The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.
Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.
Over 500 entries include key terms found in the study of:
* Logic: Argument, Turing Machine, Variable
* Set and model theory: Isomorphism, Function
* Computability theory: Algorithm, Turing Machine
* Plus a table of logical symbols.
Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.Over 500 entries include key terms found in the study of: Logic: Argument, Turing Machine, Variable Set and model theory: Isomorphism, Function Computability theory: Algorithm, Turing Machine Plus a table of logical symbols.Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

This volume of essays tackles the main problem that arises when considering an epistemology for mathematics, the nature and sources of mathematical justification. Focusing both on particular and general issues, the essays from leading philosophers of mathematics raise important issues for our current understanding of mathematics. Is mathematical justification "a priori" or "a posteriori"? What role, if any, does logic play in mathematical reasoning or inference? And how epistemologically important is the formalizability of proof? The companion volume "Proof, Knowledge and Formalization" is also available from Routledge. Contributors include Michael Detlefsen, Michael D. Resnik, Stewart Shapiro, Mark Steiner, Pirmin Stekeler-Weithofer, Shelley Stillwell, William J. Tait and Steven J. Wagner. This book should be of interest to advanced students and lecturers of philosophy of logic and maths.

These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,