Mathematical Thought and Its Objects

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.

ISBN	0521452791	Pages	398
ISBN13	9780521452793 (What's this?)	Volumes	1
Publisher	Cambridge University Press	Weight (grammes)	648
Imprint	Cambridge University Press	Published in	Cambridge
Format	Hardback	Height (mm)	228
Publication date	24 Dec 2007	Width (mm)	152
Library of Congress	QA8.4 .P366 2008	Spine width (mm)	27
DEWEY	510.1	Academic level	Professional / Scholarly
DEWEY edition	DC22

1	Objects and logic	1
2	Structuralism and nominalism	40
3	Modality and structuralism	80
4	A problem about sets	117
5	Intuition	138
6	Numbers as objects	186
7	Intuitive arithmetic and its limits	235
8	Mathematical induction	264
9	Reason	316
	Bibliography	343
	Index	365

'This complete presentation of structuralism as a foundation programme in the philosophy of mathematics enriches significantly the debate and anyone interested in this area of studies will need to consider its relevance.' Minds & Machines

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