[FOM] book announcement: Brouwer meets Husserl
mark van atten
Mark.vanAtten at univ-paris1.fr
Tue Nov 14 14:35:56 EST 2006
A revised and somewhat expanded version of my dissertation has just
been published. Details below.
Brouwer meets Husserl. On the Phenomenology of Choice Sequences.
Mark van Atten (CNRS, Paris)
Synthese Library, Volume 335. Berlin: Springer.
November 2006. Hardcover, xiii+206 pp.
List price EUR 99.95
Can the straight line be analysed mathematically such that it does not
fall apart into a set of discrete points, as is usually done but through
which its fundamental continuity is lost? And are there objects of pure
mathematics that can change through time?
The mathematician and philosopher L.E.J. Brouwer argued that the two
questions are closely related and that the answer to both is "yes''. To
this end he introduced a new kind of object into mathematics, the choice
sequence. But other mathematicians and philosophers have been voicing
objections to choice sequences from the start.
This book aims to provide a sound philosophical basis for Brouwer's
choice sequences by subjecting them to a phenomenological critique in
the style of the later Husserl.
"It is almost as if one could hear the two rebels arguing their case in
a European café or on a terrace, and coming to a common understanding,
with both men taking their hat off to the other, in admiration and
gratitude. Dr. van Atten has convincingly applied Husserl's method to
Brouwer's program, and has equally convincingly applied Brouwer's
intuition to Husserl's program. Both programs have come out the better."
Piet Hut, professor of Interdisciplinary Studies, Institute for Advanced
Study, Princeton, U.S.A.
Preface. Acknowledgements.- 1 An Informal Introduction.-
2 Introduction.- 3 The Argument.- 4 The Original Positions.- 5 The
Phenomenological Incorrectness of the Original Arguments.- 6 The
Constitution of Choice Sequences.- 7 Application: an Argument for Weak
Continuity.- 8 Concluding Remarks.- Appendix: Intuitionistic Remarks on
Husserl's Analysis of Finite Number in the Philosophy of Arithmetic.
Notes. References. Name and citation index.- Subject index.
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