Stuart Shapiro's unique work is divided into four parts, which comprehensively expounds the philosophical problems and positions related to mathematics. The book discusses the mathematical problems that philosophers have been thinking about since human beings began rational activities. In The Synthesis of History, the author discusses the position of mathematics in the minds of Plato, Aristotle, Kant and Mill.
It also discusses the three main positions of the whole 20th century: mathematics is logic (logicism), the essence of mathematics is the operation of characters according to rules (formalism), and revisionist philosophy (intuitionism) holds that mathematics is a spiritual activity. Finally, Shapiro examines contemporary positions and works and leads readers to the forefront of this field.
Extended data:
Stuart Shapiro is a philosophy professor at Ohio State University and a regular visiting professor at St Andrews University in Scotland. He is an important mathematical philosopher at present. His thought belongs to structuralism, and he thinks that the object of mathematical research is structure rather than individual.
This idea is considered to have originated from the great German mathematician Richard Dai Deking, and is an influential school in contemporary mathematical philosophy. Shapiro's major works include Philosophy of Mathematics: Structure and Ontology, Philosophy of Mathematics: Reflection on Mathematics, and Without Fundamentalism: A Case of Second Order Logic.