Gnomes in the Fog The Reception of Brouwers Intuitionism in the 1920s [Hardcover]

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.

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.

1 Kronecker, the semi-intuitionists, Poincar?.- 1.1 Introduction.- 1.1.1 Mathematical prerequisites.- 1.2 Kronecker.- 1.2.1 Kroneckers conflicts.- 1.2.2 Kroneckers views.- 1.3 The French semi-intuitionists.- 1.3.1 The French semi-intuitionists main conflict.- 1.3.2 The French semi-intuitionists views.- 1.4 Poincar?.- 1.4.1 Poincar?s conflicts.- 1.4.2 Poincar?s views.- 1.5 Conclusion.- 2 The genesis of Brouwers intuitionism.- 2.1 Introduction.- 2.2 The early years.- 2.2.1 Brouwers youth.- 2.2.2 Brouwers profession of faith.- 2.2.3 Mannoury.- 2.2.4 Brouwers mysticism.- 2.3 The first act of intuitionism.- 2.3.1 Brouwers dissertation.- 2.3.2 The unreliability of the logical principles.- 2.4 Topology.- 2.5 Intuitionism and formalism.- 2.6 The second act of intuitionism.- 2.6.1 Intuitionistic set theory.- 2.6.2 Further development of intuitionistic mathematics.- 2.7 The Brouwer lectures.- 2.7.1 Berlin.- 2.7.2 Amsterdam.- 2.7.3 Vienna.- 2.8 The Mathematische Annalen and afterwards.- 2.9 Brouwers personality.- 2.10 Conclusion.- 3 Overview of the founlÓ!