In Mathematical Thought and Its Objects, Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a nature than that confers on them."

William Parsons (1800 67), third Earl of Rosse, was responsible for building in 1845 the largest telescope of his time, nicknamed the 'Leviathan'. It enabled the Earl to make unprecedented astronomical discoveries, including the discovery of the spiral nature of galaxies. Rosse (then Lord Oxmantown) began publishing scientific papers on telescopes in 1828, and for the rest of his life made regular contributions to scientific journals in Ireland, England and Scotland. He served as President of the British Association for the Advancement of Science in 1843, and of the Royal Society from 1848 to...

Hao Wang (1921-1995) was a prolific researcher and writer in mathematical logic, computer science, and philosophy. He is known for the close relation he developed with Kurt Godel during the last decade of the latter's life and the two books about Godel that he published after Godel's death. This volume of essays covers to some extent each of these fields of Wang's activity but with greatest emphasis on philosophy. Wang spent the first twenty-five years of his life in China and continued to identify himself as Chinese, and in later years he returned to China several times. The volume adds to...

Kurt Godel (1906 1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Godel s centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Godel s writings are among the topics covered. Several chapters discuss his intellectual development...