Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact SciencesThis 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. |
Contents
Metaphysical Inertness | 3 |
Metaphysical Inertness and Reference | 6 |
The Virtues of SecondOrder Theft | 11 |
Intuitions about Reference and Axiom Systems | 18 |
Comparing Mathematical Terms and Empirical Terms I | 31 |
Comparing Mathematical Terms and Empirical Terms II 48 | 48 |
The Epistemic Role Puzzle | 55 |
Benacerrafs Puzzle | 58 |
Application and Truth | 88 |
Systems Application and Truth | 94 |
Quines Objections to Truth by Convention | 105 |
Grades of Ontological Commitment | 118 |
Multiply Interpreting Systems | 132 |
Intuitions about Reference Revisited | 139 |
Introduction | 153 |
Some Observations on Metamathematics | 171 |
Other editions - View all
Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of ... Jody Azzouni No preview available - 2008 |
Common terms and phrases
algorithms applied axioms Benacerraf branches of mathematics Cambridge claim classical co-empirical conceptual scheme consider context Definition derivation discussion ematical empirical sciences epistemic epistemological errors example explain fact first-order logic first-order predicate calculus formal functions Hilary Putnam ical inference rules infinite intuitionistic intuitions involved justified kind terms L₁ language linguistic logical truths Maddy math mathematical objects mathematical posits mathematical practice mathematical terms mathematical truths mathematicians mathematics and logic matical metalanguage mishaps model theory nonstandard notation notion numbers particular philosophers philosophy of mathematics possible postulate basis predicate calculus primary A-mishaps principles priori truth problem proof Putnam puzzle quantifiers Quine Quine's Quinean refer second-order logic Section seems semantics sense sentential calculus sentential variable set of sentences set theory simply singular terms sort statement syntactically Tarski terminology theorem thin posits things tion true truth conditions truth predicate truth values University Press vocabulary