ISBN: 9789048194162
ID: 9789048194162
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilbert`s program of consistency proofs he explores `implicit definition` (a generalization of definition by abstraction) and indicates how this technique yields an `empiricist` reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Essays on the Foundations of Mathematics by Moritz Pasch: Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilbert`s program of consistency proofs he explores `implicit definition` (a generalization of definition by abstraction) and indicates how this technique yields an `empiricist` reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Arithmetic Axiomatics Decidability Empiricism Geometry History of Mathematics mathematics B Philosophy, general Philosophy of Science History of Mathematical Sciences Mathematics and Statistics, Springer Netherland
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ISBN: 9789048194162
ID: 9789048194162
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilberts program of consistency proofs he explores &apos implicit definition&apos (a generalization of definition by abstraction) and indicates how this technique yields an &apos empiricist&apos reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Essays on the Foundations of Mathematics by Moritz Pasch: Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilberts program of consistency proofs he explores &apos implicit definition&apos (a generalization of definition by abstraction) and indicates how this technique yields an &apos empiricist&apos reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Philosophie MATHEMATICS / History & Philosophy, Springer-Verlag Gmbh
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ISBN: 9789048194162
ID: 9789048194162
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilbert`s program of consistency proofs he explores `implicit definition` (a generalization of definition by abstraction) and indicates how this technique yields an `empiricist` reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Essays on the Foundations of Mathematics by Moritz Pasch: Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science he provides axioms for the combinatorial reasoning essential to Hilbert`s program of consistency proofs he explores `implicit definition` (a generalization of definition by abstraction) and indicates how this technique yields an `empiricist` reconstruction of set theory he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Philosophie MATHEMATICS / History & Philosophy, Springer-Verlag Gmbh
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ISBN: 9789048194162
ID: 93894565
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilberts program of consistency proofs; he explores ´´implicit definition´´ (a generalization of definition by abstraction) and indicates how this technique yields an ´´empiricist´´ reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics. Moritz Pasch is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers he published between 1917-1926. eBook eBooks>Fremdsprachige eBooks>Englische eBooks>Sach- & Fachthemen>Mathematik, Springer Netherlands
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2010, ISBN: 9789048194162
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Titel: | Essays on the Foundations of Mathematics by Moritz Pasch |
ISBN-Nummer: | 9789048194162 |
Detailangaben zum Buch - Essays on the Foundations of Mathematics by Moritz Pasch
EAN (ISBN-13): 9789048194162
ISBN (ISBN-10): 9048194164
Erscheinungsjahr: 2010
Herausgeber: Springer Netherland
245 Seiten
Sprache: eng/Englisch
Buch in der Datenbank seit 28.08.2011 13:10:47
Buch zuletzt gefunden am 05.08.2016 19:56:54
ISBN/EAN: 9789048194162
ISBN - alternative Schreibweisen:
90-481-9416-4, 978-90-481-9416-2
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