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

Placek, Tomasz

Hardcover

ISBN 10: 0792356306 ISBN 13: 9780792356301

Publisher: Springer, 1999

Synopsis

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.

About this title

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1999
• Language: English
• ISBN 10: 0792356306
• ISBN 13: 9780792356301
• Binding: Hardcover
• Number of pages: 232