The Space of Mathematics

Frontmatter -- Table of Contents -- Acknowledgments -- Introductory afterthoughts -- Structural Dimensions -- The Protean Character of Mathematics / MACLANE, SAUNDERS -- Categories of Space and of Quantity / LAWVERE, F. WILLIAM -- Structural Analogies Between Mathematical and Empirical Theories / IBARRA, ANDONI / MORMANN, THOMAS -- Reduction and Explanation: Science vs. Mathematics / RANTALA, VEIKKO -- Reality, Truth, and Confirmation in Mathematics – Reflections on the Quasi-Empiricist Programme / NIINILUOTO, ILKKA -- Tacit Knowledge in Mathematical Theory / BREGER, HERBERT -- Structure-Similarity as a Cornerstone of the Philosophy of Mathematics / GRATTAN-GUINNESS, IVOR -- Dimensions of Applicability -- Applying Mathematics and the Indispensability Argument / RESNIK, MICHAEL D. -- Mathematical Structures and Physical Necessity / TORRETTI, ROBERTO -- The Role of Mathematics in Physical Science / SCHEIBE, ERHARD -- The Status of Set-theoretic Axioms in Empirical Theories / SCHMIDT, HEINZ-JÜRGEN -- Suppes Predicates for Classical Physics / COSTA, NEWTON C. A. DA / DORIA, F. ANTONIO -- Mathematics in Philosophy / HOWSON, COLIN -- Historical Dimensions -- Are There Revolutions in Mathematics? / DAUBEN, JOSEPH W. -- Observations, Problems and Conjectures in Number Theory – The History of the Prime Number Theorem / ECHEVERRIA, JAVIER -- Historical Aspects of the Foundations of Error Theory / KNOBLOCH, EBERHARD -- A Structuralist View of Lagrange’s Algebraic Analysis and the German Combinatorial School / JAHNKE, HANS NIELS -- Constructivism and Objects of Mathematical Theory / OTTE, MICHAEL -- Turing’s “Oracle”: From Absolute to Relative Computability – and Back / FEFERMAN, SOLOMON -- Computers and Mathematics: The Search for a Discipline of Computer Science / MAHONEY, MICHAEL S. -- Global Dimensions of Knowledge: Information, Implementation, and Intertheoretic Relations -- Theories and the Flow of Information / MOSTERIN, JESUS -- Structuralism and Scientific Discovery / SNEED, JOSEPH D. -- Towards a Typology of Intertheoretical Relations / MOULINES, C. ULISES -- Index of Names -- Backmatter