Phenomenology of choice sequences (Q2703586)

This extraordinary and important dissertation defended at the University of Utrecht aims at a philosophical, more precisely, phenomenological justification of L. E. J. Brouwer's choice sequences. In order to achieve this, the author attempts to overcome the putative incompatibility between Edmund Husserl's phenomenology and Brouwer's intuitionism. The point of deviation between the two directions in the foundations of mathematics is seen in differences concerning the possibility of dynamical mathematical objects. Whereas Husserl advocated a static view according to which all mathematical objects are omnitemporal, Brouwer claimed that no mathematical objects are omnitemporal. The author argues for a middle way: at least some mathematical objects are not omnitemporal: choice sequences. He achieves this by showing that neither Husserl's nor Brouwer's arguments concerning the dynamical or non-dynamical nature of mathematics are correct given phenomenological standards. Therefore there must be a third argument either for Husserl's or for Brouwer's conclusion. The author advocates a phenomenological reconstruction of Brouwer's argument, thereby justifying choice sequences as a special kind of dynamic objects. NEWLINENEWLINENEWLINEThe author provides deep and readable insights into the phenomenological and the intuitionistic approaches to the ontology of mathematical objects. His arguments in favor of a phenomenological epistemology against Brouwer's rather dark transcendentalism are mostly convincing, although one of the author's main points, the criticism of the irreflexivity of Brouwer's philosophy, i.e., its incapability of serving as a foundation for itself, seems to be defective in the light of common circularity arguments.