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Brouwer Meets Husserl

Part of the Synthese Library Book Series (volume 335)

DOI: 10.1007/978-1-4020-5087-9

ISBN: 978-1-4020-5086-2

Publisher: Springer Netherlands - Springer Journals

Jan 1, 2007

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Chapter 1An Informal Introduction

van Atten, Mark

Pages: 1 –4

[The aim is to use phenomenology to justify Brouwer’s choice sequences as mathematical objects]
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Chapter 2Introduction

van Atten, Mark

Pages: 5 –8

[The aim is to use phenomenology to justify Brouwer’s choice sequences as mathematical objects.]
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Chapter 3The Argument

van Atten, Mark

Pages: 9 –10
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Chapter 4The Original Positions

van Atten, Mark

Pages: 11 –52

[The purpose of this chapter is to bring out a conflict between Brouwer’s and Husserl’s philosophies of mathematics. I will begin by locating a particular point of disagreement, and pin down what it consists in. Disagreement by itself does not warrant speaking of a conflict. A further condition...
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Chapter 5The Phenomenological Incorrectness of the Original Arguments

van Atten, Mark

Pages: 53 –83

[The purpose of this section is threefold. First, to provide a standard to evaluate Husserl’s and Brouwer’s original positions by. Secondly, to let this standard be the methodological clue to the reconstruction of choice sequences in chapter 6. Thirdly, to justify the revisionism implied in that...
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Chapter 6The Constitution of Choice Sequences

van Atten, Mark

Pages: 85 –101

[In section 5.1, it was argued that with regard to pure mathematics, phenomenology is capable of ontological judgements. Generally, complete justification for asserting the existence of a supposed object consists in giving a strict constitution analysis; what is specific to the case of pure...
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Chapter 7Application: An Argument for Weak Continuity

van Atten, Mark

Pages: 103 –110

[In chapter 5, I explained Husserl’s principle that transcendental phenomenology provides the ontology for the a priori sciences. What the basic objects, and the axioms governing them, in an a priori science are, is to be disclosed in phenomenological analysis. Now I want to show this idea in...
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Chapter 8Concluding Remarks

van Atten, Mark

Pages: 111 –111

[One correct, phenomenological argument on the issue whether mathematical objects can be dynamic is not Husserl’s (negative) argument, but a reconstruction of Brouwer’s (positive) one. This I have argued by an attempt to justify, phenomenologically, the existence of one particular kind of dynamic...

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