Positive Topology
A New Practice in Constructive Mathematics
Seiten
2025
Oxford University Press (Verlag)
978-0-19-923288-8 (ISBN)
Oxford University Press (Verlag)
978-0-19-923288-8 (ISBN)
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This book contains the first systematic exposition of a new discipline called positive topology, which brings many conceptual and mathematical innovations and many benefits for mathematical practice and applications, for the first time extending Darwin's evolutionary vision to the practice of mathematics.
Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline.
In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself.
The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.
Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline.
In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself.
The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.
Giovanni Sambin has been doing research in logic and the foundations of mathematics since the 1970s. He is among the founders of provability logic and has been developing the field of topology since the 1990s, adopting a dynamic view in mathematical practice, leading to positive topology, a new, richer approach to constructive topology based on a dynamic vision of the nature of mathematics. He was the first president of the Italian Association of Logic and its Applications (AILA).
| Erscheint lt. Verlag | 6.3.2025 |
|---|---|
| Reihe/Serie | Oxford Logic Guides |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Geisteswissenschaften ► Sprach- / Literaturwissenschaft ► Sprachwissenschaft | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-19-923288-1 / 0199232881 |
| ISBN-13 | 978-0-19-923288-8 / 9780199232888 |
| Zustand | Neuware |
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