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There are four ages of modern Vienna. Before the First World War, it was cultured and rich; from 1918 until the Anschluss with Nazi Germany, it was cultured and poor; from 1938 to the end of the Allied occupation, it was just poor; and from 1955 to the present, it has just been rich.

One thing about early-twentieth-century Vienna we think we know is that everyone who mattered was Jewish

Viennese high culture thus lasted only about 40 years, from the late 1890s to the late 1930s. In that brief span, it was the laboratory for many experiments: some that helped to create our world; others that came close to destroying it. Creative destruction, as Joseph Schumpeter called it, was as Viennese as Sachertorte. It was the misfortune of the most brilliant minds to emerge there, however, that their most creative ideas were seen by the envious, incomprehending multitudes as destructive of everything they held dear. Why were the first two periods, under the Habsburg Dual Monarchy and the First Austrian Republic, so much more creative than the era since? It was hardly a question of prosperity, for the postwar hyperinflation wiped out the savings of the bourgeoisie who patronised high culture. A century later, David Edmonds observes in a stimulating, scintillating new book on the Vienna Circle, the city has recovered its wealth but not its energy. While the coffee houses are still flourishing, their denizens argue about money and politics, never ideas. The difference between pre-war and present-day Vienna is, of course, the absence of the largest Jewish minority of any capital in Europe. The truth is that the Viennese got rid of their Jews and replaced them with tourists. Maybe they found tourists more gemütlich.

One thing about early-twentieth-century Vienna we think we know is that everyone who mattered was Jewish, or at least half-Jewish. But this is a myth. Klimt, Schiele, Webern and Musil were not Jewish; Freud, Mahler, Wittgenstein and Schnitzler were. Many Jewish geniuses worked closely with non-Jewish ones: Schoenberg and Berg, Mises and Hayek, Kraus and Loos. The miracle of Vienna was that for a significant segment of the intellectual elite, the distinction between Jew and Gentile hardly mattered any more. As Ernst Gombrich said, “I prefer to leave that enquiry to the Gestapo.”

The Vienna Circle is a case in point. The majority of its core members were Jewish, at least by Nazi racial criteria, but some of these did not consider themselves as such, or even saw their heritage as a burden. This ultimately became a matter of survival. One example: after leaving Vienna for what turned out to be exile in Cambridge, Ludwig Wittgenstein became embroiled in negotiations with the Nazi authorities to have one of his three Jewish grandparents reclassified as non-Jewish, so that his sisters, now in grave danger, would be granted the coveted Mischling (mixed race) status.

They were saved, but at a price: 1.4 tonnes of gold. For “Luki”, as Ludwig was known to his siblings, the moral imperative to rescue his sisters was clear. What made the bribe — for that is what it was — a lasting cause of bitterness for the family was not the loss of the Wittgenstein fortune for the benefit of the Nazis, but the denial of their identity, with all that this implied.

The title chosen by Edmonds (The Murder of Professor Schlick, Princeton University Press, £22) is itself a reminder of these ambiguities. The professor in question, though leader of the Circle, was actually neither Jewish nor Viennese. Moritz Schlick was a physicist who had studied under Max Planck, wrote also on the philosophy of science and came from Berlin to hold Vienna’s chair in natural philosophy, on the recommendation of Albert Einstein.

Academic titles mattered. That chair had once been held by Ernst Mach, the scientist after whom the unit of supersonic travel is named. Edmonds rightly argues that the Vienna Circle saw themselves as his disciples and heirs. He it was who had imported a radical form of empiricism from the British philosopher David Hume. It was Mach who inaugurated some of the key preoccupations of the Circle. Philosophy’s function was not to engage in metaphysical speculation or ethical preaching, but to explore and explain the astonishing progress in the natural and social sciences.

Above all, philosophy was materialist — though not materialistic. Medieval philosophy had been the handmaiden of theology; in the twentieth century, it was to perform the same service for science. Mach’s remarkable book Die Mechanik in ihrer Entwicklung (The Science of Mechanics) exercised a decisive influence on Einstein by denying Newton’s notion of absolute time and space, so paving the way for relativity. The introduction to the first edition of Die Mechanik in 1883 describes its tendency as “an enlightening one or, to put it more clearly, an anti-metaphysical one”. That was also the motto of the Vienna Circle.

