Charles Parsons examines the notion of object, with the aim to
navigate between nominalism, denying that distinctively
mathematical objects exist, and forms of Platonism that postulate a
transcendent realm of such objects. He introduces the central
mathematical notion of structure and defends a version of the
structuralist view of mathematical objects, according to which
their existence is relative to a structure and they have no more of
a 'nature' than that confers on them. Parsons also analyzes the
concept of intuition and presents a conception of it distantly
inspired by that of Kant, which describes a basic kind of access to
abstract objects and an element of a first conception of the
infinite.
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