Proof and Other Dilemmas: Mathematics and PhilosophyBonnie Gold, Roger A. Simons MAA, 2008 - 346 oldal For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics. |
Tartalomjegyzék
Proof and How it is Changing | 1 |
Mathematics Jonathan Borwein | 33 |
On the Roles of Proof in Mathematics Joseph Auslander | 61 |
Social Constructivist Views of Mathematics | 79 |
The Nature of Mathematical Objects and Mathematical Knowledge | 129 |
The Nature of Mathematics and its Applications | 243 |
What is Mathematics? A Pedagogical Answer to a Philosophical Question | 265 |
Glossary of Common Philosophical Terms | 341 |
Gyakori szavak és kifejezések
abstract accept according addition algebraic analysis answer applied argument arithmetic axioms belief called chapter claim complex concept concerning consider consistent construction course defined definition described determine discussion empirical entities example exist experience explain expressed fact field formal Foundations function geometry give given human ideas important interest interpretation intuition involved kind knowledge language learning least logic Math mathematical objects mathematicians matter means methods natural numbers Oxford particular philosophy of mathematics physical platonism possible practice precise presented principle probability problem proof properties prove question realism reasoning refer relations result role rule seems sense sentence set theory shows simply social social constructivism solution solve space standard statements structure suggests theorem theory things thinking thought true truth understanding University Press York