A key aspect of Mach’s philosophy was his deconstruction of the unity of the self. In his major work, Die Analyse der Empfindungen (The Analysis of the Sensations, first published in 1885), Mach declared: “Das Ich ist unrettbar.” (“The self is beyond saving.”) Following the ideas of Hume, underpinned by experimental evidence, Mach’s materialism depicted man as a bundle of sense data. Not only did the self have to go, but the soul and anything beyond the senses with it.

Austere beauty of the Modernist kind does not always make for comfort

Some reacted to this bleak but bracing vision with despair. Vienna’s leading poet, Hugo von Hofmannsthal, wrote a key Modernist text, The Lord Chandos Letter, incorporating Mach’s ideas in a self-portrait of an Elizabethan nobleman whose personality is disintegrating. Lenin was so appalled that he wrote an entire book, Materialism and Empirio-criticism, to refute “Machist gentlemen” like Hofmannsthal. Lenin’s book later became the bible of Soviet philosophers — so much so that when, decades later, the FBI visited Philipp Frank, one of the Vienna Circle, in his Harvard exile to ask about his alleged communist connections, he was able to show the two detectives a passage in Materialism and Empirio-Criticism in which Frank was denounced by Lenin as a Machist. The FBI men “practically saluted him, and left speedily and satisfied”.

As Mach’s successor, Schlick was the natural leader of what, in the mid-1920s, had become known as the Wiener Kreis, the Vienna Circle: a motley gathering of thinkers from various fields, united by their commitment to a wissenschaftliche Weltauffassung, or “scientific world conception”, which Edmonds, following academic usage, calls logical empiricism, but is better known as “logical positivism”. Their public face was the Ernst Mach Society, which held open meetings and lectures, but the Circle was by invitation only. And the invitation had to come from Schlick. He saw their common goal of ushering in a new Enlightenment as a blessing for humanity, not least by countering the rising irrationalism of the day, but he was resolutely apolitical.

Schlick followed the gospel according to Wittgenstein. It was an ascetic aestheticism, given physical embodiment in the Palais Stonborough, the house he built for his sister Margaret on the Kindmanngasse. Austere beauty of the Modernist kind does not always make for comfort. Though the mysterious, wandering scholar never actually attended the Circle or any of the international conferences organised in its name, his early philosophy was embodied in the only book he ever allowed to be published, written during the war: the Logisch-Philosophische Abhandlung, later translated as Tractatus Logico-Philosophicus. In this austere, introspective world of pure logic, there could be no place for systems of philosophy, let alone for politics. “Whereof one cannot speak, thereof one must be silent.”

For Schlick, the Tractatus had the status of holy writ; accordingly, the Circle treated it as such. In his own remarkable little book, Problems of Ethics (published in the Circle series Schriften zur wissenschaftlichen Weltauffassung in 1930), Schlick bases his ethics not on the Kantian foundation of absolute duty — then fashionable in Austro-German culture — but on probability: “Moral rules, too, must refer to the average.” Schlick advocated the “ethics of kindness”.

His ethics were supposed to be empirical, eschewing Wittgenstein’s more mystical approach. But it was the latter who escaped the Viennese snake pit; Schlick did not get out in time. Perhaps he was too gentle to survive there. Some of Schlick’s more radical colleagues wanted to invest the Circle with a political — indeed, an explicitly socialist — mission. Chief among them was Otto Neurath, the group’s biggest personality in every sense.

This portly but indefatigable polymath signed his letters with an elephant. He had set up a central planning office for the short-lived postwar Bavarian republic, organised adult education and social housing projects for “Red Vienna”, worked for the Soviets (they never paid up) and created a Museum for Society and Economy, based on a system of pictorial presentation, Isotypes — the ancestor of today’s icons and emojis. Isotypes were original, but still too complex to make Neurath’s fortune: “Simplicity was rarely simple.” His grand publishing project, The Encyclopaedia for Unified Science, was never finished: of a hundred volumes, 20 actually appeared.

Yet, despite exile in Amsterdam, escape by sea from the Nazis and internment on the Isle of Man, Neurath never gave up. Like the original French Encyclopédistes, he believed in the perfectibility of man, accelerated by a benign elite. He ended up employed by the small town of Bilston, Staffordshire, to advise on the replacement of urban slums. The local press dubbed Neurath the “sociologist of happiness” and he gave a talk on the BBC entitled: “Vienna comes to Bilston”. “You cannot organise kindness,” he said, “but you can organise the conditions for it.”

