophical logic, metaphysics, and language, including the first accessible book on the new symbolic logic, A Modern Introduction to Logic. Stebbing continued to suffer severe attacks of Ménière’s disease but used these periods of illness to read books in English, French, and German, often publishing her thoughts as a book review. As a result of her extensive reading and trilingualism, Stebbing was one of the first outside of continental Europe to see the significance of logical positivism. She published a detailed study of the movement (Reference StebbingStebbing, 1933b) three years before Ayer published his Language, Truth, and Logic. Stebbing’s publications on logical positivism did much to introduce it to the British philosophical scene. In the late 1930s, Stebbing, increasingly alarmed by the rise of fascism and generally conscious that the general public would benefit from the ability to detect and resist fallacious argumentation and manipulative uses of language by those in authority, began to write on the application of critical thinking to ethics and politics. She also worked with Jewish refugees, work which she continued until her death in 1943.

2.1 Stebbing’s Views on Logic

Stebbing was the author of the first accessible book on the new, symbolic logic. Her Modern Introduction to Logic (Reference StebbingStebbing, 1930, Reference Stebbing1933a) is often described as a ‘text-book’, but although Stebbing’s intended audience was students, to speak of a logic ‘text-book’ is apt to conjure up, for the twenty-first-century reader, an image of a short book, focussed on exercises for students, which details the views of others without originality. Stebbing’s book, by contrast, was a 500-page behemoth, taking in Western formal and philosophical logic from Aristotle to Russell and Whitehead’s Principia Mathematica and Wittgenstein’s Tractatus, in which Stebbing frequently defended original philosophical viewpoints of the sort we would now expect to find in a monograph. A short publication like this one permits only a whistle-stop tour of Stebbing’s philosophy of logic (see also Reference Janssen-LauretJanssen-Lauret, 2017, Reference Janssen-Lauret, Peijnenburg and Verhaegh2022a; Reference Douglas and NassimDouglas & Nassim, 2021). As we shall see, Stebbing expressed original views on logicality – the question what makes a theory logic – where she emphasised the importance of formality conceived as universal applicability; on the nature of logical consequence, where she advocated for material consequence; and on the continuity between logic and scientific methodology, which she viewed in hypothetico-deductive terms. Stebbing’s best-known contribution to logic pertains to her views on analysis, logical constructions, and incomplete symbol theory, which I will cover first.

Stebbing’s innovations in the theory of philosophical analysis also inform her metaphysics and, I argue in what follows, her philosophy of science. Her work on logic and its role in facilitating philosophical analysis stressed that what philosophers analyse is language, not propositions or judgments, that the logical form of a sentence is context-dependent, and that logical construction needs careful definition. This work prepared the way for her celebrated distinction between grammatical or same-level analysis – analysis of language in terms of a further stretch of language, which may be analytic or a priori – and metaphysical or directional analysis, which specifies what simple elements in what configuration there are in the world in case the sentence is true (see Section 4).

To appreciate the novelty of Stebbing’s contributions, we need a brief sketch of the historical backdrop, beginning with how Stebbing’s predecessors, especially Moore and Russell but also Constance Jones, reacted to those authors whom Stebbing labelled the ‘traditional logicians’. Stebbing’s ‘traditional logicians’ included the idealists Bosanquet and Bradley, whose logic was Aristotelian but, by Stebbing’s lights, had lost sight of the most positive features of Aristotle’s thought, the formalism which Aristotle shared with mathematical logic (Reference StebbingStebbing, 1930: x–xii) by mistakenly setting ‘form’ in opposition to ‘Reality’ and proposing instead a ‘metaphysical logic’ governed by the principle of ‘identity-in-diversity’.

Russell and Moore’s first venture into anti-idealism, the New Philosophy, had rebelled against idealism, with Bradley as their main foil. According to Bradley’s (and Bosanquet’s) identity-in-diversity view, what we think of as ordinary identity claims or subject-predicate statements never represent reality correctly. Bradley and Bosanquet claimed that true identity between subject and predicate could not be asserted due to the ‘difference in meaning’ (Reference BradleyBradley, 1883: 28), that we ‘cannot speak of the coincident part as the same, except by an ideal synthesis which identifies it first with one of the two outlines and then with the other’ (Reference BosanquetBosanquet, 1888: 358). Bradley maintained that our thoughts and language must always radically misrepresent reality, because reality is fundamentally one, completely without structure. By contrast, thought and language are composed of parts and concatenated with a definite structure in order to represent. Rejection of the Bradley–Bosanquet line does not require rejection of Aristotelian syllogistic logic. Constance Jones, who adhered in the main to Aristotelian formal logic despite replacing one of its covering laws with her New Law of Thought, had already raised the worry that Bradley’s view ‘seems to me to depend on a confusion between identity and similarity’ (Reference JonesJones, 1890: 50 n.1). The young Reference MooreMoore (1899, Reference Moore1900–01) and Reference RussellRussell (1903: §46) did not initially take Jones’s sensible way out; Jones expressed polite puzzlement that Moore, in 1900, fell into the same mistake as Bosanquet of running together qualitative and quantitative identity, when they are easily distinguished in ordinary language (Reference MooreJones, 1900–01; see also Reference Janssen-LauretJanssen-Lauret, in press-c). Rather, Moore and Russell at first responded by offering, instead of the idealist modus ponens – if reality does not resemble our thoughts and language, then we cannot represent it correctly, and reality indeed fails to resemble our thoughts and language – a modus tollens: our thoughts and language certainly can represent reality correctly. Therefore reality does resemble our thoughts. Each of our words is a symbol complete in itself, whose task is to refer to some component of reality. Reality does divide into parts, and our minds can reach out and grasp, and name, components of reality directly. This ‘all-words-refer’ model ran aground. It made it impossible to make non-existence claims and to distinguish true statements from false ones.

The mathematical, symbolic logic which Russell increasingly turned to, having first read Frege in 1902, provided a basis to solve the New Philosophers’ problems. In short, they moved to a model on which it is not the case that every word stands for something but every true proposition (or judgement) does stand for something, namely for a fact. Falsity, then, is the property a proposition or judgement has when it fails to stand for a fact. Russell used symbolic logic and its theory of quantification to account for falsity and negative existentials. Symbolic logic had grown out of new developments in nineteenth-century mathematics, the revolution in rigour which made mathematicians turn their attention to their deductive proof methods. Previously, logicians and mathematicians had been content to build their systems up from principles which appeared to them to be intuitively true. But intuition proved no fit guide for mathematicians exploring novel systems, like Cantor’s theory of transfinite numbers, and the new theory of classes, which introduced higher and lower levels of infinity. Mathematicians’ only guide was adherence to clearly laid-out proof methods. Instead of relying on syllogistic forms, where each premise or conclusion has just one quantifier, rigorous new treatments of arithmetic and geometry also needed statements with multiple quantifiers, such as ‘for each number, there is another number which is its successor’ or ‘in between any two points on a line, there is another point’. They needed a polyadic (that is, multiple-quantifier) logic, like Frege’s Begriffsschrift (Reference Frege1879). Frege thought of his quantifiers as higher-order properties: to say that so-and-sos exist is to say that the so-and-so property has instances. Russell put such quantifiers to work in accounting for negative existentials. A negative existential proposition does not single out, say, a unicorn and say of it that it does not exist; the proposition says that there are no instances of the unicorn property.

