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Alfred Tarski (1901-1983)
Alistair MacFarlane thinks through the life of a godfather of logic.
Together with Aristotle, Gottlob Frege, and Kurt Gödel, Alfred Tarski is widely regarded as one of the greatest logicians of all time – an opinion he wholeheartedly endorsed. Like Gödel, Tarski revolutionised twentieth century logic, through his conception of semantic truth, the theory of models, and many advances in metalogic (the logic of logic). Yet unlike the reclusive, painfully shy Gödel, he was self-important, vain, and grandiloquent, in both manner and speech. Entering a packed room, he would walk in an undeviating straight line through the crowd like Moses parting the Red Sea. Short in stature yet grand in presence, he was often described as Napoleonic. He was a magnificent lecturer and public speaker. Although by no means handsome, he exuded an aura of energy, intensity and sensuality. Like Picasso, he had supreme confidence in his own talent and ability, and he regarded himself as the very personification of an intellectual. Women students rapidly learned to handle him with at least as much care as they devoted to their subject. His friends could find him embarrassing: when once asked to compare himself to other great logicians, he replied, “I’m the sane one.” Although given to exaggeration, he became deservedly famous for his work on truth.
Truth is the most important concept in philosophy. Many would say that it is what philosophy is all about. In Problems of Philosophy (1912), Bertrand Russell set out three conditions guiding any concept of truth:
• It must enable a distinction between truth and falsity.
• It must admit both beliefs and statements as bearers of truth.
• Whatever is declared to be true or false must be so by virtue of something external to the believer.
In Correspondence Theories of truth, a statement is true if it corresponds to the facts. In Semantic Theories of truth, truth is dependent on the form of certain statements. Tarski developed the first rigorous semantic theory of truth.
The need for technical theories of truth of Tarski’s semantic sort arises from the fact that in a natural language such as English, statements cannot be relied on to be unambiguous. This is usually illustrated using some variant of the Liar Paradox – the statement ‘This statement is false’ is true if and only if it is false, which is absurd. Such paradoxes are unacceptable to a logician. This led Tarski to conclude that the definition and discussion of truth requires the use of a special language that excludes the possibility of paradoxes of this sort. He therefore introduced the concept of a suitably devised meta-language, to be used in the discussion of any statement in an object language such as everyday English. The convention introduced by Tarski is to enclose statements in the object language within quotation marks and leave the statements in the meta-language without quotes. He therefore introduced constructions of the form: “p” is true if and only if q, where:
• “p” is a statement in the object language, identified as such by the use of quotation marks, and
• q is an equivalent statement in a meta-language, in which a statement in the object language can be shown true or false.
Constructing an appropriate statement in the meta-language is a job for experts in logic. The trouble for a non-expert is that simple illustrative examples, in which p without the quote marks is merely the same as q, and at first sight seem mere tautologies. Tarski himself gave the famous example: “Snow is white” is true if and only if snow is white.
When the logician and philosopher of science Karl Popper first saw this he is said to have exclaimed “Of course!” Lesser mortals tend to react with bewilderment. However, Tarski’s idea, shorn of technicalities, is very simple. The basic idea can be accurately conveyed by analysing the form of this example. The truth-bearers in the object language are the words ‘snow’ and ‘white’. Tarski asks: what makes these two words truth-bearers? And the answer is that ‘snow’ refers to that substance identifiable as snow, and ‘white’ is a condition of satisfaction for something if and only if it is demonstrably white. Or in more general terms, if we are to claim that a statement is true, we must be able to specify a reference for the subject of the proposition – such as the word ‘snow’ referring to snow, ‘the dog’ to the dog, etc; and a condition of satisfaction for the predicate – such as the conditions for snow being white, or the dog barking, etc. The difficult parts of Tarskian theory arise in the technical details of how this analysis can be done for sentences with much more complicated structures than ‘X is Y’.
Why is all this important? Because it shows how a simple common-sense conception of truth can be underpinned by a solid logical foundation. Tarski’s semantic theory of truth has successfully survived nearly a century of rigorous examination.
Alfred Tarski by Gail Campbell, 2015
Alfred Tarski was born on 14 January 1901 in Warsaw, Poland, to Isaac (later Ignacy) Tajtelbaum and Rosa (née Prussak). Both parents came from well-established, moderately wealthy, Jewish families. At that time, Warsaw had the second-largest Jewish community in the world.
Tarski’s name was changed twice. Born Alfred Tajtelbaum to parents keen to assimilate a Polish identity, the surname was soon changed to Teitelbaum. In 1923, he and his brother Waclaw then changed it to Tarski when they converted to Roman Catholicism. Shortly after arriving in the United States, Tarski was interrupted whilst giving a seminar by someone saying that all this work had already been done by Teitelbaum. Enraged by the suggestion of plagiarism, Tarski shouted: “I am Teitelbaum!”
