Dunlop, Katherine Laura (Author)
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.
...MoreDescription Cited in Diss. Abstr. Int. A 67/05 (2006): 1756. UMI pub. no. 3218638.
Article
Domski, Mary;
(2013)
Kant and Newton on the a priori Necessity of Geometry
(/isis/citation/CBB001320266/)
Article
Giovanelli, Marco;
(2010)
Urbild und Abbild: Leibniz, Kant und Hausdorff über das Raumproblem
(/isis/citation/CBB001230056/)
Article
Engelhard, Kristina;
Mittelstaedt, Peter;
(2008)
Kant's Theory of Arithmetic: A Constructive Approach?
(/isis/citation/CBB001230070/)
Chapter
Pulte, Helmut;
(2001)
Order of Nature and Orders of Science: On the Material Philosophy of Nature and Its Changing Concepts of Science from Newton and Euler to Lagrange and Kant
(/isis/citation/CBB000101471/)
Article
Sutherland, Daniel;
(2005)
Kant on Fundamental Geometrical Relations
(/isis/citation/CBB000670505/)
Book
Parsons, Charles;
(2012)
From Kant to Husserl: Selected Essays
(/isis/citation/CBB001253011/)
Article
Francesca Biagioli;
(2020)
Ernst Cassirer's transcendental account of mathematical reasoning
(/isis/citation/CBB961648354/)
Book
Potter, Michael;
(2000)
Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap
(/isis/citation/CBB000110939/)
Book
Stekeler-Weithofer, Pirmin;
(2008)
Formen der Anschauung: eine Philosophie der Mathematik
(/isis/citation/CBB000951513/)
Article
Heis, Jeremy;
(2011)
Ernst Cassirer's Neo-Kantian Philosophy of Geometry
(/isis/citation/CBB001035116/)
Chapter
Sutherland, Daniel;
(2010)
Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant
(/isis/citation/CBB001033539/)
Chapter
Gerhard Heinzmann;
(2016)
Kant et l'intuition épistémique
(/isis/citation/CBB981942154/)
Article
Shabel, Lisa;
(2003)
Reflections on Kant's Concept (and Intuition) of Space
(/isis/citation/CBB000340870/)
Chapter
Shabel, Lisa;
(2006)
Kant's Philosophy of Mathematics
(/isis/citation/CBB001035269/)
Article
Domski, Mary;
(2010)
Kant on the Imagination and Geometrical Certainty
(/isis/citation/CBB001034596/)
Thesis
Rohloff, Waldemar;
(2007)
Kant and Frege on the a priori Applicability of Mathematics
(/isis/citation/CBB001561363/)
Chapter
Carlo Casolo;
(2018)
La Biblioteca Universale
(/isis/citation/CBB604701261/)
Article
Ferraro, Giovanni;
Panza, Marco;
(2012)
Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method
(/isis/citation/CBB001220403/)
Article
Yap, Audrey;
(2011)
Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness
(/isis/citation/CBB001024184/)
Article
Petrie, Bruce J.;
(2012)
Leonhard Euler's Use and Understanding of Mathematical Transcendence
(/isis/citation/CBB001251201/)
Be the first to comment!