Intuition and the Axiomatic MethodEmily Carson, Renate Huber Springer Science & Business Media, 2006 M01 24 - 324 páginas Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics. |
Contenido
Locke and Kant on Mathematical Knowledge | xi |
Kant on the Arithmetical Method before Intuition | 15 |
The Relation of Logic and Intuition in Kants Philosophy of Science Particularly Geometry | 41 |
Edmund Husserl on the Applicability of Formal Geometry | 61 |
The NeoFregean Program in the Philosophy of Arithmetic | 81 |
Godel Realism and Mathematical Intuition | 107 |
Intuition Objectivity and Structure | 127 |
Physical Aspects | 149 |
The Puzzle of Incongruent Counterparts | 151 |
a ReAssessment | 175 |
Intuition and the Axiomatic Method in Hilberts Foundation of Physics | 207 |
John von Neumann on Method and von Neumanns Method in the Physical Sciences | 229 |
The Intuitiveness and Truth of Modern Physics | 245 |
Functions of Intuition in Quantum Physics | 261 |
Intuitive Cognition and the Formation of Theories | 287 |
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