Full Description
The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.
Contents
1 Kronecker, the semi-intuitionists, Poincaré.- 1.1 Introduction.- 1.2 Kronecker.- 1.3 The French semi-intuitionists.- 1.4 Poincaré.- 1.5 Conclusion.- 2 The genesis of Brouwer's intuitionism.- 2.1 Introduction.- 2.2 The early years.- 2.3 The first act of intuitionism.- 2.4 Topology.- 2.5 Intuitionism and formalism.- 2.6 The second act of intuitionism.- 2.7 The Brouwer lectures.- 2.8 The Mathematische Annalen and afterwards.- 2.9 Brouwer's personality.- 2.10 Conclusion.- 3 Overview of the foundational debate.- 3.1 Introduction.- 3.2 Quantitative inquiry.- 3.3 Qualitative inquiry.- 3.4 Conclusion.- 4 Reactions: existence and constructivity.- 4.1 Introduction.- 4.2 The beginning of the debate.- 4.3 The debate widened.- 4.4 Later reactions.- 4.5 Conclusion.- 5 Reactions: logic and the excluded middle.- 5.1 Introduction.- 5.2 The beginning of the debate.- 5.3 The debate widened.- 5.4 Later reactions.- 5.5 Conclusion.- 6 The foundational crisis in its context.- 6.1 Introduction.- 6.2 Metaphors.- 6.3 Philosophy.- 6.4 Physics.- 6.5 Art.- 6.6 Politics.- 6.7 Moderne and Gegenmoderne.- 6.8 Conclusion.- Conclusion.- A Chronology of the debate.- B Public reactions to Brouwer's intuitionism.- C Logical notations.- Dankwoord/ Acknowledgements.
