Javier Echeverria & Andoni Ibarra 
The Space of Mathematics [PDF ebook] 
Philosophical, Epistemological, and Historical Explorations

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