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Brief Lives

Rudolf Carnap (1891-1970)

Alistair MacFarlane looks at the possibilities of a logical life.

Rudolf Carnap has a major place in the history of analytic philosophy. He was entranced by the promise that Bertrand Russell’s and A.N. Whitehead’s Principia Mathematica (1912) seemed to hold out for creating a logical foundation for mathematics, and by extension, philosophy. He was even more excited by Russell’s Our Knowledge of the External World (1914), in which Russell called for a reconstruction of all knowledge on the basis of our sense experiences alone, and urged a search for the narrowest selection of basic concepts needed for this purpose. Carnap accepted this immense challenge, and produced Der Logische Aufbau der Welt (1928, translated as The Logical Structure of the World, 1967). His ideas were enthusiastically taken up by positivist philosophers, and the Aufbau is often regarded as the quintessential statement of a positivistic approach to the philosophy of science. Like Principia Mathematica, the Aufbau is now considered a heroic failure, but one that has had a huge impact on philosophy.

Carnap’s second major undertaking, to develop a sound basis for scientific reasoning, occupied him for most of the rest of his working life, and represents his greatest achievement.

Rudolf Carnap
Rudolf Carnap portrait by Darren McAndrew, 2017

Early Life

Rudolf Carnap was born on 18 May 1891, in Ronsdorf, near Dusseldorf, then in the Rhine Province of Prussia. His father Johannes Carnap came from a family of poor weavers, but after long and hard work became the prosperous and respected owner of a ribbon-making factory. Rudolf’s mother Anna (née Dorpfeld) was a teacher and an aspiring author. As he watched his mother write, the young Rudolf became fascinated by what he came to regard as the magical activity of putting words on paper. Few philosophers have imbibed at such an early age what was to become their major preoccupation: how do we create reliable descriptions of the world?

Rudolf had one sister (whose name he neglects to mention in his autobiography!). Their mother obtained permission to teach the children at home, but did so for only an hour a day. His father died when he was only four years old. Then the family moved to Barmen. He attended the local school, where both mathematics and Latin attracted him, one by the exactness of its concepts, the other by its expressive but rational structure.

In 1909 the family moved to Jena, where Carnap entered the University. Physics and philosophy became his major fields, and the pattern of his intellectual life, and the problems it would bring him were beginning to take shape. At that time Gottlob Frege (1848-1925), one of the greatest of all logicians, was an associate professor in Jena, and Carnap attended his lectures on conceptual notation (Bergriffsschrift). He became fascinated by their intellectual implications, and the course of his philosophical life was set.

The outbreak of war in 1914 proved a traumatic experience. Although viscerally opposed to war, Carnap accepted a duty to serve his fatherland, and volunteered to serve in the German army. After three years in the front line he was transferred to Berlin to work on wireless telegraphy.

During the war he married Elizabeth Schöndube. They had four children, but divorced in 1929. In 1933 he married Elizabeth Ina Stögren. This second marriage flourished, lasting until her death in 1964. The couple addressed each other as Carnap and Ina, the latter to be always written in lower case. Carnap hated the name Rudolf and refused to be so called; Ina just wanted to be different.

In 1918, at the war’s end, he returned to Jena to resume his studies. A combination of poverty and the chaos in post-war Germany made it impossible for him to find the books for his proposed field of research. He was rescued by an extraordinary act of kindness by Bertrand Russell. The impoverished student wrote to Russell describing both his proposed research topic and his inability to acquire a copy of Russell’s Principia. Russell replied by sending him a lengthy manuscript in which he had personally copied out and annotated all the relevant parts of that work. Vastly encouraged, and now suitably equipped, Carnap set out to write a dissertation, Der Raum (Space), in which he showed that the contradictions in the theories of space maintained by mathematicians, physicists, and philosophers were caused by their use of entirely different approaches while all using the same terminology.

When he submitted his thesis, the Physics department said it was too philosophical and the Philosophy department said it was all physics. Both rejected it. Carnap had the good sense to swallow his pride, re-write it using a conventional Kantian approach, and re-submit it to the Philosophy department, which, suitably mollified, accepted it. He had by now seen how to formulate a positivistic approach to philosophy, but had received a warning that it would not be easy to communicate and promulgate his ideas in the way he sought.

At a conference in 1923 he had the good fortune to meet a kindred spirit in Hans Reichenbach. Reichenbach introduced him to Moritz Schlick, and in 1926 Schlick offered him a position in the University of Vienna. Carnap moved to Vienna and became a member of the Vienna Circle.

The Vienna Circle and Logical Positivism

The Vienna Circle was a group of like-minded philosophers who sought to establish philosophy on solid logical foundations, in a way that would allow all its conclusions to be rigorously verified. They called their approach ‘Logical Positivism’ although a more accurate name would be ‘Logical Empiricism’. It offered the beguiling prospect of banishing all metaphysical speculation; but this prospect vanished when its fundamental principle of verifiability proved untenable.

The Circle developed in the University of Vienna under leadership of Schlick, who had succeeded the great scientist and positivist philosopher Ernst Mach in 1922. Its guiding ideas had emerged from discussions starting around 1907 between the sociologist Otto Neurath, the physicist Philip Franck, and the mathematician Hans Hahn. As it developed, the Circle attracted the participation of philosophers with a training in, or an attraction to, logic, mathematics, or science. The Circle sought to show that the various types of scientific activity had a common intellectual structure, and argued that philosophy should be re-cast in this scientific form. In its early stages the Circle attracted the attention and participation of many leading philosophers, including Wittgenstein, Karl Popper, A.J. Ayer and Alfred Tarski.