Where the early Russell–Moore view had assumed that all words are complete symbols, whose only function is to refer, their new, improved model introduced incomplete symbols, whose function is different. Their contribution to meaning is revealed through analysis. Russell focussed in particular on definite descriptions, which look, grammatically, like they stand for some component of reality but whose grammatical form misleads us. Although ‘the present Queen of France is an equestrian’ looks very similar to the true statement ‘the present Queen of England is an equestrian’, it is neither true that the present Queen of France is an equestrian nor that she never rides, because there is no present Queen of France. Russell’s solution was to say that ‘the present Queen of France’ is not referential. It is a disguised quantifier phrase, which disappears upon analysis: ‘The proposition “a is the so-and-so” means that a has the property so-and-so, and nothing else has’ (Reference RussellRussell, 1910–11: 113). Proper names, complete symbols, stand for constituents of propositions known to us directly. Definite descriptions, by contrast, have no meaning in isolation, so their function is not referential. They do not introduce a referent as the constituent of a proposition; they say of a property that it has exactly one instance. Descriptions, definite or indefinite, are useful in explaining that non-existence claims do not ascribe the property of non-existence to a constituent of a proposition but amount to the assertion that it is not the case that exactly one thing has the so-and-so property. They also help us account for falsity. A false proposition is likewise an incomplete symbol, which arranges words in a way in which nothing is arranged in the world.

It is not just ‘the present Queen of France’, but also ‘the present Queen of England’, which is an incomplete symbol according to Russell. Assuming that the reader is not personally acquainted with the Queen, they know her only by description: they know that there is presently one unique instance of the Queen-of-England property. Even those acquainted with the Queen are acquainted only with a visible surface of her – her face, for example, not the back of her head – at a specific time. Although they know that she otherwise exists as a complex arrangement of mental and physical states, they know this descriptively, not directly. The Queen is, to them, a logical construct, or, as Russell sometimes said, a logical fiction, someone whose existence and nature we know of through descriptive knowledge of her properties. Russell’s mature view at this time preserved the assumption, so central to his and Moore’s first venture into anti-idealism, that our minds can reach out and grasp, and name, constituents of reality directly.

Complete symbols or proper names, encoding in language a sign of immediate acquaintance with something in the world, remained. Russell stressed that we need them, as they are where analysis terminates: ‘Every proposition which we can understand must be composed wholly of constituents with which we are acquainted’ (Reference RussellRussell, 1910–11: 117). On Russell’s view, analysis terminates in ‘sense-data’. Although sense-data are now generally thought of as mental states, such an account of them is not necessary. Moore considered an interpretation on which sense-data are identical with the surfaces of objects (Reference Moore and MuirheadMoore, 1925: 59). Russell at times admitted acquaintance with universals and the self, not merely with mental states.

Stebbing enthusiastically embraced incomplete symbol theory for its potential to account for negative existentials. Stebbing considered it ‘plain common sense’ that ‘negative existential propositions are true if there is no individual in the actual world to which the descriptive phrase applies’ (Reference StebbingStebbing, 1930: 56). She also mentioned negative existentials as playing an important role in science. She contrasted the planet Neptune, posited to explain irregularities in the orbit of Uranus, and subsequently observed, thus confirming the hypothesis, with the positing of the planet Vulcan to explain irregularities in the orbit of Mercury. Vulcan was never observed, because there is no such planet. The irregularities in Mercury’s orbit are explained instead by Einsteinian general relativity (Reference StebbingStebbing, 1930: 346, 398). While Stebbing also embraced the project of logical construction, she sought to improve on Russell’s version of it.

One feature of Stebbing’s thought which sets it apart from that of Russell and Moore is her insistence that what philosophers analyse is not propositions, judgements, or things themselves but language, and specifically sentences or other expressions used on some occasion, in some context. The early Russell had explicitly held the view that ‘symbols were always, so to speak, transparent’, that is, that language is a medium we need not pay attention to, whose only job is to stand for something outside itself. In Principia, an occurrence of a term is called ‘referentially transparent’ iff nothing is said of it but by means of it something is said of something else (Reference Whitehead and RussellWhitehead & Russell, 1964 [1910]: appendix C). Stebbing was among the first to stress the importance of context in interpreting occurrences of expressions, as Quine was also to do in his development of referential transparency (Reference QuineQuine, 1953: 124). But neither of them was the first to do so. Russell admitted that he had first seen a rebuttal of the transparency of language in ‘Lady Welby’s work on the subject, but failed to take it seriously’ (Reference RussellRussell, 1926: 118).

Stebbing argued that Russell’s claim that ‘the proposition “a is the so-and-so” means that a has the property so-and-so, and nothing else has’ is not independent of context because some sentences of the form ‘a is the so-and-so’ do not contain definite descriptions. For example, ‘the whale is a mammal’ is usually used to express a taxonomical claim about whales and has the form of a universal generalisation, equivalent to ‘all whales are mammals’. A sentence such as ‘the dog is fond of peanut butter’ is ambiguous. It can be used to make a generalisation about all dogs, in which case it is a universal generalisation, or to make a statement about a particular dog, identified by context (I might say it about my dog Daphne; Stebbing might have said it about her dog Smoodger), in which case it contains an incomplete symbol. Stebbing thus recommended a refined account of incomplete symbols, which she credited to Moore in correspondence, “‘S, in this usage, is an incomplete symbol” = “S, in this usage, does occur in expressions which express propositions, and in the case of every such expression, S never stands for any constituent of the proposition expressed” ’ (Reference StebbingStebbing, 1930: 155). Stebbing credited her criticisms of Russell on incomplete symbols to the influence of Moore, in discussions and correspondence with him rather than his published work. But there are some potential signs that Stebbing was overly modest here, and her view is more original than it appears. It is notable, for example, that Moore consistently spoke of the objects of analysis as propositions (e.g. Reference Moore and MuirheadMoore, 1925; see also Section 4 in this Element). By contrast, even in 1930 Stebbing’s criticisms already clearly turn on thinking of analysis as analysis of language: ‘in logical analysis there are not two things but two expressions which mean the same’ (Reference StebbingStebbing, 1930: 441).

