Synopses & Reviews
This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all. Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers. The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves.
Review
"Azzouni's book is a well-conceived and worthwhile contribution. ...it is altogether closely argued, and stimulates serious reflection." Canadian Philosophical Reviews"Interesting, important and well worth reading." Mark Balaguer, Journal of Symbolic Logic". . . this is a very interesting and stimulating book. . . I repeatedly return to it to study its ideas and arguments, and to test my own views against them" --Michael D. Resnik, Philosophia Mathematica"Metaphysical Myths is written in an engaging style and contains a wealth of informative references . . . . the book is rich with arguments that will more than repay careful study." --Philosophical Books
Synopsis
Jody Azzouni argues that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence.
Synopsis
Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similiar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isnât really about those sorts of things as well. Jody Azzouni argues that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyses the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics both sensitive to mathematical practice, and to the ontological and epistemological issues that concern philosophers.
Description
Includes bibliographical references (p. 235-244) and index.
Table of Contents
Part I. Mathematical Practice and its Puzzles: 1. Metaphysical inertness; 2. Metaphysical inertness and reference; 3. The virtues of (second-order) theft; 4. Intuitions about reference and axiom systems; 5. Comparing mathematical terms and empirical terms I; 6. Comparing mathematical terms and empirical terms II; 7. The epistemic role puzzle; 8. Benacerraf's puzzle; Quineâs approach I; Quineâs approach II; Part II. The Stuff of Mathematics: Posits and Algorithms: 1. Introduction; 2. An initial picture; 3. Application and truth; 4. Systems, application and truth; 5. Quineâs objections to truth by convention; 6. Grades of ontological commitment; 7. Multiply interpreting systems; 8. Intuitions about reference revisited; Part III. The Geography of the A Priori: 1. Introduction; 2. Algorithms again; 2. Some observations on metamathematics; 4. Incorrigible co-empiricalness; 5. Why there are no incorrigible co-empirical truths; 6. Normative considerations, the success of applied mathematics, concluding thoughts; Appendix; Bibliography; Index.