Contents -- Preface -- Acknowledgments -- Part I: Introductory Chapters -- 1. Productive Ambiguity: Galileo contra Carnap -- 1.1. Galileo's Demonstration of Projectile Motion -- 1.2. Carnap on Language and Thought -- 1.3. From the Syntactic to the Semantic to the Pragmatic Approach -- 1.4. A Pragmatic Account of Berzelian Formulas -- 2. Analysis and Experience -- 2.1. Analysis -- 2.2. Mathematical Experience -- Part II: Chemistry and Geometry -- 3. Bioorganic Chemistry and Biology -- 3.1. What Lies Between Representing and Intervening -- 3.2. The Reduction of a Biological Item to a Chemical Item -- 3.3. Formulating the Problem -- 3.4. Constructing the Antibody Mimic -- 3.5. Testing the Antibody Mimic -- 3.6. Conclusions -- 4. Genetics and Molecular Biology -- 4.1. Objections to Hempel's Model of Theory Reduction -- 4.2. The Transposition of Genes: McClintock and Fedoroff -- 4.3. McClintock's Studies of Maize -- 4.4. J. D. Watson's Textbook -- 4.5. Fedoroff's Translation of McClintock -- 4.6. The Future of Molecular Biology -- 5. Chemistry, Quantum Mechanics, and Group Theory -- 5.1. Symbols, Icons, and Iconicity -- 5.2. Representation Theory -- 5.3. Molecules, Symmetry, and Groups -- 5.4. Symmetry Groups, Representations, and Character Tables -- 5.5. The Benzene Ring and Carbocyclic Systems -- 5.6. Measuring Delocalization Energy in the Benzene Molecule -- Part III: Geometry and Seventeenth Century Mechanics -- 6. Descartes's Geometry -- 6.1. Locke's Criticism of Syllogistic -- 6.2. Descartes' Geometry as the Exemplar of Cartesian Method -- 6.3. Diagrams as Procedures -- 6.4. Generalization to the Construction of a Locus -- 6.5. Generalization to Higher Algebraic Curves -- 7. Newton's Principia -- 7.1. Philip Kitcher on History -- 7.2. Jean Cavaillès on History -- 7.3. Book I, Propositions I and VI in Newton's Principia.

7.4. Book I, Proposition XI in Newton's Principia -- 8. Leibniz on Transcendental Curves -- 8.1. The Principle of Continuity -- 8.2. Studies for the Infinitesimal Calculus -- 8.3. The Principle of Perfection -- 8.4. The Isochrone and the Tractrix -- 8.5. The Catenary or La Chainette -- Part IV: Geometry and Twentieth Century Topology -- 9. Geometry, Algebra, and Topology -- 9.1. Vuillemin on the Relation of Mathematics and Philosophy -- 9.2. Euclid's Elements and Descartes' Geometry Revisited -- 9.3. Kant's Transcendental Aesthetic: Extrinsic and Intrinsic Intuition -- 9.4. The First Pages of Singer and Thorpe -- 9.5. De Rham's Theorem -- 9.6. Nancy Cartwright on the Abstract and Concrete -- 10. Logic and Topology -- 10.1. Penelope Maddy on Set Theory -- 10.2. A Brief Reconsideration of Arithmetic -- 10.3. The Application of Logic to General Topology -- 10.4. Logical Hierarchies and the Borel Hierarchy -- 10.5. Model Theory and Topological Logics -- 10.6. Coda -- List of Illustrations -- Glossary -- Bibliography -- Books -- Articles -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.