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This work explores the intricate relationships between mathematics and various dimensions of knowledge. It begins with structural dimensions, discussing the protean nature of mathematics and its categories of space and quantity. The text examines structural analogies between mathematical and empirical theories, delving into the distinctions between reduction and explanation in science versus mathematics. It reflects on reality, truth, and confirmation in mathematics, emphasizing tacit knowledge and structure-similarity as foundational concepts. The applicability of mathematics is analyzed through the indispensability argument, the necessity of mathematical structures in physical science, and the status of set-theoretic axioms in empirical theories. The role of mathematics in philosophy is also considered. Historical dimensions are addressed, questioning whether revolutions occur in mathematics and investigating the history of the prime number theorem and error theory. A structuralist perspective on Lagrange’s algebraic analysis and the evolution of constructivism in mathematical theory is presented. The discourse extends to Turing's concept of computability and the relationship between computers and mathematics. Finally, the work explores global dimensions of knowledge, focusing on theories, information flow, structuralism in scientific discovery, and intertheoretical relations, culminating in a comprehensive index of names
Acquisto del libro
The space of mathematics, Javier Echeverría
- Lingua
- Pubblicato
- 1992
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- (Copertina rigida)
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