Beginning in the nineteenth century, mathematics' traditional
domains of 'number and figure' became vigorously displaced by
altered settings in which former verities became discarded as no
longer sacrosanct. And these innovative recastings appeared
everywhere, not merely within the familiar realm of the
non-Euclidean geometries. How can mathematics retain its
traditional status as a repository of necessary truth in the light
of these revisions? The purpose of this Element is to provide a
sketch of this developmental history.
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