Brouwer meets Husserl. On the phenomenology of choice sequences
type: Item
instance of: scholarly article
title: Brouwer meets Husserl. On the phenomenology of choice sequences
zbMATH Open document ID: 1119.03001
author: Mark van Atten
published in: Synthese Library
publication date: 2006-11-08T00:00:00Z
review text: Philosophers in the English-speaking tradition have shown great interest in an intuitionism cleansed of Brouwer's philosophy, as the latter is seen as, to put it mildly, out of place. In their view, Brouwer stumbled upon a remarkable discovery, for which he provided the wrong underlying philosophy -- an outgrowth of personal idiosyncrasies -- which can be safely ignored. This view calls for an entirely different justification for intuitionism, which is what philosophers in that tradition (first and foremost Dummett) have done. For `continental' philosophers the problem has been not that of discarding Brouwer from intuitionism, but that of placing Brouwer's intuitionism into the mainstream of `continental' philosophy by finding points of contact with established philosophies or ways to justify intuitionistic practice from tenets closely resembling Brouwer's but put forward by a different philosopher in a different context. As its title suggests, van Atten's book belongs to this category, which includes the reviewer's [``Mathematik, Intuition und die Existenzweise des Seins'', in: Wissenschaft vom Menschen: Jahrbuch der Internationalen Erich-Fromm-Gesellschaft, Münster, Vol. 3, 87--119 (1992; Zbl 0763.00003)], \textit{M. Detlefsen} [``Constructive existence claims'', in: M. Schirn (ed.), The philosophy of mathematics today. Oxford: Clarendon Press, 307--335 (1998; Zbl 0922.03006)], \textit{J. Largeault} [Intuition et intuitionisme. Paris: Librairie Philosophique J. Vrin (1993; Zbl 0866.03002)], \textit{T. Koetsier} [``Arthur Schopenhauer and L. E. J. Brouwer: a comparison'', in: T. Koetsier et al. (eds.), Mathematics and the divine. Amsterdam: Elsevier/North-Holland, 569--593 (2005; Zbl 1078.01016)], and \textit{Z. Fraser} [``The law of the subject: Alain Badiou, Luitzen Brouwer and the Kripkean analysis of forcing and Heyting calculus'', Cosm. Hist. 2, 94--133 (2006; Zbl 1117.03010)]. Its purpose is to show that Brouwer's argument for choice sequences, which are not …
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 5071201
zbMATH Keywords: choice sequences
zbMATH Keywords: intuitionism
zbMATH Keywords: Husserl
zbMATH Keywords: Brouwer
zbMATH Keywords: phenomenology
reviewed by: Victor V. Pambuccian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5071201