Background
Alfred Tarski was born in Warsaw, Poland on January 14, 1902. Tarski was the elder of two sons born to Ignacy Tajtelbaum, a shopkeeper of modest means, and Rose (Iuussak) Tajtelbaum, who was known to have an exceptional memory.
( First published in Polish in 1936, this classic work wa...)
First published in Polish in 1936, this classic work was originally written as a popular scientific book one that would present to the educated lay reader a clear picture of certain powerful trends of thought in modern logic. According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge. Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here. Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.
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( Published with the aid of a grant from the National End...)
Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.
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( This graduate-level book is well known for its proof th...)
This graduate-level book is well known for its proof that many mathematical systems—including lattice theory, abstract projective geometry, and closure algebras—are undecidable. Based on research conducted from 1938 to 1952, it consists of three treatises by a prolific author who ranks among the greatest logicians of all time. The first article, "A General Method in Proofs of Undecidability," examines theories with standard formalization, undecidable theories, interpretability, and relativization of quantifiers. The second feature, "Undecidability and Essential Undecidability in Mathematics," explores definability in arbitrary theories and the formalized arithmetic of natural numbers. It also considers recursiveness, definability, and undecidability in subtheories of arithmetic as well as the extension of results to other arithmetical theories. The compilation concludes with “Undecidability of the Elementary Theory of Groups."
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logician mathematician scientist writer
Alfred Tarski was born in Warsaw, Poland on January 14, 1902. Tarski was the elder of two sons born to Ignacy Tajtelbaum, a shopkeeper of modest means, and Rose (Iuussak) Tajtelbaum, who was known to have an exceptional memory.
During his teens Tarski helped supplement the family income by tutoring. He attended an excellent secondary school, and although he was an outstanding student, he, surprisingly, did not get his best marks in logic. Biology was his favorite subject in high school, and he intended to major in this discipline when he first attended the University of Warsaw. However, as Steven R. Givant pointed out in Mathematical Intelligence, “what derailed him was success.” In an early mathematics course at the university, Tarski was able to solve a challenging problem in set theory posed by the professor. The solution led to his first published paper, and Tarski, at the professor’s urging, decided to switch his emphasis to mathematics.
Tarski received Doctor of Philosophy degree from the University of Warsaw in 1924.
Tarski served in the Polish army for short periods of time in 1918 and 1920. While working on his doctor's project he was employed as an instructor in logic at the Polish Pedagogical Institute in Warsaw beginning in 1922. After graduating he became a docent and then adjunct professor of mathematics and logic at the University of Warsaw beginning in 1925. That same year he also took a full-time teaching position at Zeromski’s Lycee, a high school in Warsaw, since his income from the university was inadequate to support his family. Tarski remained at both jobs until 1939, despite repeated attempts to secure a permanent university professorship. Some have attributed Tarski’s employment difficulties to anti-semitism, but whatever the reason, his lack of academic prominence created problems for the young mathematician. Burdened by his teaching load at the high school and college, Tarski was unable to devote as much time to his research as he would have liked. He later said that his creative output was greatly reduced during these years because of his employment situation. The papers he did publish in this period, however, quickly marked Tarski as one of the premiere logicians of the century. His early work was often concentrated in the area of set theory. He also worked in conjunction with Polish mathematician Stefan Banach to produce the Banach-Tarski paradox, which illustrated the limitations of mathematical theories that break a space down into a number of pieces. Other research in the 1920s and 1930s addressed the axiom of choice, large cardinal numbers, the decidability of Euclidean geometry, and Boolean algebra.
Tarski’s initial research on semantics took place in the early-1930s. He was concerned here with problems of language and meaning, and his work resulted in a mathematical definition of truth as it is expressed in symbolic languages. He also provided a proof that demonstrated that any such definition of truth in a language results in contradictions. A London Times obituary on Tarski noted the groundbreaking nature of his work in this area, proclaiming that the mathematician’s findings “set the direction for all modern philosophical discussions of truth.” Tarski expanded this early work in semantics over the ensuing years, eventually developing a new field of study—model theory—which would become a major research subject for logicians. This area of study examines the mathematic properties of grammatical sentences and compares them with various models of linguistic communication.
Additionally, Tarski pursued research in many other areas of math and logic during his career, including closure algebras, binary relations and the algebra of relations, cylindrical algebra, and undecidable theories. He also made a lasting contribution to the field of computer science. As early as 1930 he produced an algorithm that was capable of deciding whether any sentence in basic Euclidian geometry is either true or false. This pointed the way toward later machine calculations, and has also had relevance in determining more recent computer applications.
In 1939 Tarski left Poland for a conference and speaking tour in the United States, intending to be gone for only a short time.
Shortly after his departure, however, the German Army invaded and conquered Poland, beginning World War II. Unable to return to his homeland, Tarski found himself stranded in the United States without money, without a job, and without his wife and children who had remained in Warsaw. The family would not be reunited until after the war, and in the meantime, Tarski set about finding work in America. He first served as a research associate in mathematics at Harvard University from 1939 to 1941. In 1940 he also taught as a visiting professor at the City College of New York. He had a temporary position at the Institute for Advanced Study at Princeton beginning in 1941, and in 1942 he obtained his first permanent position in the United States when he was hired as a lecturer at the University of California at Berkeley. The university would remain his professional home for the rest of his career.
Tarski became an associate professor at the university in 1945, was appointed to the position of full professor the following year, and was named professor emeritus in 1968.
Tarski’s contributions to mathematics and science were enhanced by his role as an educator. He established the renowned Group in Logic and the Methodology of Science at Berkeley, and over his long tenure he taught some of the most-influential mathematicians and logicians to emerge after World War II, including Julia Robinson and Robert Montague. His stature was further enhanced through his service as a visiting professor and lecturer at numerous U.S. and international universities. In 1973 Tarski ended his formal teaching duties at Berkeley, but he continued to supervise doctoral students and conduct research during the final decade of his life.
Alfred Tarski is regarded as the cofounder of metamathematics and one of the founders of the discipline of semantics.
Tarski received many awards and honors throughout his career. In 1966 he received the Alfred Jurzykowski Foundation Award, and in 1981 he was presented with the Berkeley Citation, the university’s highest faculty honor.
( First published in Polish in 1936, this classic work wa...)
( This graduate-level book is well known for its proof th...)
( Published with the aid of a grant from the National End...)
The Tarski brothers converted to Roman Catholicism, Poland's dominant religion. When Tarski was married, he was baptized a Catholic, his wife’s religion. Alfred did so even though he was an avowed atheist.
Tarski was elected to the National Academy of Sciences and the Royal Netherlands Academy of Sciences and Letters, and was also made a corresponding fellow in the British Academy.
He was a member in many professional organizations, including the Polish Logic Society, the American Mathematical Society, and the International Union for the History and Philosophy of Science.
He was also a president of the Association of Symbolic Logic.
It is believed that the young mathematician was in his early-twenties when he changed his name from Tajtelbaum to Tarski. His son, Jan, told interviewer Jeanne Spriter James that this step was taken because Tarski believed that his new Polish-sounding name would be held in higher regard at the university than his original Jewish moniker.
Quotes from others about the person
"Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models." - Anita and Solomon Feferman
Tarski married Maria Witkowski on June 23, 1929, and later they had two children, Jan and Ina.
