Thinking about Mathematics

This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in such thinkers as P...

This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill. The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline. Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy. It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their mathematics.

斯图尔特·夏皮罗(stewart shapiro)，俄亥俄州立大学的哲学教授，同时也是苏格兰圣·安德鲁斯大学的定期访问教授。他是当今一位重要的数学哲学家，其思想属于结构主义，认为数学的研究对象是结构而不是个体。这种思想被认为是源自德国伟大的数学家理查德·戴德金，是当代数学哲学中较为有影响的一派。夏皮罗的主要著作包括《数学哲学：结构与本体论》、《数学哲学：对数学的思考》，以及《没有基础主义的基础：一个二阶逻辑的案例》。他还是《牛津数学哲学与逻辑手册》的主编。...