The Space of Mathematics

Javier Echeverria, Andoni Ibarra, Thomas Mormann, Javier Echeverria, Andoni Ibarra, Thomas Mormann

• Editorial: De Gruyter
• Año: 2012
• ISBN:
  9783110870299
• Edición: 1
• Categoría: Mathematik
• Categoría: Mathematik Allgemein

Índice

• Acknowledgments
• Introductory afterthoughts
• 1. 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
• 2. Dimensions of Applicability
• Applying Mathematics and the Indispensibility 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
• 3. 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
• 4. 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