La matematica è ancora vera?
This article takes into consideration the profound change that has taken place in the very conception of mathematics, particularly regarding the meaning and the truth value of mathematical propositions. By means of a brief survey of the highlights of the history of mathematical thought, the natural...
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| Format: | Electronic Article |
| Language: | Italian |
| Check availability: | HBZ Gateway |
| Fernleihe: | Fernleihe für die Fachinformationsdienste |
| Published: |
Ed. Pontificia Univ. Gregoriana
1973
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| In: |
Gregorianum
Year: 1973, Volume: 54, Issue: 1, Pages: 61-89 |
| Online Access: |
Volltext (lizenzpflichtig) |
| Summary: | This article takes into consideration the profound change that has taken place in the very conception of mathematics, particularly regarding the meaning and the truth value of mathematical propositions. By means of a brief survey of the highlights of the history of mathematical thought, the natural evolution of mathematics is seen to be toward a greater generalization and abstraction which has led to a breakdown of the overly rigid framework of the « mathematical science of quantity » left to us by Greek thought in favor of a « mathematical science of the structures of sets ». The author brings out the advantages at the level of syntax of a pure mathematics organized in a more unified and coherent vision of mathematical theories which can lead to a natural classification of these theories, a classification in which the concepts of meaning and truth do not seem to be excluded but rather conceived in a more general way. Nor is intuition completely excluded; it keeps its irreplaceable heuristic and expressive role. This liberalization of the concept of mathematics has a special significance at the semantic level of the physical interpretation of the abstract structures of pure mathematics in which the role of experience can be seen clearly, as well as the a posteriori character of natural science by which it is distinguished from mathematics. In conclusion, the change in mathematical thought seems particularly rich in material for philosophical reflection. It even seems to demand such reflection, because a philosophy of mathematics tends to lead into a metaphysics, not in the sense that metaphysics as queen should dictate laws to mathematics, but in the sense that metaphysics — respecting the complete autonomie of mathematics — should help it to find it's place in a more universal vision which can give it a more human aspect. This task, however, would seem to demand a transcendence of the rupture between humanist philosophy and philosophy of science. |
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| Contains: | Enthalten in: Gregorianum
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