Stebbing criticised Russell for speaking loosely about logical constructions. She took exception to his calling them ‘fictions’ and not distinguishing between incomplete symbols – which are expressions of language – and logical constructions, as, for example, when he wrote, ‘classes are, in fact, like descriptions, logical fictions, or (as we say) “incomplete symbols” ’ (Reference RussellRussell, 1919: 181–2), a line Stebbing described as ‘extremely confused’ (Reference StebbingStebbing, 1930: 157). She also expressed hesitation about Russell’s claim that a definition in mathematics is the ‘expression of a volition’ – ‘a declaration that a certain newly-introduced symbol or combination of symbols is to mean the same as a certain other combination of symbols of which the meaning is already known’ (Reference Whitehead and RussellWhitehead & Russell, 1964 [1910]: Introduction). Stebbing here took Russell to be running together defining on the one hand, which is a relation between expressions, with analysis of concepts on the other hand. Unlike definition, conceptual analysis takes the form of stating which properties are conjoined in a given concept. Stebbing maintained, first of all, that definitions were relations between expressions but not merely syntactic items. Rather, ‘the definiendum and the definiens express the same referend’ (Reference StebbingStebbing, 1930: 441), that is, they stand for the same thing. Similarly, Stebbing maintained that a mathematical definition can elucidate a concept but is not a definition of the concept. It ‘marks an advance in knowledge’ rather than telling us only what we already knew (Reference StebbingStebbing, 1930: 441).

Stebbing maintained from early in her career that, if logical construction theory was true and useful, it had to be defined in terms of incomplete symbol theory. As Russell had provided only examples and no definition, Stebbing proposed one: she defined ‘Any X is a logical construction’ as ‘X is symbolised by “S” and “an S” is an incomplete symbol’ (Reference StebbingStebbing, 1930: 157). In 1930, Stebbing said little about her own original views concerning logical construction theory, which may indicate that at that time she was hesitant to endorse it fully. Although she felt able to declare that classes were logical constructions (Reference StebbingStebbing, 1930: 455), she seemed less certain about macro-physical objects. She raised a worry that, if macro-physical objects such as lions are logical constructions, then lions turn out not to be particulars (Reference StebbingStebbing, 1930: 159 n.2); only sense-data are to be counted as particulars on such a view.

By the second edition of her book (Reference StebbingStebbing, 1933a), Stebbing had come around to a firmer, and original, view on logical construction theory. She added to the discussions above an appendix providing a clear statement of the view that ‘there are good reasons for supposing that … persons are logical constructions’ (Reference StebbingStebbing, 1933a: 502; see also Reference StebbingStebbing, 1933a: 146 n.1). Stebbing remained resolutely opposed to calling logical constructions ‘fictions’ and hesitant about the nomenclature of ‘logical construction’, ‘for it suggests that something is constructed, which is not the case … to say that the table is a logical fiction (or construction) is not to say that the table is a fictitious, or imaginary, object; it is rather to deny that, in any ordinary sense, it is an object at all’ (Reference StebbingStebbing, 1933a: 502). Stebbing’s position on logical construction differed from Russell’s. Unlike Russell, Stebbing did not hold that analysis terminates in sense-data, nor that we can name sense-data. In the sections that follow on Stebbing’s philosophy of science and metaphysics, we will see Stebbing’s reasons for dispensing with sense-data and substituting observations, or perceptual objects.

In short, Stebbing saw no need to require that analysis terminates in something which ‘Russell … could regard as an indubitable datum’ (Reference StebbingStebbing, 1933a: 503). According to Stebbing, analysis need not terminate in indubitable data, or objects of acquaintance (see also Section 4). In another paper in the same year, Stebbing also cast doubt on Russell’s contention that our language allows for pure reference without any discursive content: ‘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. … Pure demonstration is a limit of approximation’ (Reference StebbingStebbing, 1933d: 342; see also Reference Janssen-LauretJanssen-Lauret, 2017: 14–15).Footnote ¹

Stebbing also expressed original views on what the distinctive characteristics of logic are, tracing out a line stretching from Aristotle to twentieth-century symbolic logic which stresses formality. Although Reference Beaney and ChapmanBeaney and Chapman (2021: §2) state that Stebbing’s book covers ‘traditional, Aristotelian logic’, Stebbing herself sharply distinguished between Aristotle’s logic and that of those she called ‘Traditional Logicians’, certainly including the idealists Bosanquet and Bradley. Among Stebbing’s original views on logic is the doctrine that Aristotle’s logic shares with the symbolic logic of Frege, Peano, Russell, and Whitehead, but not with the thought of traditional logicians, a focus on formality. Early modern logicians and their successors argued over whether logic was an art, the ‘art of thinking’ – as in the title of the 1662 Port Royal Logic, La logique ou l’art de penser (Reference StebbingStebbing, 1930: 163) – or a science, and whether logic was psychologistic, that is, descriptive of reasoning, or normative, prescribing to us how we ought to think and argue. Stebbing’s college principal Jones caused much controversy with her bold, anti-psychologistic stance that logic was the science of the relations between propositions (Reference JonesJones, 1890).

Mathematical logic, which Stebbing called ‘symbolic logic’, cast new light on the question of the distinctive characteristics and subject matter of logic, the question now generally called ‘logicality’. Previously, logicians and mathematicians had been content to build their systems up from principles which appeared to them to be intuitively true, or self-evident. But late nineteenth-century mathematicians had begun to find that coherent proof systems remained when some allegedly self-evident principles were given up. Non-Euclidean geometries, for example, no longer assumed that parallel lines never meet. Dedekind’s definition of an infinite set assumes that such a set has a proper part which has the same (infinite) size as it, contradicting the intuitive principle that wholes are larger than their proper parts. And these kinds of unintuitive systems were soon given useful application in the new Einsteinian physics. Stebbing saw the importance of both the tendency of the new mathematical logic to rely increasingly on proof-theoretic methods and its applications to non-mathematical reality. She brought the two together in her philosophy of logic. Stebbing rejected Wittgenstein’s view that logical truths do not say anything (Reference WittgensteinWittgenstein, 1922: 4.0312) because they are tautologous. She wrote, ‘I think that the assertion of a tautology is a significant assertion … Further, I think that it is not absurd to say that a tautology is true’ (Reference StebbingStebbing, 1933c: 196).

Stebbing held that the success of modern symbolic logic, which places no reliance on intuitive self-evidence, gives us good reason to dispense with self-evidence as a condition of logicality. It also places limits on the role played by modal notions in logic: ‘We cannot answer that an axiom is a proposition that is necessarily true, for we do not know what necessarily true means’ (Reference StebbingStebbing, 1930: 175). According to Stebbing, what is necessarily true is at best a relative notion given in terms of what is implied by what (Reference StebbingStebbing, 1930: 176). She also argued that we cannot rely on the notion of ‘logical priority’. To speak of one truth being ‘logically prior’ to another is obscure and adds an inappropriate dose of metaphysics to our logic (Reference StebbingStebbing, 1930: 175). Stebbing concluded that ‘no deductive system can be regarded as demonstrating necessarily true propositions by means of necessary primitive propositions or axioms’ (Reference StebbingStebbing, 1930: 176–7) because truth cannot be established by proof in the sense of demonstration; to find out what is true we must turn to the empirical. What we can do is, in a given system, to take certain notions as undefined, and some statements as not for present purposes standing in need of proof, without their being taken to be absolutely indefinable or indemonstrable. These are called ‘primitives’ after Peano (Reference StebbingStebbing, 1930: 175). But what is the property that makes a system logic? Stebbing’s answer was ‘formality’, not in the sense of involving only proof without invoking truth but in the sense of universal applicability.

