The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations

Description

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.