Philosophy Lexicon of Arguments

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Relations, philosophy: relations are that what can be discovered or produced in objects or states when compared to other objects or other states with regard to a selected property. For example, dimensional differences between objects A and B, which are placed into a linguistic order with the expression "larger" or "smaller" as a link, are determinations of relations which exist between the objects. Identity or equality is not accepted as a relation by most authors. See also space, time, order, categories, reflexivity, symmetry, transitivity.
 
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I 328
Relations/topology/Simons: Let R be a binary relation and a is a class of objects - Definition left closed under R: is a, if no R-relationship runs from the outside to the inside - E.g. If nobody third owes Jack and Jill money, the pair is left closed under debt - while everyone can owe something the other or any third party (external). - conversely to that: Definiton right closed under R: if no R-relationship runs from the inside to the outside - E.g. neither Jack nor Jill owes a third something, regardless of whether they are creditors of a third party or among themselves.

Si I
P. Simons
Parts Oxford New York 1987


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Ed. Martin Schulz, access date 2017-05-27