The Space of Mathematics: 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 --
Backmatter.