The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations

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Javier Echeverrķa, Andoni Ibarra, Thomas Mormann
Walter de Gruyter, Jan 1, 1992 - Mathematics - 422 pages
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Revised versions of papers presented by philosophers, historians of science, and mathematicians at a multidisciplinary symposium on Structures in Mathematical Theories, held at the University of the Basque Country (UPV/EHU) in Donostia/San Sebastian (Basque Country, Spain), September 1990. The 23 papers are organized within four broad areas: structural dimensions; dimensions of applicability; historical dimensions; and global dimensions of knowledge--information, implementation, and intertheoretic relations. No subject index. Annotation copyright by Book News, Inc., Portland, OR
  

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Contents

The Protean Character of Mathematics
3
Categories of Space and of Quantity
14
Structural Analogies Between
31
Reduction and Explanation Science vs Mathematics
47
Reality Truth and Confirmation in Mathematics
60
Tacit Knowledge in Mathematical Theory
79
Structuresimilarity as a Cornerstone of
91
Applying Mathematics and the Indispensibility
115
Mathematics in Philosophy
192
Are There Revolutions in Mathematics?
205
Observations Problems and Conjectures in Number
230
Historical Aspects of the Foundations of Error Theory
253
A Structuralist View of Lagranges Algebraic
280
Constructivism and Objects of Mathematical Theory
296
Turings Oracle From Absolute to Relative
314
Computers and Mathematics The Search
349

Mathematical Structures and Physical Necessity
132
The Role of Mathematics in Physical Science
141
The Status of Settheoretic Axioms
156
Suppes Predicates for Classical
168
Theories and the Flow of Information
367
Towards a Typology of Intertheoretical Relations
403
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