Michael Potter is Professor of Logic at Cambridge University, his studies in the history of analytic philosophy and the philosophical foundations of mathematics include an overview of philosophies of arithmetic from Kant to Carnap – Reason’s Nearest Kin (2000), a critical introduction to set theory – Set Theory and Its Philosophy (2004), and a study of Wittgenstein’s Notes on Logic (2008). His most recent book, The Rise of Analytic Philosophy, 1879-1930, is a comprehensive introduction to the work of four philosophers, Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey, in the half century, from 1879 (the year in which Frege’s Begriffsschrift was published), till Ramsey’s death in 1930.
Analytic philosophy is one of the most important sources for modern philosophy of logic and mathematics, for philosophy of language, and for philosophy of mind. According to some philosophers and historians of philosophy, it is not only one of the most important developments in twentieth-century philosophy, but the most important one, at least in the English-speaking world (cf. Beaney 2007: 1). Michael Dummett has famously defined it in the following way:
“A succinct definition would be: analytical philosophy is post-Fregean philosophy. Frege’s fundamental achievement was to alter our perspective in philosophy, to replace epistemology, as the starting point of the subject, by what he called ‘logic’. What Frege called ‘logic’ (…) embraced precisely what is now called ‘philosophy of language’.” (Dummett 1978: 441).
Though the above definition is far from being uncontroversial, there is a general consensus that the achievements of Frege, Russell, and Wittgenstein were crucial for the early developments of analytic philosophy; with the work of Ramsey featuring less prominently in historical overviews. Several general and more detailed studies have already investigated the origins of this movement in considerable detail (it will suffice to mention the works by Michael Beaney, Michael Dummett, Hans-Johan Glock, Scott Soames, and Stephen Schwartz). However, there is still a need for studies analyzing, reanalyzing and contextualizing the achievements of Frege, Russell, Wittgenstein, and Ramsey. This is precisely what Potter does; additionally, the author’s ambition is to trace the changes within the philosophers’ thought (the ‘genetic approach’).
The choice of the four philosophers in Potter’s monograph is connected with their unquestionable and durable relevance to current philosophy: Frege’s notions of sense and reference are central to modern semantics, Russell’s theory of descriptions may be regarded as a “paradigm of philosophy”, philosophy of language continues to be influenced by Wittgenstein’s picture theory, and Ramsey’s argument against the particular/universal distinction retains its validity (2). Assuming that analytic philosophy originated in 1879 with the publication of Frege’s Begriffsschrift and the birth of quantifier-variable logic, it might be claimed that further work by Frege, and also by Russell, (early) Wittgenstein, and Ramsey, flowed directly from this new logic. Throughout his study, Potter hopes to convey “a sense of the exhilarating progress they made, and of the extent to which modern analytic philosophy is in their debt” (3).
The detailed organization of this book is similar to the approach characteristic of the author’s former studies. The book is divided into four parts, further divided into numerous chapters (21 devoted to Frege, 24 to Russell, 18 to Wittgenstein, and 10 to Ramsey), and each chapter is followed by concise suggestions for further reading. The book concludes with an extensive bibliography and a detailed index. Each part starts with a short biographical sketch (in the case of Russell and Wittgenstein, concentrating on the relevant time span), in which Potter contextualizes the life of the respective philosopher. Further contextualization, which takes into consideration appropriate ideas and developments, is provided in the more thematic chapters. Thus conceived, the parts offer a detailed chronological and thematic guide to the work and legacy of the individual philosophers.
Gottlob Frege (1848-1925) is generally associated with developments in modern predicate logic and analyses of sense and reference crucial for contemporary philosophy of language. He devised a symbolic language for logic, provided the seminal analysis of the meaning of an expression, offered a semantic analysis of identity statements, and formulated the context principle; he is also credited with putting forward the assumptions that lead to formulation of the compositionality principle and introducing the notion of presupposition (of the assertion). In the part on Frege (5-144), Potter provides an overview of logic before 1879, from the Stoics, through Aristotelian logic, transcendental logic, empiricism and idealism, to Boole’s early example of modern axiomatic logic. Potter observes that The Mathematical Analysis of Logic (1847) is the only plausible competitor as the harbinger of modern logic; however, even though Boole “had devised an algebraic calculus of considerable sophistication for solving problems in categorical and hypothetical logic, it fell short of unifying the Aristotelian and Stoic traditions” (19).
Potter devotes five chapters exclusively to the Begriffsschrift (the German title is rendered by the author as ‘Concept-Script: A formula language, modelled on that of arithmetic, for pure thought’), one of “the most remarkable books in the history of human thought” (21). The five chapters are concerned with foundations of logic, propositional logic, quantification, identity, and the ancestral. In order to fully appreciate Frege’s achievements it is necessary to understand the aim of his concept-script, the significance of his notation, usage of particular symbols, and, especially, the revolutionary introduction of a notation of quantifier and variable to express generalizations, all explained by Potter. In the short presentation of Frege’s account of function and argument, Potter observes that three features are worth stressing: the fact that in the decomposition of sentences a function is obtained by removing part of an expression, not part of its content; the possibility of replacing grammatical predicates; and, most importantly, Frege aimed to “decompose, and hence discern function-argument structure in already existing sentences, not to explain how the sentences acquired their meanings in the first place” (29).
