The Determinate World : Kant and Helmholtz on the Physical Meaning of Geometry

This book offers a new interpretation of Hermann von Helmholtz??s work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz??s Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature ""completely comprehensible"", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz??s work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed. Introduction The empirical determination of physical concepts in Kant Metaphysical foundations of natural science Conceptual determination Phenomenology and the determination of motion Phoronomy Dynamics Mechanics Regulative and constitutive principles The parallelogram law Helmholtz on the comprehension of nature Helmholtz's arguments for force centrality in the conservation of energy The philosophical argument The mathematical argument Helmholtz's later criticisms of his determinacy argument Empirical determinacy and geometry Colour-theory and manifolds Newton's barycentric colour-wheel Helmholtz's 1852 Ber die theorie der zusammengesetzten farbena Gramanna's 1853 zur theorie der farbenmischung Helmholtz's 1855 ber die zusammensetzung von spectralfarbena Maxwell's 1855 experiments on colour The road to empirical geometry Phase 1 Phase 2 Phase 3 Helmholtz on geometry, 1868-1878 The four papers The papers of 1868 Ber den ursprung und bedeutung der geometrischen axiome Ber den ursprung und sinn der geometrischen stzea. Review text: "David Hyder's The Determinate World is ambitious and challenging. It is an exciting and tough read, and it covers a great deal of ground. Hyder constructs a careful and stimulating narrative, to make a number of significant and well-constructed arguments concerning Helmholtz's epistemology, his relationship to Kant, and his empirical geometry. The Determinate World is an excellent contribution to the history of philosophy of 19th century science - those who work in the field will need to engage with this book."Lydia Patton in: http://ndpr.nd.edu/review.cfm?id=20627 This study examines the place of Hermann von Helmholtz’s seminal papers on geometry in his philosophy of science. The arguments of these papers are traced back to his prior work on the theory of magnitudes, as well as to Helmholtz’s early, Kantian position. The author claims that Helmholtz should be understood not as opposing Kant, but as modifying the latter’s theory of magnitudes so as to remove obstacles to their common project of constructing a complete system of natural science. The Determinate World......Page 1 Acknowledgments......Page 3 Contents......Page 5 1. Introduction......Page 7 2. The Empirical Determination of Physical Concepts in Kant’s......Page 25 3. Helmholtz on the Comprehension of Nature......Page 82 4. Colour-theory and Manifolds......Page 111 5. The Road to Empirical Geometry......Page 140 7. Conclusion......Page 203 Bibliography......Page 221 Index......Page 226