Mathematical thought and its objects /
Parsons, Charles, 1933-
Mathematical thought and its objects / Mathematical Thought & its Objects Charles Parsons. - Cambridge : Cambridge University Press, 2008. - 1 online resource (xx, 378 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Objects and logic -- Structuralism and nominalism -- Modality and structuralism -- A problem about sets -- Intuition -- Numbers as objects -- Intuitive arithmetic and its limits -- Mathematical induction -- Reason.
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.
9780511498534 (ebook)
Mathematics--Philosophy.
Object (Philosophy)
Logic.
QA8.4 / .P366 2008
510.1
Mathematical thought and its objects / Mathematical Thought & its Objects Charles Parsons. - Cambridge : Cambridge University Press, 2008. - 1 online resource (xx, 378 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Objects and logic -- Structuralism and nominalism -- Modality and structuralism -- A problem about sets -- Intuition -- Numbers as objects -- Intuitive arithmetic and its limits -- Mathematical induction -- Reason.
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.
9780511498534 (ebook)
Mathematics--Philosophy.
Object (Philosophy)
Logic.
QA8.4 / .P366 2008
510.1