Points of Intersection Between Mathematical and Process Philosophical Ideas

Contents

Contents
Preface
Acknowledgements 
Introduction
Chapter 1. Bolzano as a precursor in the study of the continuum 
1. Introduction 
2. Bolzano and Aristotle 
3. Some achievements of contemporary mathematics
4. Bolzano's contribution to contemporary mathematics
5. Conclusion 
Chapter 2. Brentano’s intuition of the continuum 
1. Introduction
2. Main aspects of Brentano’s philosophy 
3. Brentano’s conception of the continuum
3.1. Phenomenological description of the continuum
and directions of research
3.2. Essence and characteristics of Brentano’s continuum
4. Brentano’s conception and the philosophical continuums
Chapter 3. Poincaré’s sense perceived continuum
1. Introduction

2. Poincaré’s philosophical views
2.1. General philosophical views
2.2. Connections with Husserl’s phenomenology
3. Poincaré’s two types of continuum
4. The relationship of Poincaré
with the philosophies of Russell and Whitehead 
Chapter 4. Russell’s criticism of Bergson’s views
about continuity and discreteness 
1. Introduction
2. The essence of Russell’s criticism of Bergson
3. Russell’s criticism of Bergson’s views
on continuity and discreteness 
3.1. Russell’s The Philosophy of Bergson (1912)
3.2. Russell’s Principles of Mathematics (1903)
3.3. Russell’s Our Knowledge of the External World (1914) 
4. Conclusion: Russell’s misunderstanding of Bergson
Chapter 5. The transition of Russell
from atomism to holism 
1. Introduction
2. The period after 1919: The Analysis of Matter (1927) 
3. A comparison of Russell’s views after 1919
with Whitehead’s
4. Conclusion
Chapter 6. Contemporary neopragmatism
and process philosophy
1. Introduction
2. The neopragmatist synergy between Peirce
and process philosophy

3. The neopragmatic reconstruction
of Whitehead’s continuum
4. Conclusion
Chapter 7. Capek, the Bergsonian process philosopher.
1. Introduction 
2. The early Capek
3. The mature views of Capek
4. The late Capek 
5. Conclusion
Chapter 8. Brouwer and Weyl on the continuum
1. Introduction
2. The intuitionistic continuum of Luitzen Brouwer
3. Hermann Weyl’s Das Kontinuum (1918)
4. Logical and mathematical aspects of Weyl’s views
5. Philosophical ideas that have influenced Weyl’s views
Chapter 9. Applications of process philosophy
to mathematics
1. Introduction
2. Whitehead’s theory of extension in the context
of the 20th century mathematics
2.1. Prolegomena 
2.2. Whitehead’s attitude towards Euclidean geometry
2.3. Whitehead’s theory of extension from the point of view of the
Erlangen’s program
2.4. "Nicolas Bourbaki" as representatives of post-modern science

3. Recent mereotopological developments
of Whitehead’s theory of extension
3.1. Prolegomena
3.2. What is mereotopology?
3.3. The problem
3.4. The reasons 
3.5. A way for overcoming the problem 
3.6. A mereotopological model of Whitehead’s theory of time:
Dynamic contact algebras
4. Conclusion
Chapter 10. The role of mathematics for teaching
and understanding the humanities 
1. Introduction
2. The achievement of knowledge
in the process of education
3. Whitehead on the educational revolution
in modern times
4. The increasing of the role of mathematics in education
5. Characteristics of mathematics
that are relevant for education
6. Principles for the mathematical education of scholars 
7. Conclusion
General conclusion
Bibliography
Name index