The most original and lasting contributions made by the Circle had little to do with progressive programmes

All this social engineering was remote from the philosophy of Wittgenstein. Neurath was in the habit of muttering “metaphysics” at Circle meetings, but he and his allies ended up as system-builders after all. In 1929, while Schlick was away from Vienna, they published a manifesto that set out the Circle’s “scientific” Weltauffassung. Schlick, for whom the pamphlet was intended as a gift, was appalled, while Wittgenstein thought its “boastfulness” invited ridicule: “‘Renunciation of metaphysics!’ As if that were something new! What the Vienna school has achieved, it ought to show not say.”

The most original and lasting contributions made by the Circle had little to do with progressive programmes. Kurt Gödel’s incompleteness theorems in mathematics, Rudolf Carnap’s Der Logische Aufbau der Welt (“The Logical Construction of the World”) and Karl Popper’s The Open Society and its Enemies are cases in point. Popper spent most of his life repudiating any connection with the Circle; he even claimed that he had “killed” logical positivism by refuting its cardinal principle of verification, replacing it instead with the idea of falsifiability.

But Edmonds shows that in Vienna Popper had been considered a member of the Circle, even if he was never invited to its meetings. And he was not too proud to claim such membership when applying for the job in New Zealand that enabled him to escape the Nazis.

The world beyond Vienna’s Ringstrasse took greater cognisance of the Circle only in 1936, with the appearance of A.J. (“Freddie”) Ayer’s Language, Truth and Logic. This sprightly and deliberately provocative little book established the image of logical positivism in English-speaking countries more vividly than any other school of philosophy. Statements that could not be verified — including moral, aesthetic, religious or political sentiments — were nonsense.

Even in 1972, Tom Stoppard’s Jumpers could depict their verbal gymnastics literally on stage — and still expect his audiences at the Old Vic to know what he was talking about. Questioned by Inspector Bones, investigating the murder of one of the eponymous jumpers, George, the professor of moral philosophy (played by Michael Hordern) replies: “Logical positivists, mainly, with a linguistic analyst or two, a couple of Benthamite Utilitarians . . . lapsed Kantians and empiricists generally . . . and of course the usual Behaviourists . . . a mixture of the more philosophical members of the university gymnastics team and the more gymnastic members of the Philosophy School.”

George’s wife Dotty (played by the late Diana Rigg) dismisses her husband as “the last of the metaphysical egocentrics”, adding the — very Viennese — reflection that the moon landings had shown the limits of truth: “The truths that have been taken on trust, they’ve never had edges before, there was no vantage point to stand on and see where they stopped.” Later Dotty makes a spectacular entrance on a spangled crescent moon, accompanied by the leaping logical positivists.

What caused the Vienna Circle to vanish like a dream was a real-life murder. By 1936, Schlick was celebrated enough to have acquired a stalker: Johann Nelböck, one of his former students. This paranoid and schizoid psychopath was known to be dangerous, but nobody expected him to shoot the professor dead on the steps of his university. Yet that is what happened. The vituperative reaction to the victim, rather than the murderer, told the Circle everything they needed to know about the descent of Vienna into the swamp.

The Vienna Circle had been brought together by a love of logic and a loathing of kitsch

Edmonds has no time for the Church, but one of the few decent tributes came from Dietrich von Hildebrand, a leading Catholic opponent. Schlick was widely assumed to be Jewish, or at least to be a representative of Jewish ideas. At his trial, Nelböck echoed these claims. His antisemitism earned him a lenient sentence of ten years, but when the Nazis marched into Vienna two years later, he was soon released. After the war, when he was described in print by one of the Circle as a paranoid psychopath, Nelböck sued — and won. It is hard to know what is more depressing: the fact that an Austrian court sided with a murderer, or the fact that Nelböck preferred people to think he was bad rather than mad. The taboo on mental illness was evidently stronger than that on Nazism.

By then, many of the Circle had fled Vienna; the rest soon followed. The notoriety of their ideas turned them all into targets. Gödel, the greatest logician of his day, was beaten up by thugs who assumed he was a Jew. The Vienna Circle had been brought together by a love of logic and a loathing of kitsch. They were scattered across the globe by the new political religion, as Erich Voegelin called National Socialism, which anathematised their ideas. Though they all somehow escaped the Nazis, flourishing in exile was, for some, like squaring the Circle.

