TAILIEUCHUNG - A Structural Account of Mathematics

This work develops and defends a structural view of the nature of mathematics, which is used to explain a number of striking features of mathematics that have puzzled philosophers for centuries. It rejects the most widely held philosophical view of mathematics (Platonism), according to which mathematics is a science dealing with mathematical objects such as sets and numbers—objects which are believed not to exist in the physical world. Instead, it makes use of the constructibility theory of my earlier work, Constructibility and Mathematical Existence (Oxford University Press, 1990), to develop a view of mathematics that is distinct from Structuralism and yet makes use of some key ideas of Structuralism | OXFORD A Structural Account of Mathematics CHARLES A Structural Account of Mathematics Charles Chihara develops and defends a structural view of the nature of mathematics and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that in order to understand how mathematical systems are applied in science and everyday life it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work in which he presented a new system of mathematics the constructibility theory which did not make reference to or presuppose mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by w. V. Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field. Charles s. Chihara is Emeritus Professor of Philosophy at the University of California Berkeley. This page intentionally left .

• Kế toán - Kiểm toán
• Mathematicians Regarding
• Nature of Mathematics
• Fourth Puzzle
• Multiple Reductions
• Ordinary Structures
• Indispensability Argument