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From Past to Future: Graßmann's Work in Context Graßmann Bicentennial Conference, September 2009

:	Steve Russ, Jörg Liesen, Albert C. Lewis, Hans-Joachim Petsche
:	Hans-Joachim Petsche, Albert C. Lewis, Jörg Liesen, Steve Russ
:	From Past to Future: Graßmann's Work in Context Graßmann Bicentennial Conference, September 2009
:	Birkhäuser Basel
:	9783034604055
:	1
:	CHF 85.40
:

:	Allgemeines, Lexika
:	English

:	580
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century.

This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics.In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Graßmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper 'On the concept and extent of pure theory of number'' by Justus Graßmann (the father).

	Contents	6
	Preface	12
	Abbreviations for works of Hermann Grassmann	18
	On the lives of the Grassmann brothers	22
	Description of the life of Hermann Grassmann by his son Justus Grassmann, probably written shortly after the death of his father, 1877	24
	Life history of Robert Grassmann, written by himself (1890)	29
	Historical contexts of Hermann Grassmann's creativity	36
	Discovering Robert Grassmann (1815–1901)	37
	An overlooked prolific polymath	37
	Plan of the paper	38
	Books by the score	38
	Before GW: Robert's Wissenschaftslehre	40
	The first planned version of GW	43
	The house that Robert Grassmann built: the structure and chronology of GW	43
	Some characteristics of GW	47
	Robert Grassmann on the calculus and logic	49
	Four final queries	51
	Acknowledgements	51
	53	51
	Hermann Grassmann's theory of religion and faith	54
	I	54
	II	55
	Why have people stopped believing in miracles?	56
	Where does the knowledge of mankind come from?	57
	Where do we find absolute knowledge?	58
	Is the Bible the absolute word?	59
	Who interprets scripture?	61
	III	62
	The Significance of Naturphilosophie for Justus and Hermann Grassmann	65
	The philosophy of Christian Samuel Weiss	67
	Emergence of matter	68
	Concept of extension	70
	The question of influence	74
	Justus and Hermann Grassmann: philosophy and mathematics	76
	Institutional development of science in Stettin in the first half of the nineteenth century in the time of Hermann Grassmann	86
	Pomerania at the turn of the nineteenth century	86
	The time of the Bourgeois reformers	88
	Johann August Sack: governor and reformer in Pomerania	89
	Stettin and its Marienstift Gymnasium	90
	The Pommersche Provinzial: Blätter für Stadt und Land 1820–1825	91
	The founding of the ``Society for Pomeranian History and Classical Studies''	94
	The establishment of the Stettin Provincial Archives	95
	The flowering of scientific life in Stettin	96
	Philosophical and methodological aspects of the work of the Grassmann brothers	99
	Brief outline of a history of the genetic method in the development of the deductive sciences	100
	I	100
	II	101
	III	102
	IV	102
	V	103
	VI	103
	VII	103
	Grassmann's epistemology: multiplication and constructivism	104
	Introduction	104
	The product between extensive magnitudes	105
	Extensive magnitudes	106
	The product between extensive magnitudes	107
	A comparative philosophical analysis	108
	The product between vectors and multivectors	109
	Domain and homogeneity	110
	Conclusion	111
	Axiomatics and self-reference Reflections about Hermann Grassmann's contribution to axiomatics	114
	The (never ending?) debate	114
	The place of axiomatics in the Lehrbuch der Arithmetik (1861): the positions of Gottlob Frege, Judson Webb, and Hao Wang	116
	Hans-Joachim Petsche's interpretation	120
	An alternative interpretation: axiomatics and self-reference	122
	Instead of a conclusion	128
	Concepts and contrasts: Hermann Grassmann and Bernard Bolzano	130
	Introduction	130
	Some parallels of context	131
	Some divergences of working	133
	The nature and classification of mathematics	134
	What shall we do with geometry?	136
	What makes a Presentation ``Scientific''?	137
	Conclusion	139
	Diversity of the influence of the Grassmann brothers	141
	New forms of science and new sciences of form: On the non-mathematical reception of Grassmann's work	142
	Grassmann outside mathematics	142
	Grassmann in psychology and physiology	143
	Basic structures and operations: relations, order and abstraction