Poincaréan intuition revisited: what can we learn from Kant and Parsons?

Studies in History and Philosophy of Science Part A 41 (2):138-147 (2010)
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Abstract

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.Keywords: Immanuel Kant; Charles Parsons; Henri Poincaré; Quasi-concrete object; Sensible intuition; Sensibility.

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References found in this work

Science and method.Henri Poincaré - 1914 - Mineola, N.Y.: Dover Publications. Edited by Francis Maitland.
Systems of predicative analysis.Solomon Feferman - 1964 - Journal of Symbolic Logic 29 (1):1-30.
X*—Mathematical Intuition.Charles Parsons - 1980 - Proceedings of the Aristotelian Society 80 (1):145-168.
On the Foundations of Geometry.Henri Poincaré - 1898 - The Monist 9 (1):1-43.
Immanuel Kant's Critique of Pure Reason.[author unknown] - 1931 - Humana Mente 6 (21):111-115.

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