Alfred Tarski

Life and Logic
Author: Anita Burdman Feferman,Solomon Feferman
Publisher: Cambridge University Press
ISBN: 9780521802406
Category: Biography & Autobiography
Page: 425
View: 4868
Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His mathematical work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in philosophy, linguistics and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon-vivant and a womanizer, who played the 'great man' to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism, but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of war saved his life and turned his career around, even while it separated him from his family for years. By the war's end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full length biography places Tarski in the social, intellectual and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man, interlaced with an account of his major scientific achievements.

Essays on the Foundations of Mathematics and Logic

Author: Giandomenico Sica
Publisher: Polimetrica s.a.s.
ISBN: 8876990143
Category: Mathematics
Page: 351
View: 9968

The Princeton Companion to Mathematics

Author: Timothy Gowers,June Barrow-Green,Imre Leader
Publisher: Princeton University Press
ISBN: 9781400830398
Category: Mathematics
Page: 1056
View: 5150
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

Carnap, Tarski, and Quine at Harvard

Conversations on Logic, Mathematics, and Science
Author: Greg Frost-Arnold
Publisher: Open Court
ISBN: 0812698371
Category: Philosophy
Page: 270
View: 7887
During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard: Bertrand Russell, Alfred Tarski, Rudlof Carnap, W. V. Quine, Carl Hempel, and Nelson Goodman were all in residence. This group held regular private meetings, with Carnap, Tarski, and Quine being the most frequent attendees. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the most prominent question is: if the number of physical items in the universe is finite (or possibly finite), what form should scientific discourse, and logic and mathematics in particular, take? This question is closely connected to an abiding philosophical problem, one that is of central philosophical importance to the logical empiricists: what is the relationship between the logico-mathematical realm and the material realm studied by natural science? Carnap, Tarski, and Quine’s attempts to answer this question involve a number of issues that remain central to philosophy of logic, mathematics, and science today. This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine’s break from Carnap), and relates them when possible to contemporary treatments of these issues. Nominalism. The founding document of twentieth-century Anglophone nominalism is Goodman and Quine’s 1947 “Steps Toward a Constructive Nominalism.” In it, the authors acknowledge that their project’s initial impetus was the conversations of 1940-1941 with Carnap and Tarski. Frost-Arnold's exposition focuses upon the rationales given for and against the nominalist program at its inception. Tarski and Quine’s primary motivation for nominalism is that mathematical sentences will be ‘unintelligible’ or meaningless, and thus perniciously metaphysical, if (contra nominalism) their component terms are taken to refer to abstract objects. Their solution is to re-interpret mathematical language so that its terms only refer to concrete entities—and if the number of concreta is finite, then portions of classical mathematics will be considered meaningless. Frost-Arnold then identifies and reconstructs Carnap’s two most forceful responses to Tarski and Quine’s view: (1) all of classical mathematics is meaningful, even if the number of concreta is finite, and (2) nominalist strictures lead to absurd consequences in mathematics and logic. The second is familiar from modern debates over nominalism, and its force is proportional to the strength of one’s commitment to preserving all of classical mathematics. The first, however, has no direct correlate in the modern debate, and turns upon the question of whether Carnap’s technique for partially interpreting a language can confer meaningfulness on the whole language. Finally, the author compares the arguments for and against nominalism found in the discussion notes to the leading arguments in the current nominalist debate: the indispensability argument and the argument from causal theories of reference and knowledge. Analyticity. Carnap, Tarski, and Quine’s conversations on finitism have a direct connection to the tenability of the analytic-synthetic distinction: under a finitist-nominalist regime, portions of arithmetic—a supposedly analytic enterprise—become empirical. Other portions of the 1940-41 notes address analyticity directly. Interestingly, Tarski’s criticisms are more sustained and pointed than Quine’s. For example, Tarski suggests that Gödel’s first incompleteness theorem furnishes evidence against Carnap’s conception of analyticity. After reconstructing this argument, Frost-Arnold concludes that it does not tell decisively against Carnap—provided that language is not treated fundamentally proof-theoretically. Quine’s points of disagreement with Carnap in the discussion notes are primarily denials of Carnap’s premises without argument. They do, however, allow us new and more precise characterizations of Carnap and Quine’s differences. Finally, the author forwards two historical conjectures concerning the radicalization of Quine’s critique of analyticity in the period between “Truth by Convention” and “Two Dogmas.” First, the finitist conversations could have shown Quine how the apparently analytic sentences of arithmetic could be plausibly construed as synthetic. Second, Carnap’s shift during his semantic period toward intensional analyses of linguistic concepts, including synonymy, perhaps made Quine, an avowed extensionalist, more skeptical of meaning and analyticity. Unity of Science. The unity of science movement originated in Vienna in the 1920s, and figured prominently in the transplantation of logical empiricism into North America in the 1940s. Carnap, Tarski, and Quine’s search for a total language of science that incorporates mathematical language into that of the natural and social sciences is a clear attempt to unify the language of science. But what motivates the drive for such a unified science? Frost-Arnold locates the answer in the logical empiricists’ antipathy towards speculative metaphysics, in contrast with meaningful scientific claims. I present evidence that, for logical empiricists over several decades, an apparently meaningful assertion or term is metaphysical if and only if that assertion or term cannot be incorporated into a language of unified science. Thus, constructing a single language of science that encompasses the mathematical and natural domains would ensure that mathematical entities are not on par with entelechies and Platonic Forms. The author explores various versions of this criterion for overcoming metaphysics, focusing on Carnap and Neurath. Finally, I consider an obstacle facing their strategy for overcoming metaphysics: there is no effective procedure to show that a given claim or term cannot be incorporated within a language.

