By common consent, the three founders of the modern analytic tradition of philosophy are, in chronological order, Gottlob Frege, Bertrand Russell and Ludwig Wittgenstein. The biggest project in my professional life has been to write biographies of the second and third of these men. But of the three, it is Frege who is—100 years on from his retirement—held in the greatest esteem by the philosophers of today.
His essay “On Sense and Reference” (1892) offered a philosophical account of linguistic meaning that broke new ground in sophistication and rigour, and it is still required reading for anyone who wants to understand contemporary philosophy of language. It is scarcely an exaggeration to say that he invented modern logic: he developed the basic ideas (if not the symbols now in use) of predicate logic, considered by most analytic philosophers to be an essential tool of their trade and a required part of almost every philosophy undergraduate degree programme. His book TheFoundations of Arithmetic (1884) is still hailed as a paradigm of the kind of crisp, rigorous prose to which every analytic philosopher should aspire.
Frege’s insights have been influential outside philosophy, in areas including cognitive science, linguistics and computer science. Among the public, however, he is almost completely unknown, especially when put beside Wittgenstein and Russell. Most people have some idea who Russell was. Many have seen clips of his frequent appearances on television, can picture his bird-like features crowned with his mane of white hair, and recognise his unique voice, high-pitched, precise and aristocratic in an impossibly old-fashioned way (one imagines that no-one has spoken like that since the Regency). Even better known is Wittgenstein, the subject of a Derek Jarman movie and several poems, whose name is dropped by journalists, novelists and playwrights, confident that their audiences will have some idea who he is. But Frege? How many people know anything about him?
Even to professional philosophers, Frege is a shadowy figure. Apart from the fact that he was a professor of mathematics at the University of Jena, and—as we shall see, held some decidedly unsavoury political views—almost everything known about him arises out of his connections with other philosophers, most notably Wittgenstein and Russell.
It is, for example, widely known among philosophers that Wittgenstein used to tell his friends about how, when his interest in philosophy was first aroused, he travelled to Jena to discuss his ideas with Frege, who “had wiped the floor” with him. Throughout his life, Wittgenstein would talk about how much he admired Frege, even going so far on occasion as describing himself as a “disciple.” In the preface to his Tractatus Logico-Philosophicus, first published in 1921, Wittgenstein acknowledges that he owes the stimulation of his thoughts to “the great works of Frege and the writings of my friend Bertrand Russell.” In my life of Wittgenstein, I describe how anxious he was to receive Frege’s reaction to the book and the efforts which he made, from a prisoner of war camp, to ensure he got the manuscript to his “great” inspiration.
Russell, for his part, never met Frege, but also took every opportunity he could to record his admiration for him. Most strikingly, when in 1962 he was asked for permission to reprint his correspondence with Frege, Russell wrote: “As I think about acts of integrity and grace, I realise that there is nothing in my knowledge to compare with Frege’s dedication to truth.”
The particular act of integrity and grace that Russell had in mind was Frege’s reaction to a letter that Russell sent him in 1902 pointing out a fundamental problem in the theory to which he had dedicated his whole career. As Russell tells the story:
"His entire life’s work was on the verge of completion… his second volume was about to be published, and upon finding that his fundamental assumption was in error, he responded with intellectual pleasure clearly submerging any feelings of disappointment. It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known."
Actually, Russell is over-egging it here. The exchange he is referring to concerns what has become known to all philosophers, logicians, mathematicians and computer scientists as “Russell’s Paradox.” It takes some effort to grasp this paradox, but, as its discovery was one of the pivotal moments in the intellectual history of the 20th century, it is, I think, worth the effort. The backdrop was that both Frege and Russell were committed to a project known as “logicism,” which aimed to establish that mathematics, properly understood, is a branch of logic. They saw this as important because they thought it was obvious that logic was objective, whereas many philosophers at that time followed Kant in regarding mathematics as essentially subjective, a construction of the human mind rather than a body of objective truths.
