| 书目名称 | Essays on the Foundations of Mathematics by Moritz Pasch |
| 编辑 | Stephen Pollard |
| 视频video | |
| 概述 | Gives English speaker access to an important body of work from a turbulent and pivotal period in the history of mathematics.Helps us look beyone the familiar triad of formalism, instuitionism and logi |
| 丛书名称 | The Western Ontario Series in Philosophy of Science |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Book 2010 |
| 关键词 | Arithmetic; Axiomatics; Decidability; Empiricism; Geometry; History of Mathematics; mathematics |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-90-481-9416-2 |
| isbn_softcover | 978-94-007-3314-5 |
| isbn_ebook | 978-90-481-9416-2Series ISSN 1566-659X Series E-ISSN 2215-1974 |
| issn_series | 1566-659X |
| copyright | Springer Science+Business Media B.V. 2010 |
发表于 2025-3-21 18:49:33
