Mathematical Thought and its Objects

Cambridge University Press (2007)

Abstract
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.
Keywords Mathematics Philosophy  Object (Philosophy  Logic
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Reprint years 2008, 2009
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Call number QA8.4.P366 2008
ISBN(s) 9780511498534   9780521452793
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The Nature of Intuitive Justification.Elijah Chudnoff - 2011 - Philosophical Studies 153 (2):313 - 333.
Experimental Attacks on Intuitions and Answers.John Bengson - 2013 - Philosophy and Phenomenological Research 86 (3):495-532.
Intuitive Knowledge.Elijah Chudnoff - 2013 - Philosophical Studies 162 (2):359-378.
From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
Awareness of Abstract Objects.Elijah Chudnoff - 2013 - Noûs 47 (4):706-726.

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