In the remaining chapters in this part, Potter discusses in detail other studies and ideas of Frege: the Grundlagen (in 4 chapters), sense and reference (3 chapters), the Grundgesetze (2 chapters). Potter also tackles the development of early philosophy of logic, the Frege-Hilbert correspondence, the importance of Frege’s late writings. The discussed issues include the crucial components of Fregean semantics and philosophy of mathematics: the context principle, the concept and object distinction, the status of numbers, names and descriptions, different conceptions of sense, the reference of a sentence, (un)saturated senses, and more. Paul Pietroski remarked once that Frege “bequeathed to us some tools – originally designed for the study of logic and arithmetic – that can be used in constructing theories of meaning for natural languages” (Pietroski, 2005: 29–30). The discussion provided by Potter demonstrates the relevance of these tools for a number of current disciplines – he mentions the Fregean legacy in logic, philosophy of language (especially formal semantics and pragmatics), and mathematics. A possible addition to this list would be philosophy of mind, where Frege’s legacy is seen in, for example, contemporary discussion on different approaches to reference.
In one of his earlier studies, Wittgenstein’s Notes on Logic, Potter compared his analysis of Wittgenstein’s text to the work of a historical detective (Potter 2008: 3). Also, in The Rise of Analytic Philosophy, Potter offers analyses exemplary of a detective’s work; additionally, an important feature of his analyses is connected with discussing those ideas that were NOT followed by the individual philosophers; for example, he observes that although Frege introduced rules and basic laws of propositional logic, he did not discuss the question whether every logical truth expressible using only negation and the material conditional is provable in this system of truth-functional logic (35). Below, I mention the book Russell might have written (had he not met Wittgenstein); and, at yet another instance, Potter comments on the ‘one place we might expect to find Ramsey’s influence, given the closeness of their interactions in 1929, is in Wittgenstein’s later work, but in fact this influence is notably muted’ (468). Another example of Potter’s approach can be found in chapter 69, where he discusses Ramsey’s idea of universals, with the aim, among others, to unravel the (missing) influence on Wittgenstein’s departure from Frege’s views (the binary distinction between saturated and unsaturated entities).
Part II (145-312) is devoted to the achievements in the philosophy of Bertrand Russell (1872-1970) during the appropriate period. In the sections tracing the early influences upon the philosopher, Potter focuses on Bradleyan idealism, and McTaggart’s reading of Hegel. He also discusses Russell’s early work on geometry (An Essay on the Foundations of Geometry, 1897), moves next to Russell’s education in mathematics, and then the influence of, and further collaboration with, Alfred N. Whitehead. He also discusses G. E. Moore and his switch from absolute idealism to platonic realism, and the influence of the Italian mathematician, Giuseppe Peano. Important sections are devoted to Russell’s early, middle, and late logicism, his changing views on judgment, his studies of denoting, truth and theories of truth, types, the relationship between acquaintance and knowledge, the status and different understanding of facts, and approaches to monism. The list of topics important for Russell’s philosophy reads like an index of key topics in 20th century philosophy of language, with considerable implications outside this discipline.
The discussion demonstrates the importance of careful reading of texts, but even more so of direct contact – for Russell, meeting Peano, and the young Wittgenstein, was one of the turning points in his thinking about mathematics and philosophy of mathematics: ‘In May 1913 Russell began writing a book on the relationship between acquaintance and knowledge. He never completed it, partly as a consequence of Wittgenstein’s criticism” (365). One might only speculate about the developments in Russell’s philosophy had he not met Wittgenstein.
Russell’s (and Frege’s) influence and legacy in philosophy of language is indisputable. Potter offers an interesting comment on two crucial texts: ‘Much as Frege chose to write ‘On sense and reference’ as if it was about the philosophy of language, even though his real concern was primarily with logic, so also Russell presented ‘On denoting’ as if his concerns were with analyzing George IV’s curiosity about the authorship of Waverley rather than with solving the logical paradoxes’ (309). This resulted in both influence and controversies within analytic philosophy, and challenges offered by ordinary language philosophy, notably by Strawson. Potter notes that ‘ordinary language philosophy withered after Austin’s death (…) but its demise did not mark a return to Russellian analysis’ (312), which is a consequence of the linguistic turn in philosophy dominated by Rorty, Dummett, and Davidson. It might be added that the influence of ordinary language philosophy has been rediscovered in contemporary linguistics, especially pragmatics.
Though not directly connected with the topic of the book, it is interesting to observe that Russell ‘was the only one of the four philosophers discussed in this book to receive major public honours in his lifetime (the Nobel Prize for Literature and the Order of Merit)’ (149).