On Stebbing’s view, then, logic is a science: the science which concerns what follows from what. The question of the nature of logical consequence, or what it means to say that something logically follows from something else, is also one on which Stebbing expressed original views. Stebbing discussed different kinds of logical following-from, first describing Russell’s ‘material implication’, according to which p implies q just in case either p is false or q is true (Reference StebbingStebbing, 1930: 223). She queried Russell’s view that material implication is a plausible candidate for logical consequence. She cast doubt on that view by arguing that in ordinary language we say that, if q follows from p, then q can be deduced from p. Material implication, Stebbing countered, can hold between statements which cannot be deduced from one another. She expressed a preference for an alternative account of logical consequence, based on a relation which C. I. Lewis called ‘strict implication’ and Moore called ‘entailment’ (Reference StebbingStebbing, 1930: 222; see also Reference Douglas and NassimDouglas & Nassim, 2021). The relation of entailment holds, for example, between statements like ‘this is red’ and ‘this is coloured’, that is, it covers what is now often called ‘material consequence’. Entailment is not definable in psychological terms (Reference StebbingStebbing, 1930: 223). Although we would now categorise this kind of entailment as modal, Stebbing, in Reference Stebbing1930, resisted this characterisation, arguing that ‘impossible’ is less clear than ‘entails’ (Reference StebbingStebbing, 1930: 222 n.1). Both implication and entailment are in turn distinct from inference, which Stebbing described as ‘a mental process’ (Reference StebbingStebbing, 1930: 210), and, although of interest to logic, different from validity. Inference is psychological, but not validity (Reference StebbingStebbing, 1930: 211).

These views of Stebbing’s in turn affected her answers to the questions of extensionalism in logic and the relationship of logic to philosophy of science. The new mathematical logic’s need to overcome intuition as a guide to logical truth, and replace it as far as possible with rules of proof, led to the rise of extensionalism. The extensionalist contends that we should talk about things as they are, not about how they may or must be. ‘Mays’ and ‘musts’, modal expressions, extensionalists took to rely on intuitions or psychological principles of self-evidence, methods made obsolete by the new mathematical logic. As we have seen, Principia’s aim was to speak of objects with referentially transparency, so that any two co-referential expressions were everywhere intersubstitutable (Reference Whitehead and RussellWhitehead & Russell, 1964 [1910]: appendix C). The radical extensionalist logicians of the 1930s and 1940s, especially Tarski and Quine, thought logic should only account for differences in extension, not intension: as Tarski put it, ‘two concepts with different intensions but identical extensions are logically indistinguishable’ (Reference TarskiTarski, 1956 [1935]: 387). Quine, too, enthusiastically defended extensionalism (Reference QuineQuine, 2018 [1944]: 158; see also Reference Janssen-Lauret, Quine, Carnielli, Janssen-Lauret and PickeringJanssen-Lauret, 2018, Reference Janssen-Lauret2022b), and it was assumed that modal logics like C. I. Lewis’s couldn’t be extended to the quantified case until Ruth Barcan managed it in 1946–7 (Reference BarcanBarcan, 1946, Reference Barcan1947).

We have seen that Stebbing was circumspect about allowing modality into logic. Yet she was not as strongly opposed to intensional discourse as Quine or Tarski. Stebbing certainly had reservations about ascribing necessity, especially essence or metaphysical necessity, to the world: ‘Modern theories of organic evolution have combined with modern theories of mathematics to destroy the basis of the Aristotelian conception of essence’ (Reference StebbingStebbing, 1930: 433). But she accepted analytic truth and admitted in a later paper that, although analyticity does not exhaust entailment, analytic containment ‘involves a must which is a must of necessity’ (Reference StebbingStebbing, 1933c: 193). Stebbing also expressed moderate extensionalism in her attitude towards intensions. She objected to the view that ‘the intension of a word is commonly said to be all that we intend to mean by it’ that ‘this definition suggests an unfortunate intrusion of psychology into logic’ (Reference StebbingStebbing, 1930: 28). But Stebbing, like Frege, believed that some intensional language could be systematised and decoupled from the psychological via quantification over abstract objects. Frege thought reference was made to senses where intersubstitutivity salva veritate failed (Frege, 1892). Stebbing did not believe in Fregean senses but nevertheless thought a set might have an intension as well as an extension, if the intension was taken to be its defining property (Reference StebbingStebbing, 1930: 141).

Stebbing’s view of logic was in the main anti-psychologistic. She regarded logic as a science of what follows from what rather than one which describes how we in fact think. The anti-psychologistic view was typical of the grandparents and founders of analytic philosophy. Frege famously criticised psychologism in logic and mathematics. Jones, too, defended a view of logic as the normative science of how we ought to reason, given what the consequence relations between propositions are, rather than the descriptive science of reasoning, a branch of psychology (Reference JonesJones, 1890: 2). Stebbing agreed with the view that logic is normative rather than a descriptive science of reasoning. But, according to her, the normativity of logic is simply a by-product of its abstract nature and its formality. Logic has no distinctive set of facts of its own; it traces the general forms of reality (Reference StebbingStebbing, 1930: 474). Nevertheless, Stebbing never lost sight of logic’s connection to thinking and reasoning. She consistently described thinking as an activity. Logical reasoning she described as goal-directed, purposive thinking, separate not from action-linked thinking but from free association of thoughts or idle reverie. When giving examples of reasoning, she liked to give practical examples: a man uses his knowledge of natural laws to trace a safe path off a cliff in high tide (Reference StebbingStebbing, 1930: 1–2); a woman thinks through why it is unwise to wear a given dress to the beach, as the chemically unstable dye fades in sea air (Reference StebbingStebbing, 1930: 8); a man locked out of his flat devises hypotheses which he can test in order to determine whether the flat has been burgled (Reference StebbingStebbing, 1930: 234). Stebbing viewed logical reasoning as an activity of people, people who interact in communities and whose views are informed by the ‘intellectual climate’ (Reference StebbingStebbing, 1930: 294) in which they live.

