The Legacy Of Mario Pieri On The Foundations And Philosophy Of Mathematics PDF Download
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| Author | : Elena Anne Marchisotto |
| Publisher | : Birkhäuser |
| Total Pages | : 0 |
| Release | : 2016-03-08 |
| Genre | : Mathematics |
| ISBN | : 9780817648220 |
Download The Legacy of Mario Pieri on the Foundations and Philosophy of Mathematics Book in PDF, ePub and Kindle
Mario Pieri on the Foundations of Philosophy and Mathematics introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints, placing his life and research in context and tracing his influence on his contemporaries as well as more recent mathematicians. The text also includes translations and commentary on Pieri’s original analyses on projective geometry, transformational geometry.
| Author | : Elena Anne Marchisotto |
| Publisher | : Birkhäuser |
| Total Pages | : |
| Release | : 2016-03-08 |
| Genre | : Mathematics |
| ISBN | : 9780817672607 |
Download The Legacy of Mario Pieri on the Foundations and Philosophy of Mathematics Book in PDF, ePub and Kindle
Mario Pieri on the Foundations of Philosophy and Mathematics introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints, placing his life and research in context and tracing his influence on his contemporaries as well as more recent mathematicians. The text also includes translations and commentary on Pieri’s original analyses on projective geometry, transformational geometry.
| Author | : Elena Anne Marchisotto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2007-12-05 |
| Genre | : Mathematics |
| ISBN | : 0817646035 |
Download The Legacy of Mario Pieri in Geometry and Arithmetic Book in PDF, ePub and Kindle
This book is the first in a series of three volumes that comprehensively examine Mario Pieri’s life, mathematical work and influence. The book introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations — one in arithmetic and one in geometry. The book combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index. And yet the book requires no specialized experience in mathematical logic or the foundations of geometry.
| Author | : Elena Marchisotto |
| Publisher | : Springer |
| Total Pages | : 494 |
| Release | : 2007-05-08 |
| Genre | : Mathematics |
| ISBN | : 9780817632106 |
Download The Legacy of Mario Pieri in Geometry and Arithmetic Book in PDF, ePub and Kindle
The Italian mathematician Mario Pieri (1860-1913) played an integral part in the research groups of Corrado Segre and Giuseppe Peano, and thus had a significant, yet somewhat underappreciated impact on several branches of mathematics, particularly on the development of algebraic geometry and the foundations of mathematics in the years around the turn of the 20th century. This book is the first in a series of three volumes that are dedicated to countering that neglect and comprehensively examining Pieri’s life, mathematical work and influence in such diverse fields as mathematical logic, algebraic geometry, number theory, inversive geometry, vector analysis, and differential geometry. The Legacy of Mario Pieri in Geometry and Arithmetic introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints, placing his life and research in context and tracing his influence on his contemporaries as well as more recent mathematicians. The text also provides a glimpse of the Italian academic world of Pieri's time, and its relationship with the developing international mathematics community. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations—his postulates for arithmetic, which Peano judged superior to his own; and his foundation of elementary geometry on the basis of point and sphere, which Alfred Tarski used as a basis for his own system. Combining an engaging exposition, little-known historical information, exhaustive references and an excellent index, this text will be of interest to graduate students, researchers and historians with a general knowledge of logic and advanced mathematics, and it requires no specialized experience in mathematical logic or the foundations of geometry.
| Author | : Paolo Mancosu |
| Publisher | : OUP Oxford |
| Total Pages | : 632 |
| Release | : 2014-01-09 |
| Genre | : Philosophy |
| ISBN | : 0191021997 |
Download The Adventure of Reason Book in PDF, ePub and Kindle
Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.
| Author | : |
| Publisher | : |
| Total Pages | : 22 |
| Release | : 1923 |
| Genre | : Geometry |
| ISBN | : |
Download The Teaching of Elementary Geometry Book in PDF, ePub and Kindle
| Author | : Jeremy Gray |
| Publisher | : Princeton University Press |
| Total Pages | : 528 |
| Release | : 2022-12-13 |
| Genre | : History |
| ISBN | : 0691242046 |
Download Plato's Ghost Book in PDF, ePub and Kindle
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
| Author | : Joan Roselló |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 230 |
| Release | : 2011-10-18 |
| Genre | : Mathematics |
| ISBN | : 1443834793 |
Download From Foundations to Philosophy of Mathematics Book in PDF, ePub and Kindle
From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Gödel. Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell’s type theory, Zermelo’s set theory and Gödel’s incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.
| Author | : Lukas M. Verburgt |
| Publisher | : Bloomsbury Publishing |
| Total Pages | : 321 |
| Release | : 2023-01-26 |
| Genre | : Philosophy |
| ISBN | : 1350228850 |
Download Aristotle's Syllogism and the Creation of Modern Logic Book in PDF, ePub and Kindle
Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.
| Author | : S. G. Dani |
| Publisher | : Springer Nature |
| Total Pages | : 759 |
| Release | : 2019-10-18 |
| Genre | : Mathematics |
| ISBN | : 3030136094 |
Download Geometry in History Book in PDF, ePub and Kindle
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