When I was at Oxford and Cambridge in the late 1970s and early ’80s, a few survivors and witnesses of this intellectual milieu were still alive. I once gave a small dinner for Friedrich von Hayek, who belonged to another circle, known as the Geist Kreis, during the 1920s. (Unlike Schlick’s group, Edmonds tells us, it did not welcome women.) With us, Hayek reminisced about Wittgenstein, his second cousin, whom he encountered in 1918 as a soldier on leave from the Italian front, at about the time when the philosopher was writing his Tractatus.

What struck him most about this intense older man, Hayek recalled in a memoir, was the “radical passion for truthfulness”, which later “became almost a fashion in that border group between the purely Jewish and the purely Gentile parts of the intelligentsia in which I came so much to move” — and which included the Vienna Circle. Like them, Hayek had also been influenced by Mach; he was among the few readers of the Tractatus when it appeared; it made a deep impression. He was less overawed when, many years later, he found himself in Wittgenstein’s presence again in Cambridge; this time Hayek thought him slightly mad, especially when he waved a poker around.

Finally, the two met by chance in the sleeping car on the train from Vienna. Wittgenstein recognised him first, exclaiming: “You are Professor Hayek!” Next day they engaged in a philosophical discussion over breakfast, but “just as it was getting really exciting” they arrived at Boulogne and had to board a ferry. There they lost one another. “Whether he regretted having become so deeply engaged, or had discovered that I was just another philistine, I do not know.” Wittgenstein already had cancer; they never met again.

I never met but corresponded with Karl Popper, who advised me to stick to my chosen field of intellectual history rather than switch to philosophy, which had become too linguistic for his taste. Popper had also had the poker treatment from Wittgenstein, but responded not with Hayek’s aristocratic politesse, but with his usual brusque manner. Popper gave as an example of a moral rule “not to threaten visiting lecturers with a poker”. Wittgenstein, “in a rage”, stormed out. This incident has sparked a whole literature, including an earlier book by Edmonds (and John Eidenow), Wittgenstein’s Poker.

He was less overawed when he found himself in Wittgenstein’s presence again in Cambridge; this time Hayek thought him slightly mad, especially when he waved a poker around

My most significant, though indirect, connection with the Vienna Circle came when I attended the weekly graduate seminar given by A.J. Ayer, by now Wykeham Professor of Logic, at New College. As a mere undergraduate who was not even reading philosophy, I was out of my depth, but I was fascinated by the spectacle of Freddie Ayer himself. By now in his late sixties, he would pace up and down, philosophising and smoking incessantly, his smooth discourse punctuated only by the click of his silver cigarette case.

My occasional tentative contributions to discussion evidently piqued his interest, for one day he pointed at me and said: “You can give us a paper next week. On sense data.” Meekly, I nodded, having only the vaguest notion of the subject; only later did it dawn on me what I had got myself into. Thanks to some frantic cramming and some coaching by Ralph Walker, one of the tutors at my college, I was able to cobble an argument together. The day came and, with fear and trembling, I gave my paper. There was a moment’s excruciating silence, broken finally by the great man. “Some interesting points,” Ayer remarked. Incredibly, I had passed muster.

The discussion that followed, I now realise, would not have been out of place at the Vienna Circle. That was where Ayer would have encountered theories of sense data and perhaps also heard them subjected to sustained critique. Later he suggested that I might like to consider abandoning history and taking up philosophy. I was flattered, certainly — but, perhaps because the offer had been made to my parents rather than to me, unpersuaded. Despite the rebuff, Freddie remained friendly to me. His respect, once gained, was unwavering.

Having long since outgrown his youthful role as an evangelist for the Vienna Circle, he told Bryan Magee on the BBC’s Men of Ideas that the eclipse of logical positivism was due to the fact that its ideas were “mostly false”. Edmonds calls Ayer “mildly autistic”. He wasn’t autistic, he was altruistic.

He might not thank me for saying so, but in moral philosophy he remained a disciple of Schlick, Neurath and the Vienna Circle. In practice, if not in theory, Freddie Ayer too lived by the ethics of kindness.