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(2013) In defense of intuitions, Dordrecht, Springer.
Introduction
Andrew Chapman , Addison Ellis , Robert Hanna , Tyler Hildebrand , Henry Pickford
pp. 137-150
Although these principles [of mathematics], and the representation of the object with which this science occupies itself are generated in the mind completely a priori, they would still not signify anything at all if we could not always exhibit their significance in appearances (empirical objects). Hence it is also requisite for one to make an abstract concept sensible, i.e., display the object that corresponds to it in intuition (Anschauung), since without this the concept would remain ... without sense, i.e., without significance. Mathematics fulfills this requirement by means of the construction of the sensible form (Gestalt), which is an appearance present to the senses (even though brought about a priori). In the same science, the concept of magnitude seeks its standing and sense in number, but seeks this in turn in the shapes, in the beads of an abacus, or in the strokes and points that are placed before the eyes. The concept is always generated a priori, together with the synthetic principles of formulas from such concepts, but their use and reference to supposed objects can in the end be sought nowhere but in experience, the possibility of which (as far as its form is concerned) is contained in them a priori.
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Full citation:
Chapman, A. , Ellis, A. , Hanna, R. , Hildebrand, T. , Pickford, (2013). Introduction, in In defense of intuitions, Dordrecht, Springer, pp. 137-150.
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