Lastly, a central aspect of Stebbing’s outlook was her view of logic as continuous with philosophy of science and scientific methodology. Stebbing did not favour a split of logic into an inductive and a deductive branch, since she believed that science must deploy both inductive and deductive reasoning (Reference StebbingStebbing, 1930: 245, 344). What is true in a natural science, unlike in a purely deductive science such as mathematics, ‘depends upon what there actually is in the world’ (Reference StebbingStebbing, 1930: 231) and relies on experience (Reference StebbingStebbing, 1930: 232). But scientific method stands in continuity with logic because the task of the natural sciences is to construct a system of the world. Stebbing carefully reflected on the nature of a system. In a certain sense, any collection of elements standing in relations is a system (Reference StebbingStebbing, 1930: 174). Deductive systems specifically are composed of propositions – defined by her as something a thinker or speaker can affirm or deny (Reference StebbingStebbing, 1930: 15) – standing in logical relations. But Stebbing also spoke of systems as composed of facts, with the requirement that the facts all be mutually consistent with each other; she speaks of facts as contradictory ‘when the propositions which would correspond to those facts are contradictory’ (Reference StebbingStebbing, 1930: 199). Following the revolution in rigour and the great success and applicability of unintuitive proof systems like transfinite arithmetic and non-Euclidean geometry, we can no longer assume that systems rest on self-evident axioms or are false when they have counter-intuitive consequences. Nor can we assume that the world itself is a system. It is certainly not logically necessary that it is. Yet science, Stebbing wrote, is concerned with finding ‘the system (if there is one) which is the system of the world’ (Reference StebbingStebbing, 1930: 199).

Since logic, according to Stebbing, is formal in a sense where it is concerned with truth, the label of ‘logic’ can be usefully applied to the kind of method which seeks increasingly abstract generalisations which take observations as a point of departure: we begin with awareness of a complex situation in which some fact is singled out as peculiar, to be accounted for, we form a hypothesis connecting it to other facts, and develop the hypothesis deductively, in order to test the consequences so deduces against observable facts (Reference StebbingStebbing, 1930: 234–5). We might now call Stebbing’s procedure here a version of the hypothetico-deductive method. Stebbing did not view the hypothetico-deductive method and the inductive method as opposed. In her view, both are involved in scientific reasoning. She viewed inductive reasoning as resulting not from mere enumeration of cases (this crow is black, that crow is black, …, therefore all crows are black) but from a combination of enumeration and analogy. Inductive reasoning consists not just of enumeration but also of finding respects of resemblance, shared properties of scientific relevance, between the instances: we can call a bird a ‘crow’ only if it resembles ‘in certain respects other others called by the same name … properties belonging to all the instances of crows constitute the total positive analogy’ (Reference StebbingStebbing, 1930: 250). Stebbing considered argument by metaphor in the scientific context especially pernicious because she regarded a metaphor as an especially weak analogy, connoting only one shared property (Reference StebbingStebbing, 1930: 253). What sort of a system is a scientific theory? Stebbing was sympathetic to the then fashionable view that science does not explain (that is, it does not answer why-questions) but instead describes; it answers how-questions. Yet she pointed out that science does not merely describe in the sense of listing propositions which recount all the scientific facts, such as exact descriptions of which motions occurred or which particles were present in which location at which time. Such descriptions are neither feasible nor useful. Scientific theorising requires abstraction and formulations of law-like generalisations: ‘constructive description’, in Stebbing’s terminology (Reference StebbingStebbing, 1930: 392).

The facts which comprise the world include those which resist systematisation without first being subjected to some abstraction in thought. When we perceive, we perceive absolutely specific shades and sounds, for which we have no words. To use words is already to abstract to some degree. To use general terms is to classify (Reference StebbingStebbing, 1930: 444). The most abstract propositions are formal ones. Their significance is independent of any specific experience (Reference StebbingStebbing, 1930: 446). How, asked Stebbing, can we link the neat, orderly, exact system of science to the ‘untidy, fragmentary world of common sense’ to which our absolutely specific, unstructured perceptions belong? We use not merely the abstractions which naming, classifying, hypothesising, and law-like generalising afford us but also the method of extensive abstraction due to Whitehead. Stebbing’s example is Whitehead’s account of points. First, we take the relation of spatial inclusion, as when a box fits inside another box. We define inclusion as a transitive, asymmetric, serial relation and say that a point is what that series of inclusion converges on. We need not know anything about the intrinsic nature of points. All we need is their formal properties (Reference StebbingStebbing, 1930: 451). Points, then, are logical constructions, but they are not fictions. They are constructed not in the sense of being made up but in the sense of discovery (Reference StebbingStebbing, 1930: 454). They help us theorise.

Stebbing’s contributions to logic are deserving of wider recognition among historians of analytic philosophy. Her Modern Introduction to Logic was the first accessible book on symbolic logic and also contained innovative material on a range of topics in the philosophy of logic. Stebbing carefully considered what formality, the hallmark of logic, means in view of new developments in proof theory which imply that logic can no longer lay claim to being self-evident or necessarily true. Stebbing gave an original and sophisticated answer, namely one in terms of the universal applicability of logic. She also made progress on the topics of analysis and incomplete symbol theory. She distinguished analytic analyses, such as mathematical definitions, from philosophical analyses, briefly sketching an account of philosophical analysis that is not analytic, and thereby laid the groundwork for her later metaphysics, and made room for a more holist approach within analytic philosophy.

3.1 Stebbing’s Early Papers: Whiteheadian Philosophy of Science, Observations, and Realism

While historians often present the origins of analytic philosophy as lying entirely with the early efforts of Russell and Moore, and thus as sparked primarily by anti-idealism, in my view an important driving force for the development of analytic philosophy was the pressure to find a philosophy to make sense of the new science and mathematics and their counter-intuitive consequences. Stebbing’s philosophy of physics was both anti-idealist and concerned to account for novel developments in mathematics and science. In Section 2.1, we saw her carefully considering the repercussions for logic of the new science and mathematics, which imply that we can no longer assume that it is necessarily true that parallel lines never meet, or that wholes are always greater in size than their proper parts, simply because they seem intuitively self-evident. It was not merely that assuming the falsity of such apparently intuitive principles led to perfectly coherent proof systems. Such proof systems, of non-Euclidean geometry and set theories which allowed for denumerable and non-denumerable infinities, were also fruitfully applied to model the space–time of Einstein’s theory of general relativity. So, what had appeared to be self-evident necessary truths about parallel lines never meeting and wholes always being greater than their proper parts now seemed to be actual falsehoods, not true of the physical world in their complete generality. Stebbing saw the need for a properly worked-out philosophy to fit around the deliverances of the new natural sciences. In her work on logic, as we have seen, she argued that we may explain ‘how the exact and tidy world of the physicist is connected with the fragmentary and untidy world of common sense [if we] demonstrate the applicability of abstract deductive systems to the world given in sense-experience’ (Reference StebbingStebbing, 1930: 452) and that we should turn to Whiteheadian extensive abstraction to carry out this project.