Tarski showed great mathematical ability in Warsaw’s Szkola Mazowiecka, but when he entered Warsaw University in 1918 he chose to study biology. He was soon persuaded to switch to mathematics, began to flourish, and became the youngest person to obtain a doctorate from a Polish university. However, a suitable job proved hard to find. He managed to survive in a variety of poorly paid high school teaching positions and by writing elementary textbooks. In 1929 he married Maria Witowska, a fellow school teacher from Minsk. They had two children, a son Jan who became a physicist, and a younger daughter Ina, who married the mathematician Andrzej Ehrenfreucht. Although unable to find a full-time university post, Tarski obtained a part-time appointment, and so was able to diligently pursue research on logic. Once he began to formulate his approach to truth, his ideas were enthusiastically welcomed and taken up by the Vienna Circle of philosophers, who saw them as underpinning their Logical Positivism. A Unity of Science movement spun off from the Circle, and Tarski became an enthusiastic member. He was accordingly invited to attend its World Congress, due to be held in Harvard in September 1939.
Although he later excelled in the academic variety, Tarski had taken no interest in international politics. As a result he was totally unaware of the danger to which he was exposing his family by setting off for America only weeks before Germany would invade Poland.
On 11th August, Tarski sailed for New York on the Gydnia-America Line’s Pilsudski. It was the last ship to leave Warsaw for this destination, and was torpedoed and sunk on its return voyage. All Tarski had with him was a small suitcase, enough money for a few weeks stay, his ticket and passport, and some summer clothing. When he arrived on 22nd August, he was, like his fellow passengers, unaware of impending disaster. On arrival they were aghast to hear rumours of a German-Soviet Non-Aggression Pact, and to realise its implications for Poland. Tarski was plunged into acute anxiety. He decided not to return to Poland, to seek diplomatic help in extricating his family, and to look for a job. He was in a desperate position – the more so because he had no friends among the Polish-Jewish diaspora, many of whom bitterly resented the way in which he had publicly renounced his religion. Nevertheless he managed to find crucial support, particularly from his fellow passenger the mathematician Stanislaw Ulam and the Harvard philosopher Willard van Orman Quine. His first urgent problem was to get a new visa. This required him to leave the country, apply for a residence visa, and then seek to re-enter. The help of American logicians and philosophers proved invaluable. It was arranged for Tarski to go to Cuba, get an appropriate visa, and return to Harvard, where a temporary fellowship was created.
Getting a permanent job proved much more difficult. No major university would offer him a position. For the next two years he survived on a series of short-term appointments and a Guggenheim fellowship. He worked desperately hard, while continuing to develop his research and seeking diplomatic help to locate and aid his family. Through the Swedish Embassy, he eventually learnt that they were still alive, but it proved impossible to get them out of Poland. His wife and children had managed to survive by moving in with her sister. Sending Jan to a Catholic school and Ina to a Catholic orphanage, they remained there until the Warsaw uprising of 1944. They then fled to Crackow to live with friends, returning to Warsaw at the end of the war.
Salvation & Reunion
While Tarski was struggling to keep his head above water on the East Coast, on the West Coast, the University of California was beginning its climb to becoming a world-class university. Griffith Evans, the chairman of the mathematics department at Berkeley, had had his eye on Tarski for some time. But in addition to being short of money, Evans had to contend with Jerzy Neyman, head of the statistics department, who bitterly opposed any approach to Tarski. Neyman was a Polish Jew and resented Tarski’s renunciation of his faith. A sudden crisis in these difficult negotiations was precipitated by the Princeton Draft Board, which served Tarski with call-up papers. After a flurry of bureaucratic and academic activity, Tarski accepted an offer from Berkeley and was granted exemption. Now forty-one, he joined the staff at Berkeley, and over the next three decades built up one of the world’s greatest departments of logic. He remained there until his retirement.
As soon as the war in Europe finished, Tarski went to Washington to seek news of his family. With much help from the Swedish Embassy they were located, and were granted an entrance visa. Travelling to Stockholm, the family then sailed on a small freighter to America, arriving in Berkeley in January 1946 to be met by a large group of photographers and reporters. The Tarskis stayed with the Evans family until a new home was found. But the terrible strains of war and distance eventually took their toll. After a few years the parents separated, and the children became estranged from their father.
On 29 January 1981 Tarski was awarded the Berkeley Citation, the highest award that it can confer, for extraordinary contributions to logic and to the university. In his acceptance speech he warned students of the need to guard against the dangerous influence of Wittgenstein, but did not specify whether he meant the early or late variety [see elsewhere in this issue for Wittgenstein].
As he approached his eighties, Tarski became increasingly frail, suffering from heart problems and emphysema. He died in Berkeley on 26th October 1983. In May 2001, to mark the centenary of his birth, a special conference was held in Warsaw to celebrate his life and work, and a statue was unveiled in the university library overlooking the River Vistula.
Tarski’s great legacy was to give a solid logical foundation to a common-sense characterisation of truth. Truth is a correspondence between a belief and the way the world is, and true sentences mean what they say.
© Sir Alistair MacFarlane 2015
Sir Alistair MacFarlane is a former Vice-President of the Royal Society and a retired university Vice-Chancellor. He has recently published a collection of Brief Lives , available online and from bookshops.