Realism in Mathematics

ISBN-13: 9780198240358 / Angielski / Miękka / 1992 / 216 str.

Penelope Maddy

Opis

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.

Recenzje

the book is written in a lively, engaging style. We hope that it serves to stimulate others to think seriously about issues in philosophy of mathematics because, as Maddy claims, these issues bear directly on mainstream philosophy.

Spis treści

Realism: Pre-theoretic realism; Realism in philosophy; Realism and truth; Realism in mathematics; Perception and intuition: What is the question?; Perception; Intuition; Godelian Platonism; Numbers: What numbers could not be; Numbers as properties; Frege numbers; Axioms: Reals and sets of reals; Axiomization; Open problems; Competing theories; The challenge; Monism and beyond: Monism; Field's nominalism; Structuralism; Summary; References; Index.