Set theory arithmetic and foundations of mathematics : theorems philosophies This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaums theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics such as interpretability; the transcript of Gödels previously unpublished 1972 1975 conversations with Sue Toledo along with an appreciation of the same by Curtis Franks; Hugh Woodins paper arguing against the generic multiverse view; Anne Troelstras history of intuitionism through 1991; and Aki Kanamoris history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics Provided by publisher The papers collected here engage each of these questions through the veil of particular technical results. For example the new proof of the irrationality of the square root of two given by Stanley Tennenbaum in the 1960s and included here brings into relief questions about the role simplicity plays in our grasp of mathematical proofs. In 1900 Hilbert asked a question which was not given at the Paris conference but which has been recently found in his notes for the list: find a criterion of simplicity in mathematics. The Tennenbaum proof is a particularly striking example of the phenomenon Hilbert contemplated in his 24th Problem Provided by publisher