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Tarski on completeness and categoricity of deductive systems
His main interests are in logic, history and philosophy of mathematics, and history and philosophy of logic.
He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (OUP 1996), From Brouwer to Hilbert. The debate on the foundations of mathematics in the 1920s (OUP 1988), and Visualization, Explanation and Reasoning Styles in Mathematics (Springer 2005). He has recently edited The Philosophy of Mathematical Practice (OUP, 2008).
Mancosu has been a Humboldt fellow (1993-1994), a fellow at the Wissenchaftskolleg zu Berlin (1997-1998), an NSF awardee (2000-2002) and a directeur de recherche associé au CNRS in Paris (2004-2005). He is a 2008 Guggenheim Fellow and next year he will be a fellow of the Institute for Advanced Studies at Princeton (spring term 2009).
He is currently working on on 20th-century explorations of the foundations of mathematics, mathematical explanation, and on Tarskian themes (truth, logical consequence, logical constants) in philosophy of logic.
(Ph.D., Stanford University). His interests lie in the philosophy of mathematics and its history, in philosophy of logic, and in mathematical logic. His written work is currently focused upon the philosophy of mathematical practice, including mathematical explanation, mathematical style, diagrammatic reasoning and visualization in mathematics. In this area, he has recently published “The Philosophy of Mathematical Practice”(OUP 2008). He has also recently completed a book on 20th-century explorations of the foundations of mathematics. The book is titled “The Adventure of Reason”. It will be published by Oxford University Press in October 2010.