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. "In Mathematical Thought and Its Objects, Charles Parsons examines the notion of object, with the aim of navigating between nominalism, which denies 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. An intuitive model witnesses the possibility of the structure of natural numbers. However, the full concept of number and knowledge of numbers involve more that is conceptual and rational. Parsons considers how one can talk about numbers, even though they are not objects of intuition. He explores the conceptual role of the principle of mathematical induction and the sense in which it determines the natural numbers uniquely." "Parsons ends with a discussion of reason and its role in mathematical knowledge, attempting to do justice to the complementary roles in mathematical knowledge of rational insight, intuition, and the integration of our theory as a whole."--BOOK JACKET In 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. 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. Includes Bibliographical References (p. 343-363) And Index.

in Mathematical Thought And Its Objects, Charles Parsons Examines The Notion Of Object.