|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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Structure/Mathematics/Bigelow/Pargetter: it has sometimes been discovered that structures originating from very different areas are sometimes identical:
This means that two relations can be coextensive. What only matters is then what they have in common.
Definition Set/Bigelow/Pargetter: are what coextensive universals have in common: their extension. This puts them relatively high in the hierarchy. That is why they appeared so late in mathematics.
Random sets/Bigelow/Pargetter: have nothing in common with anything else except their elements. That is why they are nothing that coextensive universals have in common.
Hierarchy/Sets/Bigelow/Pargetter: it is controversial, where you should place sets in the hierarchy of universals._____________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.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990