The Space of Mathematics

Frontmatter -- Table of Contents -- Acknowledgments -- Introductory afterthoughts -- Structural Dimensions -- The Protean Character of Mathematics -- Categories of Space and of Quantity -- Structural Analogies Between Mathematical and Empirical Theories -- Reduction and Explanation: Science vs. Mathematics -- Reality, Truth, and Confirmation in Mathematics Reflections on the Quasi-Empiricist Programme -- Tacit Knowledge in Mathematical Theory -- Structure-Similarity as a Cornerstone of the Philosophy of Mathematics -- Dimensions of Applicability -- Applying Mathematics and the Indispensability Argument -- Mathematical Structures and Physical Necessity -- The Role of Mathematics in Physical Science -- The Status of Set-theoretic Axioms in Empirical Theories -- Suppes Predicates for Classical Physics -- Mathematics in Philosophy -- Historical Dimensions -- Are There Revolutions in Mathematics? -- Observations, Problems and Conjectures in Number Theory The History of the Prime Number Theorem -- Historical Aspects of the Foundations of Error Theory -- A Structuralist View of Lagrange s Algebraic Analysis and the German Combinatorial School -- Constructivism and Objects of Mathematical Theory -- Turing s Oracle : From Absolute to Relative Computability and Back -- Computers and Mathematics: The Search for a Discipline of Computer Science -- Global Dimensions of Knowledge: Information, Implementation, and Intertheoretic Relations -- Theories and the Flow of Information -- Structuralism and Scientific Discovery -- Towards a Typology of Intertheoretical Relations -- Index of Names -- 423-424

Zusammenfassung
Dieses umfassende Nachschlagewerk bndelt die Ergebnisse von fast zwei Jahrhunderten internationaler Forschung im Bereich volkstmlicher Erzhltradition. Die Autoren vergleichen die reichen Sammelbestnde mndlich und schriftlich berlieferter Erzhlungen aus den verschiedensten Ethnien und zeigen die sozialen, historischen, geistigen und religisen Hintergrnde auf.