The Bloomsbury Encyclopedia of Philosophers in America

From 1600 to the Present
Author: John R. Shook
Publisher: Bloomsbury Publishing
ISBN: 1472570561
Category: Philosophy
Page: 944
View: 5775
For scholars working on almost any aspect of American thought, The Bloomsbury Encyclopedia to Philosophers in America presents an indispensable reference work. Selecting over 700 figures from the Dictionary of Early American Philosophers and the Dictionary of Modern American Philosophers, this condensed edition includes key contributors to philosophical thought. From 1600 to the present day, entries cover psychology, pedagogy, sociology, anthropology, education, theology and political science, before these disciplines came to be considered distinct from philosophy. Clear and accessible, each entry contains a short biography of the writer, an exposition and analysis of his or her doctrines and ideas, a bibliography of writings and suggestions for further reading. Featuring a new preface by the editor and a comprehensive introduction, The Bloomsbury Encyclopedia to Philosophers in America includes 30 new entries on twenty-first century thinkers including Martha Nussbaum and Patricia Churchland. With in-depth overviews of Waldo Emerson, Margaret Fuller, Noah Porter, Frederick Rauch, Benjamin Franklin, Thomas Paine and Thomas Jefferson, this is an invaluable one-stop research volume to understanding leading figures in American thought and the development of American intellectual history.

The Handy Philosophy Answer Book

Author: Naomi Zack
Publisher: Visible Ink Press
ISBN: 1578592852
Category: Philosophy
Page: 504
View: 4841
Combining a basic history of philosophical thought with the often quirky personal stories of famous philosophers, this comprehensive introduction to the world of philosophy answers more than 1,000 questions, ranging from What was the Enlightenment? to Why did the Pythagorians avoid fava beans? Analyzing the collective effort of philosophers throughout history in the pursuit of truth and wisdom, the guide explores the tangible significance of philosophical thought to modern society and civilization as a whole. With a wide range of information suitable for various knowledge bases—from junior high to junior college—this is an ideal resource for anyone looking to get a better grasp of the history of thought.

The Oxford Handbook of Atheism

Author: Stephen Bullivant,Michael Ruse
Publisher: OUP Oxford
ISBN: 0191667404
Category: Religion
Page: 784
View: 8195
Recent books by, among others, Sam Harris, Richard Dawkins, and Christopher Hitchens have thrust atheism firmly into the popular, media, and academic spotlight. This so-called New Atheism is arguably the most striking development in western socio-religious culture of the past decade or more. As such, it has spurred fertile (and often heated) discussions both within, and between, a diverse range of disciplines. Yet atheism, and the New Atheism, are by no means co-extensive. Interesting though it indeed is, the New Atheism is a single, historically and culturally specific manifestation of positive atheism (the that there is/are no God/s), which is itself but one form of a far deeper, broader, and more significant global phenomenon. The Oxford Handbook of Atheism is a pioneering edited volume, exploring atheism—understood in the broad sense of 'an absence of belief in the existence of a God or gods'—in all the richness and diversity of its historical and contemporary expressions. Bringing together an international team of established and emerging scholars, it probes the varied manifestations and implications of unbelief from an array of disciplinary perspectives (philosophy, history, sociology, anthropology, demography, psychology, natural sciences, gender and sexuality studies, literary criticism, film studies, musicology) and in a range of global contexts (Western Europe, North America, post-communist Europe, the Islamic world, Japan, India). Both surveying and synthesizing previous work, and presenting the major fruits of innovative recent research, the handbook is set to be a landmark text for the study of atheism.

Alfred Tarski and the Vienna Circle

Austro-Polish Connections in Logical Empiricism
Author: Jan Wolenski,Eckehart Köhler
Publisher: Springer Science & Business Media
ISBN: 9401706891
Category: Science
Page: 347
View: 2872
The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner.

Essays in the History of Logic and Logical Philosophy

Author: Jan Woleński
Publisher: N.A
Category: Logic
Page: 279
View: 3741


A Life in Mathematics
Author: Constance Reid
Publisher: Cambridge University Press
ISBN: 9780883855201
Category: Mathematics
Page: 123
View: 8966
Brings together the Autobiography of Julia Robinson and three articles about her.