Echeverria J., Ibarra A., Mormann T. The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations

Berlin: de Gruyter, 2012. — 411 p.FrontmatterIntroductory 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
Backmatter