Positivism, Verification and Falsification

Our knowledge can only be of three kinds:

• Innate, deriving from our genetic inheritance (breathing, balancing, walking…);

• Derived from our sensory experience; and

• Derived from thought.

‘Empiricism’ is the attitude to knowledge that takes our sensory experience as primary. Positivism is an extreme form of empiricism that admits only sensory experience as the source of knowledge. The name ‘positivism’ is due to Auguste Comte (1798-1857), who believed that the empirical discoveries of science took total precedence over all theoretical rational constructions. Logical positivism is positivism plus logic.

Carnap’s approach said that scientific knowledge uses a ‘Principle of Verification’, which demands that all theories be established by verified facts. Sir Karl Popper (1902-1994) took an opposing view concerning science. He thought that scientific progress results from the exercise of imagination producing theories which must then be tested against the facts, and if a proposed theory withstands sustained criticism and fits all the observable facts, then that’s sufficient to hold it as true until it might be refuted by newly-discovered facts. He pointed out that Carnap’s approach is unworkable, since no matter how often a theory is apparently ‘verified’ by observations, one reliable falsification is sufficient to render the theory invalid. This ‘Principle of Falsification’, Popper boasted, destroyed Carnap’s approach.

Popper’s view of science, based on falsifiability rather than verifiability, is supported by many working scientists.

Deduction, Induction and Probability

Before Popper’s demolition of his Principle of Verification, Carnap had been a strong proponent of a frequency interpretation of probability in evaluating theories. He now realised that he would have to adopt a different approach. In his philosophical autobiography, The Philosophy of Rudolf Carnap (1963), he describes how Ludwig Wittgenstein’s ideas on probability convinced him that he should seek a logical approach to the use of probability in theory evaluation. As a result he developed the approach described in his Logical Foundations of Probability (1950).

Carnap had seen a way to put inductive reasoning (argument on the basis of observations) on the same absolutely logical basis as deductive reasoning (arguments of abstract reason) by creating a unified and objective account of inductive inference specified by clear rules of procedure. Carnap had grasped how to create an objective approach by using the idea of a degree of verification. This enabled him to develop the inductive approach on which he continued to work for the rest of his life. Deductive arguments are valid when their conclusions follow from their premises. Inductive arguments, however, are very different, since they proceed from specific cases to general conclusions. These general conclusions cannot be seen as obviously true or false, but can only be seen as more or less probable given the available evidence. So inductive argument necessarily involves probabilistic reasoning. So Popper’s claim to demolish verification in science was premature: a rigid yes/no verification criterion can be relaxed into probabilities. Probabilistic argument is now an indispensable part of science.

Personality and Last Days

Carnap was logic personified. He was fabulously well-organised, maintaining an extensive card file system in which was summarised every book, significant paper, and major article he had read. This was combined with a prodigious ability to recall conversation and experience. The overwhelming impression he conveyed was one of great control and sustained momentum. One of his students compared him to a polite and friendly tank. He remained unfailingly courteous in the face of ferocious and in many cases ill-considered attacks on his work. Few people have worked for decades on such hugely difficult topics; even fewer have had the ability to carefully consider severe and sustained criticism while remaining gracious but unyielding.

Carnap’s socialist and pacifist beliefs put him in danger in an increasingly pro-Nazi Austria. He emigrated to the United States in 1935, becoming a naturalised citizen in 1941. The wisdom of this move was demonstrated by the appalling murder of Moritz Schlick on the entrance steps to the University of Vienna, in 1936.

From 1936-1952 Carnap was a Professor of Philosophy at the University of Chicago. Thanks to Willard Quine, he was able to spend the years 1939-41 in Harvard, where he, Quine, and Alfred Tarski worked together on the role of logic in philosophy. After a short spell at the Institute for Advanced Study in Princeton, he joined the Philosophy department at UCLA, where he remained until retirement. Sadly, his wife Ina committed suicide in 1964.

Carnap became seriously ill suddenly in his late seventies. He was rushed into hospital and died after a few days, on September 14, 1970. The great depth of affection and respect in which he was held became apparent when the entire Volume 8 of The Boston Studies in the Philosophy of Science (1971) was devoted to assessments of and tributes to his work.


Carnap never abandoned his belief that science and philosophy should be founded on a bedrock of logic. He remained unmoved in the face of ridicule by Karl Popper, who boasted that he had ‘killed’ Logical Positivism. He remained courteous when ferociously attacked by Nelson Goodman, who denounced his lack of recognition of humanistic values as ‘horrible’. His unshakeable support of the primacy of both deductive and inductive logic made his position an increasingly isolated philosophy during the latter part of the Twentieth Century.

Meanwhile, technology has moved on. Agency – the capacity for autonomous behaviour – can be created in a mechanical form by a combination of sensors, motors, and computing. Nowadays, for example, an unmanned aircraft can take off, travel for thousands of miles to a specified destination, and land unaided. The agency of machines will steadily increase: think of robots, unmanned vehicles, industrial processes… so Carnap’s approach will become increasingly relevant, because highly sophisticated machine agents will certainly act on a basis of logic. What better way could there be to characterise machine agency logic, than in the probabilistic manner that Carnap worked so long and so hard to develop? A comprehensive explanation of human agency may remain beyond our reach, but Rudolf Carnap’s faith in logic as the basis of one form of agency will have been vindicated.

© Sir Alistair MacFarlane 2017

Sir Alistair MacFarlane is a former Vice-President of the Royal Society and a retired university Vice-Chancellor.

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