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G. Sambin, Some points in formal topology, 2003

The third part contains my recent views on the meaning of constructivism in mathematics, topology in particular. The contents of this third part are:

3.1 The seven principles of dynamic constructivism:
1. genuine answers [not by authority or revelation]
2. constructivsim as awareness and modularity
3. forget safely [that is, do not forget what cannot be restored]
4. new foundations must give new mathematics
5. compatibility [with other foundations: the minimalist attitude]
6. importance of definitions
7. harmony, ecology and aesthetics

3.2 More concrete points:
1. mathematics and computers
2. do points exist?
3. deep connection between logic and topology
4. nothing wrong with axiomatic definitions
5. fun in doing constructive mathematics
6. Brouwer
7. Bishop

 

Philosophy, i.e. the concrete-abstract side of the world. Eucaliptus reflected on water