|Structures, philosophy: structures are properties of an object, a set, or a domain of objects which determine the constitution and possible formability of this object, this set, or this domain. The properties defining the structure may be derived from the objects, e.g. magnetic forces or electric charge or can be imprinted on the objects such as e.g. the mathematical operations of multiplication or addition. See also order, system, relations._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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|Thiel I 270
Bourbaki speaks of a reordering of the total area of mathematics according to "mother structures". In modern mathematics, abstractions, especially structures, are understood as equivalence classes and thus as sets.
Thiel I 307
Bourbaki opposes the "modern" structures to the classical "disciplines". The theory of the primes is closely related to the theory of algebraic curves. Euclidean geometry borders the theory of integral equations. The principle of organization will be one of the hierarchies of structures that goes from simple to complex and from general to particular._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Philosophie und Mathematik Darmstadt 1995