As we saw in Section 1, the prevailing narrative of Stebbing’s development has it that she was ‘converted’ to Moorean analytic philosophy as a result of a philosophical exchange with Moore in 1917–18 (e.g. Reference Beaney and ChapmanBeaney & Chapman, 2021: §3). Although Stebbing herself was to an extent responsible for this ‘conversion’ account (Reference Stebbing and SchilppStebbing, 1942: 530), it must be borne in mind that the paper in which she made this claim was explicitly a homage to Moore, written in Stebbing’s final years while she was very unwell, and with a generally self-abnegatory tone throughout, and that Stebbing was apt to be overly modest at the best of times (Reference Janssen-Lauret, Peijnenburg and VerhaeghJanssen-Lauret, 2022a; Reference Connell and Janssen-LauretConnell & Janssen-Lauret, in press: §1). It is true that Stebbing certainly did turn away from idealism and towards analytic philosophy. Still, her publications during the 1920s were not Moorean in focus. They engaged in dialogue primarily with Whitehead’s philosophy of physics and at times expressed explicit disagreement with Moore.

Whiteheadian philosophy of physics is vast, complex, and written in a language of its own full of neologisms. Space does not permit me to give a full account of his thought here, although I will highlight a few key parts (see Reference MacBrideMacBride, 2018: 115–28, for a fuller treatment). Whitehead thought that for a realist philosophy to encompass Einsteinian physics required some radical shifts in our thinking. Among these shifts was a symbolic logic to replace the Aristotelian subject-predicate model, in order to represent the relational and polyadic (multiple-quantifier) logical forms of relational statements, such as those used in his account of spatial points: in between any two points, there is another point, and neither the points nor their names can be listed. We must give up the binary opposition of subject-predicate form in logic and the grammar of our language. More than this, Whitehead thought, to grasp the new physics fully we must also dispense with the distinction between particular and universal, which results ‘from our inveterate habit of forcing all philosophies into the framework of Aristotelian categories; and finally, from an undue reliance upon the ultimate philosophical importance of Indo-European languages’ (Reference StebbingStebbing, 1924–5: 313). It was not just the two-category treatment of particular and universal which Whitehead deplored but the ‘Bifurcation of Nature’ more generally. Nature does not divide into the neat binaries we were taught by previous generations of philosophers. We must also do away with the distinctions between mind and body and primary and secondary quality. Rather, Nature must be thought of as an endless succession of events, from which both common-sense objects – plants, animals, persons, rocks, planets – and their qualities and relations are abstractions. There is no ultimate sense to be made of a distinction between the primary qualities an object really has, such as its size, shape, and motion, and the secondary qualities which are mental additions, such as colour, sound, and smell. All these qualities are to be found in Nature. All are to an extent abstractions from the panoply of events which it comprises, as is the mind itself (Reference StebbingStebbing, 1924: 292).

Stebbing agreed that the Bifurcation of Nature must be abandoned, but took a more moderate view than Whitehead. From early on, she expressed a preference for an ontology of particulars and universals – though one which included relational universals, not merely properties – which together combine into facts, instead of Whitehead’s event ontology. Yet she admitted that the nature of the particular-universal distinction was far from obvious and must be carefully revisited in view of the difficulties with its application to physics. She explicitly took issue with Moore’s common-sense derivation of the particular-universal distinction from the distinction between what is predicable and what is not: ‘Prof. Moore says “is predicable of something else” is a perfectly clear notion … I am rather doubtful’ (Reference StebbingStebbing, 1924–5: 316). By contrast, Stebbing came to embrace the Whiteheadian view that secondary qualities are really there in Nature. They are not an addition made by our minds. She further cautioned against the extrusion of mind from nature, including, as we shall see, in Philosophy and the Physicists. Her arguments for these positions, though, often differed from Whitehead’s. She put forward original views about the basis of ordinary-language observational truths needed by physics and philosophy alike.

Stebbing held that there is a certain kind of collection of facts such that they ‘can all be known, and that such facts are the basis upon which all scientific and philosophical speculation must rest’ (Reference StebbingStebbing, 1929: 147). But these were quite different in kind from the propositions Moore offered up to the reader as certain, such as ‘Hens lay eggs’ (Reference StebbingStebbing, 1933b: 8). Stebbing’s basis for scientific and philosophical speculation was what she called ‘perceptual science’ (Reference StebbingStebbing, 1929: 148), comprising statements such as:

1. 1. I am now seeing a red patch.

2. 2. I am now perceiving a piece of blotting paper.

3. 3. That is a piece of blotting paper.

4. 4. That piece of blotting paper is on the table.

5. 5. That piece of blotting paper was on the table before I saw it.

6. 6. Other people besides myself have seen that piece of blotting paper. (Reference StebbingStebbing, 1929: 147)

The view that (1)–(6) above are true and known to be true Stebbing called ‘realism’. Her ‘realism’ was clearly distinct from Moore’s ‘Common-Sense View’, often described as one according to which ‘our ordinary common-sense view of the world is largely correct’ (Reference BaldwinBaldwin, 2004: §6), even though there are some similarities. Stebbing’s range of truths was narrower, and more perception-focussed, than Moore’s. Stebbing also emphasised that she saw both philosophy and physics as starting from the same range of truths about perceptual observations, the relationship of the observer to her perceptions, and her relationship to other observing subjects. By contrast, Moore never mentioned physics when enumerating certainties or truisms. Stebbing contended that ‘the denial of realism is inconsistent with the validity of physical theories … theoretical physics has developed by the continual modification of common-sense views through a stage of what might be called perceptual science, and that unless perceptual science is true theoretical physics cannot be true’ (Reference StebbingStebbing, 1929: 148). Stebbing’s ‘perceptual science’, or ‘realism’, is commonsensical in a certain way but much more naturalistic than Moore’s ‘Common-Sense View’.

Crucially, Stebbing did not take her ‘realism’ to entail the falsity of most forms of idealism. Her realism does plausibly entail the falsity of Bradley’s realism specifically. After all, Bradley held the idiosyncratic view that Reality, being fundamentally one and without structure, could never in principle be truly described by ordinary human language. But Stebbing held that most ontologically idealist theories are not like Bradley’s. They do not say that (1)–(6) are false but rather that there is a philosophical analysis according to which the objects discussed in (1)–(6) have a mental or spiritual, rather than material, nature. Stebbing wrote, ‘does physics give us any reason to suppose that propositions such as the six propositions I asserted above are false? I cannot see that it does … It has relevance to naive realism, which is a theory about the analysis of such propositions’ (Reference StebbingStebbing, 1929: 147). Naїve realism provides a physicalist analysis of (1)–(6). Moore also placed weight on the distinction between knowing a truth and knowing its analysis, and Stebbing cited his 1925 ‘Defence of Common Sense’ here for that insight. Nevertheless, Stebbing’s view had already moved beyond Moore’s at this point. According to Stebbing, modern physical theory was in tension with naїve realism, but not with her realism, and by itself neither compelled nor ruled out an idealist interpretation of physics.

3.2 Stebbing’s Philosophy and the Physicists

Stebbing’s 1937 book Philosophy and the Physicists presented an extended argument against idealist interpretations of modern physics, largely those of the physicist Arthur Eddington and to a lesser extent James Jeans, also a physicist. As Stebbing made no positive case in favour of an alternative interpretation of modern physics, her contemporaries took her project to be wholly negative, merely cleaning up the mess made by physicists going beyond their competence and wandering into the realm of philosophy. Broad’s (otherwise complimentary) review made a rather sexist comparison between Stebbing and ‘a good housewife who has at least completed her spring-cleaning’ (Reference BroadBroad, 1938: 226). But the fact that Stebbing’s case was largely critical, and she presented no alternative interpretation of physics, does not imply that her arguments were merely of the nature of picking apart (and sweeping up) Eddington’s and Jeans’s arguments.

