Thesis ID: CBB001561682

Kant on the Reality of Mathematical Definitions (2005)

unapi

Dunlop, Katherine Laura (Author)


University of California, Los Angeles
Burge, C. Tyler


Publication Date: 2005
Edition Details: Advisor: Burge, C. Tyler
Physical Details: 531 pp.
Language: English

The dissertation considers Kant's view of mathematics in the contexts of seventeenth- and eighteenth-century theories of scientific knowledge and the transcendental philosophy of the _Critique of Pure Reason_. Kant and his peers were especially impressed by the certainty and rigor of Euclidean geometry. They did not draw our distinction between the abstract theorems of pure geometry and its interpretation in physical or perceptual space. So they thought Euclidean proof revealed the necessary features of the space around us, and sought to explain its power. I show that Kant and his predecessors believed that in geometry, we grasp concepts in a special way. They claimed that geometrical concepts had 'real' definitions, which proved the possibility of objects answering to the concepts. On Kant's view, geometrical definitions yield insight into our capacity to represent objects as given. Kant defines this capacity as 'sensible intuition'. On his view, its role in geometrical proof demonstrates its significance for all cognition. The first half of the dissertation situates Kant's view of real definition in its historical context. A British tradition understood the possibility of geometrical objects in terms of physical processes, and argued that it could be proved only perceptually. Leibnizians viewed possibility as the admissibility of a combination of features, and maintained that the possibility of an object could be proved from a definition, by adverting to the combinatory processes in which its concept was formed. Kant maintains that attention to the combinatory acts in which a concept is formed reveals what is physically possible. On his view, the formation of geometrical concepts is constrained by the structure of outer intuition. I criticize recent attempts to understand intuition in terms of motion. I argue that Kant's references to motion should be understood as replying to specific interlocutors. In the final chapters, I argue that on his view, the formation of arithmetical concepts is likewise constrained by the form of inner intuition. Kant's view of definition thus underlies a comprehensive account of mathematics.

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Description Cited in Diss. Abstr. Int. A 67/05 (2006): 1756. UMI pub. no. 3218638.


Citation URI
https://data.isiscb.org/isis/citation/CBB001561682/

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Authors & Contributors
Sutherland, Daniel
Shabel, Lisa A.
Domski, Mary
Biagioli, Francesca
Stekeler-Weithofer, Pirmin
Serfati, Michel
Concepts
Philosophy of mathematics
Mathematics
Geometry
Philosophy
Metaphysics
Arithmetic
Time Periods
18th century
19th century
17th century
20th century, early
20th century
Places
Germany
England
France
Europe
Great Britain
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