Existence and Knowledge

Existence and Knowledge

The Metaphysical Foundation of Brouwer's Intuitionism

Document Type : Research Article

Author
Gholam Hossein Moghaddam Heydari
Faculty member of the Humanities Research Institute
Abstract
Among the most pressing questions that the philosopher and the student of the foundations of mathematics confront are "what are the objects of mathematics" and "what is our knowledge of mathematics based on". The history of mathematics has shown us a number of answers to these questions. Intutionism as the foundation of mathematics was sketched by the Dutch mathematician-philosopher Luitzen Egbergtus Jan Brouwer (1881-1966). Brouwer's thoughts are complex compositions of mathematical and philosophical ideas. Others, like Poincare, Borel and Kronecker become “fore-runners of Intuitionism”. Analysing Brouwer's philosophical views one meets striking resemblances with Fichte's extreme solipsistic interepretation of Kant's subjectivism, to Schopenhauer's pessimism and Bergson's intuitionism. But these mathematicians and philosophers belonged to the era of Romanticism which reached its apogee between the last decades of the eighteenth century and about 1830 or 1840. It mainly represented a revolt against the rational culture of Enlightenment. I investigate the origin of Brouwer's intuitionism, that it was deeply rooted in the cultural and social milieu of Romanticism.
Keywords
Enlightenment
Romanticism
Intuitionistic Mathematics
Constructive Mathematics
Two-ity
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