Recent commentators have argued that Stebbing drew upon her original philosophical thought in the course of Philosophy and the Physicists, even though she did not always make clear when she did this. West (2022) argues that Stebbing defended an original view on the philosophy of entropy (Reference StebbingStebbing, 1937: chap. 11). I will show here that Stebbing also argued for her Whitehead-inspired view that secondary qualities are in Nature (Reference StebbingStebbing, 1937: 52–5), appealed to her 1930 proposal that science provides a ‘constructive description’ (Reference StebbingStebbing, 1937: 85), and used her views on philosophical analysis and logical constructions to further her argumentative case. Idealists about physics, on Stebbing’s view, believe that successive steps of analysis ultimately reveal physical objects to be logical constructions out of something mental, ‘the stuff of our consciousness’ (Reference EddingtonEddington, 1920: 200). Stebbing was not dogmatically opposed to idealist interpretations of physics. She even called some of Eddington’s statements of idealism ‘delightful’ (Reference StebbingStebbing, 1937: 208). But whether an idealist interpretation of physics is viable must depend on the merits of the philosophical analysis it provides and the arguments offered in favour of it. Stebbing judged Eddington’s arguments to be insufficient to establish idealism.Footnote ² What follows is not a full account of all of Eddington’s arguments or Stebbing’s rebuttals; due to constraints of space, I have to restrict my discussion to a few highlights.

It is important to make clear at the outset that Stebbing did not take the statement that physical objects are logical constructions out of elements which are ultimately mental or spiritual in nature to be in any way internally contradictory. Stebbing’s position was that modern theories of physics entailed neither idealism nor materialism. To suppose otherwise was, Stebbing thought, to commit the fallacy of supposing that a macro-object – that is, a logical construction, really a plurality of micro-objects in some arrangement – inherits the properties of the micro-objects which make it up, or vice versa. We saw in Section 2.1 that in her work on logical constructions, Stebbing compared this fallacy to ‘the confusion in supposing that if men are numerous and Socrates is a man, it would follow that Socrates is numerous’ (Reference StebbingStebbing, 1933a: 505).

Materialists as well as idealists may fall into the above fallacy. Nineteenth-century materialist physicists did so, Stebbing noted, when, having discovered the atom, they assumed that atoms were ‘solid, absolutely hard, indivisible billiard-ball-like … in a perfectly straight-forward sense of the words “solid” and “hard” ’ (Reference StebbingStebbing, 1937: 47). When Rutherford split the atom, physicists came to know that atoms were not, in fact, solid, but consisted of subatomic particles suspended in mostly empty space. But Eddington, too, committed a version of the fallacy which conflates the properties of the macro-objects with those of their constituent micro-objects. He did so, for example, when inferring from the fact that the atoms of which a plank in his study floor is made are mostly empty space that ‘the plank has no solidity’ (Reference EddingtonEddington, 1928: 342). To say ‘the plank is not solid’ in ordinary English is to imply that the plank is very brittle or visibly has holes in it. Stebbing maintained that it remains, despite our knowledge of subatomic particles, perfectly true to say ‘this plank is solid’ of an ordinarily robust plank free of worrisome holes. That the plank is, at the subatomic level, made up of mostly empty space is perhaps counter-intuitive but does not negate its solidity. ‘No concepts drawn from the level of common-sense thinking are appropriate to sub-atomic, i.e. microphysical, phenomena’ (Reference StebbingStebbing, 1937: 44). The macro-object, a plank, which we generally describe in ordinary language, is solid; the micro-objects, atoms, which comprise its analysis, are not themselves solid; these two statements are not mutually contradictory.

Similarly, the macro-objects are called ‘material objects’ in ordinary language, but there is no contradiction in supposing that their micro-components might, as Eddington supposed, be made of ‘the stuff of consciousness’. It may appear that a follower of Moore’s ‘Common-Sense View’ ought to find such a view contradictory. We will see in Section 4 that Moore at times seemed to incline towards the position that such a view is paradoxical. Stebbing, by contrast, did not. She was very clear that Eddington’s purported analysis, ‘the plank is material but its ultimate micro-constituents are the stuff of consciousness’, is no more internally contradictory than ‘the plank is solid but its component atoms are mostly empty space’. Stebbing’s objection to Eddington’s idealist conclusion was not that it was internally contradictory or at odds with common sense. She simply found that it did not follow from his premises.

By Stebbing’s lights, Eddington’s project went wrong early on not just by committing the fallacy of conflating macro-objects’ properties with those of their constituents but by raising the question ‘how is perception possible?’, a question which Stebbing (for Whiteheadian reasons) already considered ‘devoid of sense’ (Reference StebbingStebbing, 1937: 52), and by looking to physics for an answer to it. Stebbing, of course, held that physics itself must rest on facts about perception and observation, and relationships between observers, and although she did not cite her 1929 account of ‘perceptual science’ in Philosophy and the Physicists I will show that she made use of it. What’s more, Stebbing objected to the Bifurcation of Nature inherent in Eddington’s view that physics constructs a ‘symbolic world’. Eddington’s ‘symbolic world’ duplicates the familiar world in which, for example, Susan Stebbing stepped into her study and took pleasure in seeing and smelling ‘a crimson and scented rose’ from a bowl on her desk. On Eddington’s account, the world of physics contains ‘duplicates’ of the desk, the bowl, the rose, etcetera. It contains no duplicate of crimson but merely ‘its scientific equivalent electromagnetic wavelength … the wave is the reality … the colour is mere mind-spinning’ (Reference EddingtonEddington, 1928: 88). Stebbing felt that Eddington was correct to deny that the wave itself is coloured, for we must not ‘in one and the same sentence … mix up language used appropriately for the furniture of earth and our daily dealings with it with language used for the purpose of philosophical and scientific discussion’ (Reference StebbingStebbing, 1937: 42).Footnote ³ Nevertheless, the wave not being coloured cannot be used as a premise to support the conclusion that the rose is not really coloured (Reference StebbingStebbing, 1937: 51). The rose, a macro-object, is instead to be analysed in terms which include the electromagnetic wavelength.

The distinction between primary qualities – such as length, breadth, mass, shape, and motion – which physical objects really have, and secondary qualities assumed to be mental additions – such as colour, sound, and smell – was one Whitehead and Stebbing deplored. The distinction had nevertheless been common among philosophers since the seventeenth century. Stebbing cited examples from Newton, affirming the distinction, and from Berkeley, criticising Locke and the Cartesians for holding it (Reference StebbingStebbing, 1937: 51–5). Eddington went further than Newton, Locke, and the Cartesians had done. In his ‘scientific world’, he found not just equivalents of secondary qualities but duplicates of their subjects, too. He claimed to be writing his book sitting at two tables at once.

