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Certainty Interrupted: 'Exact Thinking In Demented Times'

As a history of ideas, this work is especially good at mapping the Vienna Circle's fascinating afterlife in the English-speaking countries where many prominent thinkers landed and flourished in the 20th century.

Exact Thinking in Demented Times: The Vienna Circle and the Epic Quest for the Foundations of Science
Karl Sigmund


Dec 2017


Karl Sigmund has written a genuinely multidisciplinary book that is philosophically interesting and thick with historically plausible arguments. The demented times of the title are those of Vienna from before the ruin of the Austro-Hungarian Empire in 1918 through to when the roof began to collapse in 1938. Throughout, Austria was haunted by the spectre of two annihilating ideologies of conquest – communism and especially Nazism – and not immune to the cultural derangements that accompanied them. "A shining pinnacle of exact thinking set against a backdrop of wild fanaticism and maniacal stupidity," Sigmund writes in his introduction.

But Austria's cultural life was also lit by the genius of Albert Einstein, Ludwig Boltzmann, and Ernst Mach, and heir to a long tradition of scientific inquiry. The aspiring practitioners of exact thinking were members of the Vienna Circle, either scientists obsessed with examining the philosophical underpinnings of their respective disciplines, or scientists at some stage of permanent migration to philosophy. There were also visual artists, novelists, economists, architects, historians, and other mavericks associated with the Circle who absorbed and attempted to work through the same or similar problems that gripped the era's scientists.

The intellectual labor for these thinkers was organized around two agendas. The first was the unification of the sciences on a firm epistemological footing. In other words, they wanted certainty for scientific knowledge and reliable methods for verifying it. This entailed attempting to answer at least the following questions: What is scientific knowledge and what is its exact relationship with mathematics? What are its logical foundations and can we prove them? And how can we understand the relationships between mathematics, logic, science, and the real world? The second agenda was to sever philosophy from metaphysics. This required rejecting the idealism of Plato, Kant, and Hegel, sweeping all religious and speculative creeds into the dustbin of history, and submitting only hard-nosed verifiable information as scientific knowledge.

Sigmund's cast of characters is huge – too huge to maintain a grip on the moving pieces – but he warns as much on the first page. "You'll just get fleeting glances," he writes, "cameo appearances through the windows of a brilliantly lit coffee house." The pace is quick. But the trade-off is Sigmund's knack for wresting interesting and illustrative work from obscure thinkers for their anecdotal value and for the light they cast upon the central mission of the Vienna Circle.

Consider Kurt Grelling, for example, a German-Jewish philosopher loosely associated with the Circle who perished in Auschwitz in 1942. He identified a paradox known to students of logic as the Grelling-Nelson Paradox, and which has implications for the first agenda item listed above. Sigmund explains it using the word non-self-descriptive, and it runs as follows.

The word huge is not huge so it is not self-descriptive. The word pentasyllabic has five syllables so it is perfectly self-descriptive. There are many more examples of words that do or do not happen to describe themselves. But is non-self-descriptive self-descriptive? Sigmund puts it this way: "If it is, then it is not; and if it is not, then it is. This, too, is a troubling state of affairs." This is one example of how Sigmund, himself a mathematician, will allow himself passage into the weeds of a tricky logic problem. The casual reader will get there with some patience.

For members of the Vienna Circle, an exercise such as this was not for idle amusement. It revealed the potential for contradictions to hide within otherwise apparently logical systems. "Can we be sure," he writes, "that there are no other still-undiscovered contradictions unsuspectedly lurking here or there?" Between 1924 and 1938 the core group of Vienna Circle philosophers generated books, articles, and lectures that promised a philosophical framework for resolving such disquieting problems and for attempting to ensure certainty, fortified only by experimentation and logical analysis.

It was bound to fail but it was failure on a grand scale. It had to fail not only because, as the philosopher Viktor Kraft remarked soon after World War II was over and Austria finally resembled a kind of depleted dystopia, "the work of the Vienna Circle has not been completed, it has been broken off." But also because matters of truth, certainty, and skepticism are deeply recalcitrant problems despite the perennial scrutiny to which they are subjected in the Western philosophical tradition.

So there are unlikely to be philosophers today who would describe themselves as logical positivists, as the members of the Circle came to be known as. But as a history of ideas, Sigmund's book is especially good at mapping the movement's fascinating afterlife in the English-speaking countries where many of these men and women – if they managed to survive the Nazis – landed and flourished over the course of the 20th century. The Vienna Circle is a river that to this day runs through the study of economics, logic, philosophy, and computer science.

Most striking of all is the role it assumed in animating the thought of Karl Popper (1902-1994), who departed for the United Kingdom in 1935. Popper's philosophy, in Sigmund's view, can be understood as both a reinterpretation and an improvement of the thinking of the Vienna Circle. His breakthrough was not to ask whether a scientific statement can be verified but rather to ask whether it can be falsified. According to this approach, scientific progress does not consist in the accumulation of observations but instead in the overthrowing of less good observations by better ones. All science is tentative and there is no secure knowledge – a turning of Vienna Circle philosophy on its head. Today the falsification principle is still a cornerstone of the scientific method. As Sigmund puts it, "Socrates is reputed to have declared: 'I know that I know nothing.' Popper liked to add: 'and frequently not even that.'"

The ability to obtain certainty proves elusive. At the same time, metaphysics proves a resilient adversary. Like Popper, the mathematician Kurt Gödel (1906-1978) was associated with, inspired by, and eventually spurned the principles of the Circle. His genius is not unfairly compared to that of Einstein. But he also quietly harbored metaphysical ideas about God and the meaning of life. Like his early modern predecessors Descartes and Leibnitz, he sketched out arguments for the existence of God rooted in mathematical logic. "The world and everything in it has a reason and meaning," he later wrote in some private correspondence, "and actually a good and indubitable meaning." In ways such as these, Popper and Gödel and others absorbed or rejected the Vienna Circle. Sigmund clarifies the unsettled historical contexts for these creative processes and makes a case for according his subject a central place in the history of 20th-century philosophy.
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