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2023
- handle: 10670/1.jhw6xc
- hal: hal-04380717
- doi: 10.1007/978-3-031-40855-7
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Vincenzo De Risi, « The Direction-Theory of Parallels: Geometry and Philosophy in the Age of Kant », HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques, ID : 10.1007/978-3-031-40855-7
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The direction-theory of parallels was a mathematical theory that gained enormous importance and popularity for about a century, from the 1770s to the 1870s. It was conceived for the purpose of proving the famous Parallel Postulate and establishing the foundations of Euclidean geometry. The development of the geometric theory was intertwined with that of mathematical epistemology. Proponents of the theory discussed at length such topics as the analyticity of mathematics, the role of intuition in geometry, mathematical constructivism, and the relationship between geometry and the structure of space. In the first few decades of its life, the direction-theory of parallels became the most important benchmark on which to test Kant's philosophy, and Kantians and anti-Kantians alike wrote articles and books on it. The directiontheory was later generally accepted by the leading post-Kantian philosophers of the nineteenth century. It was finally subjected to fatal criticism by Lewis Carroll and Gottlob Frege. 1 C.L. Dodgson, Euclid and his Modern Rivals, London, MacMillan 1879. The theory of parallels is discussed in Act Two, the direction-theory being dealt with in pp. 70-131 of the work.