It would probably be difficult to find two philosophers so different in personality and way of life as Russell and Wittgenstein. Their philosophical concepts also differ, though they strongly influenced one another. Part III (313-415) is devoted to Ludwig Wittgenstein’s (1889-1951) early work. The first sections of this part provide insight into the development of Wittgenstein’s ideas, especially those connected with ‘facts’, ‘pictures’, and ‘propositions’. Potter offers here some ‘archeological’ research into the history of ideas and discusses the Bodleianus, the version (kept now in the Bodleian Library, hence the name) preceding even the typescript known as the Prototractatus. This first version of the Tractatus was concerned with theses 1-6: ‘what stands out straightway is that the outline ends not with the injunction to silence of the final published version but with a technical claim (..) about the expressive power of a certain notation. (…) The central claim of the 1916 Tractatus is thus that the world may be pictured logically by means of propositions obtained from elementary propositions by recursive application of the N-operator’ (319).
In the following chapters, Potter elucidates the changes Wittgenstein made to the final version, with fascinating discussion of the purported ‘solipsism’ (chapter 54), i.e. thesis 5.6. (‘The limits of my language mean the limits of my world’); this discussion is continued in the chapter on ‘the metaphysical subject’. Other chapters focus on ordinary language, on ethics, and on the mystical element in the Tractatus (chapter 62). This chapter also includes a useful – though brief – note on the possible reading of the Tractatus, which would distinguish, pace James Conant and Cora Diamond, the outer part and the inner part: the outer part (the ‘frame’) would consist of senseful instructions for reading the inner nonsensical part. As succinctly observed by Potter: ‘it is not altogether clear, however, which sentences belong to which part’ (405).
The final chapter of this part discusses the legacy of the Tractatus, and concentrates on issues such as elementary propositions, the picture theory, and briefly comments on the relation to, and legacy in, Wittgenstein’s later philosophy. Potter stresses that ‘the popular conception of two Wittgensteins was always too simplistic’ (409). He concludes his discussion by observing that Wittgenstein was right ‘to dismiss as incoherent the persistent attempts of philosophers to conceive of our representation of the world as undertaken from one viewpoint among many’ (415).
The last part of the book (417-471) is devoted to Frank Ramsey (1903-1930), a British philosopher, mathematician, and economist; the least known of the four philosophers discussed by Potter, due chiefly to his premature death at the age of 27. It has to be noted, however, that recent years have seen growing interest in his work and legacy, cf. the chapters in Lillehammer and Mellor, eds. (2005), and the most recent comprehensive monograph by Misak (2020). Ramsey’s contribution to philosophy is centered predominantly around the topics of truth, knowledge, belief, and universals. Potter also discusses his work on the foundations of mathematics, and traces the possible influence of Wittgenstein’s Tractatus on Ramsey’s conception of truth. The chapters on truth and knowledge demonstrate the potential of Ramsey’s ideas for contemporary discussions not only in semantics, but also in pragmatism, and philosophy of mind. A similar observation is to be made in connection with the chapters on the foundations of mathematics; however, in the final chapter, Potter comments also on the unfortunate misunderstandings and problems with the appropriate reception of Ramsey’s work.
The four philosophers discussed in Potter’s book all contributed to the rise of analytic philosophy, their legacy is still important today in a wide variety of disciplines, including philosophy of language, philosophy of mind, philosophy of mathematics, logic, and linguistics (especially pragmatics and semantics). Michael Potter’s study constitutes a comprehensive guide to their achievements and legacy. The book should be of considerable interest to anyone studying the roots of contemporary philosophy, and especially philosophy of logic, philosophy of language, and philosophy of mind. It would be most interesting to see a comparable study tracing the parallel developments of analytic philosophy and pragmatism and phenomenology (for some preliminary studies on analytic philosophy and phenomenology, see the contributions in Beaney 2007). Such a study might contribute to the development of ‘ideochronology’, dealing with the chronological relationship between philosophical ideas (modelled after glottochronology, which deals with the chronological relationship between languages).
Readers of Potter’s earlier books will recognize his ‘detective’s approach’ in this most recent volume. Potter meticulously traces the sources of ideas, discusses mutual influences, and carefully analyzes changes and shifts in theories, which makes his study almost a log-book for analytic philosophy.
Beaney, Michael. 2007. “The analytic turn in early twentieth-century philosophy.” In: Beaney (Ed.), The Analytic Turn. Analysis in Early Analytic Philosophy and Phenomenology. New York & London: Routledge, 1-30.
Beaney, Michael (Ed.) 2007. The Analytic Turn. Analysis in Early Analytic Philosophy and Phenomenology. New York & London: Routledge.
Dummett, Michael. 1978. Truth and Other Enigmas. London: Duckworth.
Lillehammer, Hallvard and D. H. Mellor (Eds.). 2005. Ramsey’s Legacy. Oxford: Clarendon Press.
Misak, Cheryl. 2020. Frank Ramsey. A Sheer Excess of Powers. Oxford: Oxford University Press.
Pietroski, Paul M. 2005. Events and Semantic Architecture. Oxford: Oxford University Press.
Potter, Michael. 2000. Reason’s Nearest Kin. Philosophies of Arithmetic from Kant to Carnap. Oxford: Oxford University Press.
Potter, Michael. 2008. Wittgenstein’s Notes on Logic. Oxford: Oxford University Press.