Abstract
In chapters 2 and 3 we have seen the importance that Kant attributed to geometric construction and its relation with the philosophy of mathematics which was constructed at the same time as transcendental philosophy itself. In this chapter we will examine the problem of construction as it emerges in the geometric knowledge of ancient Greece.
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References
On the epistemological problems of heuristics in relation with scientific discovery cf. chapter 2, section 4, and Magnani, 1988, 1999a, 1999b, and 2001, chapter 2.
Which is in this case, we must remember, the drawing of a specific empirical image, of a single intuition, according to Kant.
Cf. chapter 6, section 1, this book.
On the relationship between analysis and synthesis in the history of geometry and on the limitations of Kantian analysis of the concept of construction cf. Lakatos, 1976.
I treated these problems in Magnani, 1978b, pp. 29–42 and in Magnani, 1977a and 1978a; as for historical and epistemological problems posed by Euclid in the Elements cf. Knorr, 1975, 1986 and Mueller, 1969, 1981.
Also called “problem”. On the notion of problem cf. the following section.
On the bimillenary history of criticisms to Euclid’s V postulate and the attempts to demonstrate it cf. Magnani, 1978b, chapters 1, 2, 4 as well as the texts indicated in note 23, chapter 2, this volume)
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© 2001 Kluwer Academic Publishers
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Magnani, L. (2001). The Φαντασία in Ancient Geometrical Knowledge. In: Philosophy and Geometry. The Western Ontario Series in Philosophy of Science, vol 66. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9622-5_4
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DOI: https://doi.org/10.1007/978-94-010-9622-5_4
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