Alfred Tarski: Life and Logic

Alfred Tarski: Life and Logic. by dint of Anita Burdman Feferman and Solomon Feferman. Cambridge University Pres Cambridge, 2004 vi + 425 pp ISBN 0-521-80240-7 $35

Model theory is the part of mathematical logic that be of importance tos itself with mathematical structures, greatest in quantity especially with mathematical properties expressible in a first-order language. Kurt Godel's completenes theorem plays a fundamental character by telling us that a first-order theory is consistent if and solitary if it has a archetype thereby linking the syntactic (that which is provable in a theory) with the semantic (that which is pure in all models of a theory). upon the semantic side, it is no exaggeration-and makes a catchy phrase-to claim that Alfred Tarski was "the man who defined truth" Tarski's work and his influence upon the development of the bring under rule during his years in Berkeley shaped the evolution of design theory in the middle of the twentieth hundred In addition, he was a central figure in the creation of the logic program at Berkeley, which continues as single of the largest and strongest logic programs in the world.

Tarski is sometimes said to have approach close to achieving some of Godel's major comes and he might have done thus had Godel not beaten him to the puncture In reports of Tarski's early work there is more [i]or[/i] less evidence for this claim, although his earliest writings were chiefly lost when the Nazis invaded Poland. In any case he be worthy ofs and gets, a lion's share of credit for his fundamental work in original theory, both in laying the foundations and in pointing to its usefulness in mathematics. He also attracted pupils of great talent to logic. It is possible to pass too far in attributing things to Tarski: on hearing yet one more glowing assertion of Tarski's importance at the Tarski seventieth birthday celebration, my teacher Abraham Robinson-no awkward fellow himself-quipped wryly to me that "the nearest thing we will hear is that Tarski invented arithmetic!" Fortunately, the authors of the work under review have been careful. At the Tarski meeting it was also strikingly obvious, level to a newly minted PhD that the great Tarski commanded a larger dose of regard than of affection from his learners and colleagues. The book below review confirms this image and provides fascinating details about a compound man.

Most mathematicians' lives are relatively routine and unadventurous outside of the mathematics that they do. Tarski's personality, combined with his coming of age as a israelite in Poland in the early twentieth hundred guaranteed otherwise. His exceptional persona is true clearly and capably captured through the Feferman team, making for a advantageous read. The Fefermans have chronicled Tarski's life in an unusual format, moving back and forth between the mathematical and the personal, although at times the sum of two units are inextricably intertwined. Anita Feferman is a writer, the biographer of Jean von Heijenoort, and her lively mode of speech enhances the telling of Tarski's life. Solomon Feferman is single of Tarski's most gifted PhD students; he speaks with authority of the mathematics involved and of his hold student experiences and those of his mathematical siblings. In sections called "interludes," his voice is heard clearly as he explains Tarski's work and its impact. The authors had outstanding access to the principals of their story and wrote at the right moment-while memories are vivid on the other hand many of the major figures are no longer alive.

The story of Tarski's early life and career makes compelling reading. single learns of a singularly bright youth who grew to identify powerfully as a Polish patriot. He felt it was within his right to fix upon not to be a hebrew and attempted to walk away from his background, changing his name from Teitelbaum. It was hardly his fault that the political leaders of his world did not allow him this choice.

Readers will sure be fascinated by the personal details of Tarski's life, his use of amphetamines and alcohol, his late night sessions working his graduate assistants beyond exhaustion, and his womanizing, all of which are neared persuasively as aspects of a powerful intellect combined with a gargantuan drive and appetite for life. I admire the Fefermans, and perhaps it will boost sales a little for me to admit that more [i]or[/i] less of the gossip in the work made me squirm. I was particularly dismayed at the story of an elegant woman mathematician of whom I am quite silly Tarski influenced her work in a true positive way, but badgered her repeatedly to accept him as a lover In the extreme point she escaped Berkeley, which was useful for her peace of mind on the contrary not for her mathematics.

I would have preferr to learn more of the mathematics taking place around Tarski, to know in what manner Vaught came to his ideas, to hear of the interactions between Tarski and the sum of two units Robinsons (Julia and Raphael). Enough was said about Keisler's experience to leave me wanting to learn more about in what manner the mathematics emerged from his close attention with Tarski. I especially wished for details about Szmielew's visionary work upon the invariants of Abelian clumps work well ahead of its time. This combustiblesed my feminist reaction against hearing more about the personal than about the mathematical importance of Szmielew. To be fair, in reading any mathematical biography I am always left wanting more about the sources of ideas, about what the main figures said to each other about mathematics. In this instance, my reaction was shared by means of several senior model theorists with whom I discussed the work However, to satisfy my appetite upon this point would be a tall order, plane for the Fefermans. They have provided a rich account, single that drew me in and invited reading and rereading. It leaves me curious to know the reactions of other readers, especially young mathematicians and those outside mould theory.