the search for mathematical roots 1870 1940 logics set theories and the foundations of mathematics from cantor through russell to godel

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The Search For Mathematical Roots 1870 1940

Author : I. Grattan-Guinness
ISBN : 1400824044
Genre : Mathematics
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While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

Handbook Of The History Of Logic Sets And Extensions In The Twentieth Century

Author : Dov M. Gabbay
ISBN : 9780444516213
Genre : Reference
File Size : 73. 47 MB
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"Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-nineteenth century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the eleventh and sixteenth centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to enquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece." -- Publisher's website.

Philosophy Of Mathematics

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ISBN : 0080930581
Genre : Philosophy
File Size : 63. 65 MB
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One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Principia Mathematica

Author : Alfred North Whitehead
ISBN : UOM:39015002922899
Genre : Logic, Symbolic and mathematical
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The Bulletin Of Symbolic Logic

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ISBN : UOM:39015072636981
Genre : Logic, Symbolic and mathematical
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Handbook Of The History Of Logic The Rise Of Modern Logic From Leibniz To Frege

Author : Dov M. Gabbay
ISBN : STANFORD:36105119461361
Genre : Induction (Logic)
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With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.

Bulletin Of The Ams

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ISBN : UOM:39076002351232
Genre : Mathematics
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Russell

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ISBN : UCSD:31822034987941
Genre :
File Size : 42. 64 MB
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Great Feuds In Mathematics

Author : Hal Hellman
ISBN : STANFORD:36105114410231
Genre : Mathematics
File Size : 75. 96 MB
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Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association

Bulletin Of The American Mathematical Society

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ISBN : UOM:49015003188654
Genre : Mathematics
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