Socially pushing mathematics into the objective. A lecture on Husserl’s Origin of Geometry

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Samenvatting

Edmund Husserl analyzed in his The Origin of Geometry (1936) extensively the construction of objectivity of ideal objects, e.g. geometry or mathematics in general (Husserl, 1970).
Based on this work we will argue that the later Husserl can be seen as a precursor of constructivism. In François (2011) I extensively elaborated on the way how Husserl explains the possibility of ideal objectivity, the objectivity of mathematics, and of objectivity of real objects, starting from the really intra subjective process of consciousness. Husserl never struggled with a solipsism nor with the radical constructivism key problem of inter-subjectivism (Martinez-Delgado 2002). Based on his idealistic transcendentalism and faithful to his basic principles of phenomenology Husserl, or let me call it, the late Husserl analyses the construction of knowledge and more the construction of objective knowledge, e.g. mathematics.
There are many similarities between von Glasersfeld’s - the founding father of radical constructivism - concept of radical constructivism and Husserl’s phenomenological ideas on the construction of (objective) knowledge. In his famous book Radical constructivism: A way of knowing and learning von Glasersfeld (1995) introduces his concept of radical constructivism in a simple and clear way. “What is radical constructivism? It is an unconventional approach to the problem of knowledge and knowing. It starts from the assumption that knowledge, no matter how it is defined, is in the heads of persons, and that the thinking subject has no alternative but to construct what he or she knows on the basis of his or her own experience. What we make of experience constitutes the only world we consciously live in. It can be sorted into many kinds, such as things, self, others, and so on. But all kinds of experience are essentially subjective, and though I may find reasons to believe that my experience may not be unlike yours, I have no way of knowing that it is the same. The experience and interpretation of language are no exception.” (von Glasersfeld 1995: 1)
In this paper we will go into the main critiques on the concept of radical constructivism of von Glasersfeld. Therefore we first will introduce the way Husserl was dealing with the construction of mathematical knowledge and how he was dealing with the ontological question.

References
Francois K. (2011) On the notion of a phenomenological constitution of objectivity. In: Tymieniecka A-T. (ed.) Analecta Husserliana, issue Transcendentalism overturned. Springer, Dordrecht: 121 - 137.
Glasersfeld E. von (1995) Radical constructivism: A way of knowing and learning. Falmer Press, London.
Husserl E. (1970) The origin of geometry. Appendix VI of the crisis of European sciences and transcendental phenomenology. An introduction to phenomenological philosophy. English translation by David Carr. Northwestern University Press, Evanston, IL: 353-378.
Martinez-Delgado A. (2002) Radical constructivism: Between realism and solipsism. Science Education 86(6): 840-855.
Originele taal-2English
TitelConference Cultures of Mathematics IV
Plaats van productieNew Delhi
StatusPublished - mrt 2015
EvenementConference Cultures of Mathematics IV - Indian National Science Academy (INSA), New Delhi, India
Duur: 22 mrt 201525 mrt 2015

Conference

ConferenceConference Cultures of Mathematics IV
Land/RegioIndia
StadNew Delhi
Periode22/03/1525/03/15

Bibliografische nota

abstracts available at conference website see url


Cultures of Mathematics IV
22-25 March 2015
New Delhi, India
http://www.math.uni-hamburg.de/spag/ml/Delhi2015/

Keynote speakers.

Tom Archibald (Simon Fraser University, Vancouver BC, Canada) Jessica Carter (University of Southern Denmark, Odense, Denmark) José Ferreiros(Universidad de Sevilla, Seville, Spain) Karen François (Vrije Universiteit Brussel, Brussels, Belgium) Albrecht Heeffer (Universiteit Gent, Gent, Belgium) Matthew Inglis (Loughborough University, Loughborough, England) Brendan Larvor (University of Hertfordshire, Hatfield, England) Madeline Muntersbjorn (University of Toledo, Toledo OH, U.S.A.) Alison Pease (Imperial College, London, England) Emil Simeonov (Fachhochschule Technikum Wien, Vienna, Austria) Keith Weber (Rutgers University, Piscataway NJ, U.S.A.)

A research community that could be described with the phrase "Practice and Cultures of Mathematics" has studied mathematics as a human subject with different practices and cultures in recent years. This research has been closely linked to the Philosophy of Mathematical Practice community and its Association for the Philosophy of Mathematical Practice, but is broader in the sense that it is interested in the study of mathematical practices and cultures independently of whether there is an interaction with traditional philosophical questions (such as epistemology or ontology).

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