In 1900, Russell was convinced that he was on the cusp of success. At the root of his approach, was a means of defining numbers as classes. The notion of “class” is a logical one, closely connected to the idea, used by logicians since Aristotle, of a proposition—a statement that is either true or false. Building on this, Russell developed the idea of a “propositional function,” which is a proposition with a variable instead of a name. So, “Aristotle is wise” and “Plato is wise” are propositions, but “x is wise” is a propositional function. All the people whose names can replace the variable x to form a true proposition (Aristotle or Plato, for example) form the class of wise people. Russell’s theory of mathematics centred on the idea that numbers are classes, thus bringing arithmetic into the domain of logic. As Russell discovered in 1902, almost the very same theory had been put forward many years earlier by Frege. In The Foundations of Arithmetic, Frege provided the philosophical case for logicism, and then in the first volume of the Basic Laws of Arithmetic (1893), he began the mathematical task of proving the laws of arithmetic, beginning with logical axioms. But by the time he discovered that he had been anticipated by Frege, Russell had discovered a major problem in the theory he and Frege had both, independently, arrived at.
Russell’s Paradox strikes at the heart of the very notion of a class. Here is how it arises—and do, please, bear with me on this. Consider the “class of all classes.” It has an unusual property: it is a member of itself. Most “ordinary” classes are not; the class of tables, for example, is not itself a table. So, some classes belong to themselves and others do not. It should be possible to form “the class of all classes that do not belong to themselves” (the class of tables and the class of chairs, for example). But, now, consider that class: is it a member of itself or not? Either way we answer that question, we seem trapped in a contradiction. If it is a member of itself, we have a contradiction, because it is the class of all classes that are not members of themselves, but if it is not a member of itself, we also have a contradiction, because it is supposed to be the class of all classes that are not members of themselves.
This is such baffling stuff that Russell felt obliged to develop a more intuitively intelligible analogy to get the point across. Imagine a barber who shaves all men, and only those men, who do not shave themselves. The question is—does he shave himself? If he does so, he breaks his own rule about only shaving men who don’t shave themselves; but if he doesn’t, then he joins the ranks of the non-self-shavers, and becomes obliged to shave himself. Neither position can hold, and we have our paradox.
Moving back from barbers to classes in general, what does this paradox mean? The upshot is that it is not true that to every propositional function there corresponds a class. For there cannot be, on pain of contradiction, any class corresponding to the propositional function “x is a class that does not belong to itself.” And so class—the basic idea upon which logicism was built—turned out not to be the simple, basic, universal concept that it had seemed. The effect was to pull the rug from under the entire theory.
Russell’s letter to Frege explaining the paradox came as a bitter blow, because until then Frege’s work had received very little attention. Thus, one of the first people to appreciate Frege’s work was also the person who showed it to be fundamentally mistaken. Frege’s response does not quite live up to Russell’s description of it, though it is admittedly impressive. Far from “clearly submerging any feelings of disappointment,” Frege told Russell that the paradox had left him feeling “thunderstruck,” having “rocked the ground on which I meant to build arithmetic.” As for taking intellectual pleasure in the paradox, the nearest thing to that in Frege’s letter is his acknowledgement that Russell’s discovery “is at any rate a very remarkable one” that “may perhaps lead to a great advance in logic, undesirable as it may seem at first sight.”
The paradox did indeed lead to advances in logic, and it has intrigued and inspired a great number of gifted people, including Wittgenstein, who abandoned his studies in aeronautics to concentrate on philosophy after becoming completely obsessed with it. Alas, though, for Frege, whatever intellectual pleasure he took in the paradox was overshadowed by the melancholic feeling that his life’s work had come to nothing. Towards the end of his days, he confided to his diary: “My efforts to get clear about what we mean by number have resulted in failure.”
Despite this, however, one thing that did come out of Russell’s discovery of the paradox was a growing appreciation among philosophers and mathematicians of Frege’s greatness. When Russell’s own book, The Principles of Mathematics, was published in 1903, it introduced Frege to a generation that had previously ignored him, and when, after the publication of Tractatus Logico-Philosophicus in 1921, Wittgenstein became the most influential philosopher of his age, Frege’s reputation soared to new heights. By the 1950s, his place as one of the founding fathers of the analytic tradition was secure. Philosophy at Oxford was then going through a golden period, and its leading practitioners—including Gilbert Ryle, Peter Strawson and AJ Ayer—were unanimous in their acknowledgement of Frege’s importance, even if they were, for the most part, in the dark about the man himself, who had, at this time, been alive a mere generation ago.