In isolation, the above might seem like a harmless metaphorical use of language. But Eddington emphasised that he meant the language of duplicates of each object existing in ‘a spiritual world alongside the physical world’ (Reference EddingtonEddington, 1928: 288) literally. On Stebbing’s view, the positing of two tables alongside each other was simply a mistake. The familiar table is a logical construct. We all understand, at the level of ordinary language, what it means to say that it is solid, coloured, and substantial. The atoms which are mostly empty space and the fields which oscillate to produce electromagnetic waves are resultants of analysis. They reside at the level of the most basic facts of physics. These basic facts are composed of elements which, as far as we know, are simple. What can correctly be predicated of them cannot be predicated of the table. At least, we cannot make such predications without careful qualification; we may be able to say, ‘at the subatomic level, the table consists mostly of empty space’. This statement sounds counter-intuitive but may constitute a summary of an appropriate, physical analysis of the ordinary, solid table. The new mathematics taught us that we cannot deny that infinite sets have proper parts the same size as them just because it sounds counter-intuitive. The same is true of the analysis of the table in terms of atoms which are themselves mostly empty space. Its counter-intuitive appearance is not grounds to declare it false. Nor does it give us reason to posit two tables, one solid and one tenuous.

Eddington’s reduplications further forced a strong and, according to Stebbing, unhelpful Bifurcation of Nature into mind and body. She described the way Eddington compared the human mind to a newspaper office providing a ‘free translation’ of ‘messages’ from the outside world. These messages we, or rather ‘the editor’ in our mind, that is, ‘the perceiving part of our mind’ (Reference StebbingStebbing, 1937: 84), ‘dress’ with colour, space, and substance which are not really there (Reference StebbingStebbing, 1937: 82). Stebbing objected that Eddington relied on the metaphor of the newspaper editor not as an illustration of something further to be explained but as an argument by analogy. Eddington offered up this argument in support of the conclusions that our belief in the external world is ‘a remote inference’ (Reference StebbingStebbing, 1937: 85), that we know the world only because ‘its fibres stretch into our consciousness’, and that yet we have grounds to identify it with what is in common between many consciousnesses (Reference StebbingStebbing, 1937: 87). We have seen in Section 2.1 that Stebbing generally deplored the use of metaphor as argument in philosophy of science because she categorised metaphors, in that context, as reasoning from weak analogy (Reference StebbingStebbing, 1930: 253–4). The ‘editor’ metaphor is no different; the analogy between the perceiving part of our mind and a newspaper editor soon breaks down. Stebbing, then, saw no reason to revise her views on the basis of Eddington’s argument from analogy. She maintained her Whiteheadian view that the external world is not inferred from perceptions but directly apprehended: ‘there is equally no doubt that we are able, as a result of our past experience, immediately to perceive that this is a so-and-so. In such immediate recognition no inference is involved’ (Reference StebbingStebbing, 1930: 211). She reiterated the same conclusion for which she had found support in her 1929 ‘perceptual science’ view that physics need not justify other minds because they are inevitably presupposed by its method: ‘Physics as a science results from the conjoint labour of many minds or persons’ (Reference StebbingStebbing, 1937: 108). Stebbing wondered whether Eddington’s mention of ‘fibres’ of consciousness constituted a further metaphor and was inclined to think not (Reference StebbingStebbing, 1937: 85); Eddington derived the conclusion that we really only know our own consciousness and that nerve impulses do not resemble the external world ‘in intrinsic nature’ (Reference StebbingStebbing, 1937: 86).

Stebbing was sympathetic to part of Eddington’s case, in particular to his suggestion that physics does not tell us the intrinsic nature of things. After all, physics abstracts away from the macro-individuals, with their absolutely determinate qualities which we are in touch with, in favour of a constructed system of generalities which details their relations to each other: their extrinsic connections. Stebbing wrote, “‘the world of physics” is nothing but a constructed system stated in terms of imperceptibles, the system being such that it permits, under certain conditions, of interpretation by reference to perceptual elements’ (Stebbing, 1933–4: 9). She could sympathise with some of Eddington’s structuralist assumptions, familiar to her from Russell and Carnap (Reference StebbingStebbing 1934b), including the suggestion that the information physics gives us allows for multiple interpretations as long as those interpretations share the structure of the information provided: ‘A constructed system may be capable of interpretation in terms of a given set of facts. It may then be adequate to this set, but it could never be exhaustive … physics is abstract’ (Stebbing, 1933–4: 25).

Stebbing’s view, dating back to her 1920s papers, that modern physics is in itself compatible with either an idealist or a materialist interpretation also provides support for the conclusion that physics does not reveal the intrinsic natures of things. She criticised the overconfidence of nineteenth-century materialist physicists who felt very sure that they knew the intrinsic nature of matter and atoms (Reference StebbingStebbing, 1937: 96). Yet Eddington (unlike Stebbing) assumed that there nevertheless is some intrinsic nature to be known and that we have reason to assume that it is conscious. He began by arguing that there are ‘(a) a mental image, which is in our minds and not in the external world; (b) some kind of counterpart in the external world, which is of inscrutable nature; (c) a set of pointer-readings, which exact science can study’ (Reference EddingtonEddington, 1928: 254). He then added the premises that the schedule of pointer-readers must be ‘attached to some unknown background’ and that ‘for pointer-readers of my own brain I have an insight which is not limited to the evidence of pointer-readings. That insight shows that they are attached to a background of consciousness’ (Reference EddingtonEddington, 1928: 259). He concludes that ‘it has a nature capable of manifesting itself as mental activity’. Stebbing was unimpressed, declaring the argument ‘a complete muddle’ (Reference StebbingStebbing, 1937: 99). Perhaps Eddington has insight into what is going on in his own consciousness, she countered, but he has no such self-knowledge about his brain, much less direct insight into the attachment of any pointer-readings concerning his brain to his consciousness. Knowledge about what the pointer-readers concerning one’s own brain say is knowledge inferred from that of pointer-readers concerning other people’s brains. There is no direct insight here.

How, then, are we to settle the question what physics is about? Stebbing believed that progress might be made by careful philosophical analysis, but this would always be a piecemeal project of assessing individual idealist or materialist proposals. Stebbing wrote,

In her final works on the question, then, Stebbing appeared to suggest what we would now call a naturalistic line. She continued to believe that analytic philosophers ought to search for a philosophy which could fit around the latest results of the sciences and was now beginning to make explicit room for at least some social sciences within this project, given her mention of psychology. Psychology had begun to separate itself from ‘mental philosophy’ from the early analytic period and was beginning to grow into a quantitative science to be reckoned with. According to Stebbing, the question whether idealism, materialism, dualism, or some other alternative is true should be addressed by collaboration between practitioners of different sciences plus well-informed philosophers of science.