References in:
Geometry as a Universal mental Construction
In Stanislas Dehaene & Elizabeth Brannon (eds.), Space, Time and Number in the Brain. Oxford University Press (2011)
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Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) 

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms. 





In this paper, I investigate an important aspect of Kant’s theory of pure sensible intuition. I argue that, according to Kant, a pure concept of space warrants and constrains intuitions of finite regions of space. That is, an a priori conceptual representation of space provides a governing principle for all spatial construction, which is necessary for mathematical demonstration as Kant understood it.Author Keywords: Kant; Space; Pure sensible intuition; Philosophy of mathematics. 