***
But there was one Oxford philosopher who made a particularly thorough study of Frege’s work and held an especially strong admiration for him. This was Michael Dummett, who would in time become a knight, the Wykeham Professor of Logic and one of Britain’s most influential 20th century thinkers. But while still in his twenties, in 1954, Dummett travelled to Germany to study what had survived of Frege’s Nachlass—that is, his papers—and made what for him was an extremely unpleasant discovery: the man he so revered, the man whose “superhuman” grace and integrity Russell had lauded, had in fact been an anti-democratic, anti-Semitic, racist right-winger, with a love of unreasoning patriotism. This was especially unsettling for Dummett, since he was throughout his life an active campaigner against racism—his knighthood would in time be awarded for services “to racial justice” as well as philosophy. On his return to England, Dummett wrote to Russell (then in his eighties and more interested in the threat of nuclear weapons than in philosophy) to tell him that among the things he had studied was “a copy of a diary Frege kept in the last year of his life, mostly about politics. His political opinions were—at least at that time—very distasteful; he was a strong nationalist, a Bismarckian conservative who believed that Bismarck’s one mistake was the introduction of parliamentarianism into Germany, and worst, of all, an anti-Semite.” Russell was comparatively untroubled by this discovery, but it continued to gnaw away at Dummett, and when he finally published his book Frege: Philosophy of Language in 1973, he felt obliged to say something in its “Introduction:” There is some irony for me in the fact that the man about whose philosophical views I have devoted, over years, a great deal of time to thinking about, was, at least at the end of his life, a virulent racist, specifically, an anti-Semite. This fact is revealed by a fragment of a diary which survives among Frege’s Nachlass, but which was not published with the rest by professor Han Hermes in Frege’s nachgelassene Schriten. The diary shows Frege to have been a man of extreme right-wing opinions, bitterly opposed to the parliamentary system, democrats, liberals, Catholics, the French and, above all, Jews, who he thought ought to be deprived of political rights and, preferably, expelled from Germany. When I read that diary, many years ago, I was deeply shocked, because I had revered Frege as an absolutely rational man, if, perhaps, not a particularly likeable one. I regret that the editors of Frege’s Nachlass chose to suppress that particular item.The editors of the Nachlass have denied that they tried to suppress the diary. It was not included in the volume of posthumous writings to which Dummett refers, they say, because that volume was confined to philosophical work. Their intention had been to publish the diary as an appendix to the biography of Frege that was then being prepared by the Leipzig philosopher Lothar Kreiser. Kreiser’s book was long delayed, however (eventually published in 2001) and so the diary was published in a German journal in 1994, an English translation following in 1996.
Dummett’s characterisation of its contents is entirely accurate. Frege repeatedly heaps praise on Bismarck, pours scorn on social democrats, gives vent to anti-Semitic feelings. He died several years before the Nazis took power, so one can do no more than speculate about how he would have reacted as their murderous rule unfolded, but it is nonetheless striking that he mentions his agreement with the views of the putschist ultra-nationalist General Ludendorff, and indeed Hitler himself. “One can acknowledge that there are Jews of the highest respectability,” runs one typical remark, “and yet regard it as a misfortune that there are so many Jews in Germany, and that they have complete equality of political rights with citizens of Aryan descent.” The single thing I can imagine Russell finding most shocking would be Frege’s endorsement of patriotism as an unreasoning prejudice. The absence of political insight characteristic of his times, Frege says, is due to “a complete lack of patriotism.” He acknowledges that patriotism involves prejudice rather than impartial thought, but he thinks that is a good thing: “Only Feeling participates, not Reason, and it speaks freely, without having spoken to Reason beforehand for counsel. And yet, at times, it appears that such a participation of Feeling is needed to be able to make sound, rational judgments in political matters.” These are surely surprising views for “an absolutely rational man” to express. The man who wanted to set mathematics on surer logical foundations, was content for politics to be based on emotional spasms. When Frege’s adoptive son Alfred sent a transcription of the diary to the editors of the Nachlass, he remarked in an accompanying letter that it would help to “complete the character sketch of my father.” In fact, frustratingly for those of us who want to get some sense of Frege’s character, this fragment of a diary does not “complete” the picture; it more or less is the picture, there being