Authors
Janet Folina
Macalester College
Abstract
The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics.
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DOI 10.15173/jhap.v6i3.3438
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References found in this work BETA

Intuitionism and Formalism.L. E. J. Brouwer - 1913 - Bulletin of the American Mathematical Society 20:81-96.
Kant on the ‘Symbolic Construction' of Mathematical Concepts.Lisa Shabel - 1998 - Studies in History and Philosophy of Science Part A 29 (4):589-621.

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