This book presents Gödel's incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics. Results are stated in the form most relevant for use in the philosophy of mathematics. An appendix considers their implications for Hilbert's Program for the foundations of mathematics. The text is self-contained, all notions being explained in full detail, but of course previous exposure to the very first rudiments of mathematical logic will help.

Presents Gödel's incompleteness theorems in a form most relevant to the philosophy of mathematics Entirely self-contained Discusses implications for Hilbert's Program

Autorentext

Carlo Cellucci is Emeritus Professor of Philosophy at Sapienza University of Rome, Italy. His recent publications include the book Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method, Springer 2013, and the papers "Top-Down and Bottom-Up Philosophy of Mathematics", "Philosophy of Mathematics: Making a Fresh Start", "Why Should the Logic of Discovery be Revived", "Does Logic Slowly Pass Away, or Has It a Future?", "Rethinking Knowledge", "Is There a Scientific Method? The Analytic Model of Science", "Theory Building as Problem Solving".

Inhalt

First-Order Logic.- Completeness.- First-Order Theories.- Primitive Recursive Arithmetic.- Encoding.- Incompleteness.- Other Limitative Results.- Second-Order Logic.- Second-Order Arithmetic.- Appendix.