000 03553nam a22004215i 4500
001 978-90-481-9416-2
003 DE-He213
005 20140220084603.0
007 cr nn 008mamaa
008 100803s2010 ne | s |||| 0|eng d
020 _a9789048194162
_9978-90-481-9416-2
024 7 _a10.1007/978-90-481-9416-2
_2doi
050 4 _aB1-5802
072 7 _aHP
_2bicssc
072 7 _aPHI000000
_2bisacsh
082 0 4 _a10
_223
100 1 _aPollard, Stephen.
_eeditor.
245 1 0 _aEssays on the Foundations of Mathematics by Moritz Pasch
_h[electronic resource] /
_cedited by Stephen Pollard.
264 1 _aDordrecht :
_bSpringer Netherlands :
_bImprint: Springer,
_c2010.
300 _aXII, 248 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aThe Western Ontario Series in Philosophy of Science,
_x1566-659X ;
_v83
505 0 _aTranslator’s Introduction -- Fundamental Questions of Geometry -- The Decidability Requirement -- The Origin of the Concept of Number -- Implicit Definition and the Proper Grounding of Mathematics -- Rigid Bodies in Geometry -- Prelude to Geometry: The Essential Ideas -- Physical and Mathematical Geometry -- Natural Geometry -- The Concept of the Differential -- Reflections on the Proper Grounding of Mathematics I -- Concepts and Proofs in Mathematics -- Dimension and Space in Mathematics -- Reflections on the Proper Grounding of Mathematics II -- The Axiomatic Method in Modern Mathematics.
520 _aMoritz 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. The book will be of interest to graduate students and researchers in logic and the foundations of mathematics.
650 0 _aPhilosophy (General).
650 1 4 _aPhilosophy.
650 2 4 _aPhilosophy.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789048194155
830 0 _aThe Western Ontario Series in Philosophy of Science,
_x1566-659X ;
_v83
856 4 0 _uhttp://dx.doi.org/10.1007/978-90-481-9416-2
912 _aZDB-2-SHU
999 _c113646
_d113646