The Theory of Gödel

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.

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

Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of eight books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall’Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017); The Making of Mathematics: Heuristic Philosophy of Mathematics (Springer, 2022).