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Mathematical Intuitionism and Intersubjectivity: A Critical Exposition of Arguments for Intuitionism: 279 (Synthese Library) - Tapa blanda

Libro 145 de 304: Synthese Library

Placek, Tomasz

 
9789048151875: Mathematical Intuitionism and Intersubjectivity: A Critical Exposition of Arguments for Intuitionism: 279 (Synthese Library)
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ISBN 10: 9048151872 ISBN 13: 9789048151875
Editorial: Springer, 2010

Sinopsis

In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.

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Reseña del editor

This book is the first modern examination of the philosophical foundations of intuitionism since Oscar Becker's (1927) Mathematische Existenz. Placek examines the three most widely-known arguments for mathematical intuitionism: Brouwer's, Heyting's and Dummett's. The examination centres on the questions of the intersubjectivity of mathematics and is concerned with understanding and evaluating the arguments. An unprejudiced stance leads to refreshing conclusions concerning Brouwer: the philosophical side of Brouwer's doctrine cannot be accused of such sins as psychologism, solipsism or the advocacy of private meaning. Similarly, examination of the Husserlian grounds of Heyting's explanation of the meaning of logical constants shows that this view of language should not be accused of violating the requirement of intersubjectivity of meaning. The approach of the work is philosophical, rather than mathematical or logico-technical.

Reseña del editor

In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo­ sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.

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Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
9048151872
ISBN 13 
9789048151875
Encuadernación
Tapa blanda
Número de páginas
236
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