precious little else to go on. When the biography that Lothar Kreiser was working on in 1970s finally appeared in 2001, it was a huge disappointment. It ran to over 600 pages but, by general agreement, added very little to our understanding of the man. There are two chief reasons for this. One is the scarcity of truly personal documents. His original papers were destroyed by enemy action in the Second World War (what Dummett consulted were copies that had been made before the war, almost exclusively of philosophical, rather than personal, documents), and very little of any biographical significance has come to light in the papers of other people. Aside from the correspondence with Russell regarding the collapse of logicism, Frege’s replies to Wittgenstein’s urgent dispatch of the manuscript of the Tractatus stands out as another rare example of a letter that tells us something of the man, albeit of a rather negative sort. Frege quibbled in decidedly pedantic ways with the first couple of sentences, and gives little sign of engaging much beyond this. Certainly, he was entirely blind to the aesthetic ambitions of the book, which has an intricate architecture of interlocking propositions. He suggested that Wittgenstein might instead publish it as a series of papers. This suggests a definite narrowness of mind, at least by contrast with Russell, who cheerfully passed the book as a Cambridge PhD doctorate, even as its author clapped him on the shoulder and said “Don’t worry, I know you will never understand it.” The second reason however, beyond the dearth of documents, lies in the nature of Frege’s personality, which seems to have left curiously little mark not only on paper, but also on those around him. This is in stark contrast to Wittgenstein and Russell, who were such memorable and charismatic characters that countless memoirs of them were written by their relatives, friends and even casual acquaintances. As I remarked in the introduction to my biography of Wittgenstein, recollections of him have been published by, among others, the lady who taught him Russian, the man who delivered peat to his cottage in Ireland, and the man who happened to take the last photographs of him. Something similar is true of Russell. But where are the memoirs of Frege? Poor Kreiser, then, was unable to quote from letters in which Frege’s personality shines forth, or from recollections in which we see the impression he made on others. His book, entitled (with a presumably unconsciously revealing use of hyphens, drawing attention, as they do, to the lack of connections between Frege’s life, work and times) Gottlob Frege: Leben—Werke—Zeit, has more Werke and Zeit in it than Leben. Long discussions of Frege’s books and articles are interspersed with official documents from the University of Jena and the recitation of publicly available facts about, for example, how much tax Frege paid and the changing price of wheat in 19th-century Germany. Meanwhile, Frege himself remains unseen and unheard.***
Quentin Bell, in discussing the curious elusiveness of the central character in Virginia Woolf’s novel, Jacob’s Room, writes: “Imagine a figure made of clay and encased in a mould of Italian plaster. Suppose the clay is destroyed. The plaster remains: it looks utterly unlike the clay figure but it encloses a void, the room that was occupied by the clay.” This describes perfectly what Kreiser has given us. It is “Gottlob’s Room.” And perhaps that is all we will ever have—a placeholder for the man that housed a great mind, an unknown “x,” as it were, in the propositional function. We know the externals of Frege’s life. We know that he was born in 1848 in the Baltic port of Wismar in northern Germany, that he studied mathematics at Jena and Göttingen, that he taught mathematics at Jena from 1874 until his retirement in 1917, and that he died in 1925 in Bad Kleinen, close to where he had been born. He married in 1887 and the marriage was childless, though he and his wife adopted Alfred. Apart from that, despite the many years of research pursued by Lothar Kreiser, we know very little that adds anything to that decidedly unappealing diary fragment of 1924 and to the hints about his personality contained in his philosophical writing. One is reminded of the words with which Martin Heidegger (a philosopher whose personal standing would in time be battered because of his very public Nazi leanings) is said to have begun his lectures on Aristotle: “Regarding the personality of a philosopher, our only interest is that he was born at a certain time, that he worked, and that he died.” And, actually, in the case of Frege, we can drop the pretence that there is any interest in the unremarkable facts about his birth and death. That just leaves us with his work, which, apart from his poisonous but private remarks about the politics of 1920s Germany (which remain difficult to connect to anything else he said or wrote), is all that survives of the man. And yet that is sufficient to establish him as one of the most enduringly influential philosophers of the 19th century. As a biographer, it pains me to say this, but: so much for biography. Now read
