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From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Goedel.Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell's type theory, Zermelo's set theory and Goedel's incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.

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9781443834599

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Joan Rosello received his PhD from the University of Barcelona in 2003 with a thesis on logic and the foundations of mathematics. He has written several articles and reviews, mainly on the history and philosophy of logic and mathematics, in collections such as Donde no habita el olvido (Montesinos, 2005), international journals such as Theoria (2009), and congresses such as the VI Congress of the Society of Logic, Methodology and Philosophy of Science in Spain (2009) and the Second Catalan Congress of Philosophy (2011). He has also participated as an independent scholar in different international meetings such as the European Summer School in Logic, Language and Information (Copenhagen, 2010) and the more recent summer school and conference on Set Theory and Higher-Order Logic, Foundational Issues and Mathematical Developments (London, 2011). In 2010, he was awarded the Joaquim Carreras i Artau prize by the Institut d'Estudis Catalans, the prestigious Catalan Academy of Sciences and Humanities, for his essay Els teoremes de Goedel i la incompletabilitat de les matematiques ( Goedel's theorems and the Incompletability of Mathematics ).

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