relation
Philosophically relations are interesting because of the historic prejudice, given its most forceful expression by Leibniz, that they are somehow ‘unreal’ compared to the intrinsic, monadic properties of things. A way of putting the idea is that if all the monadic properties of the objects of a domain are fixed, then the relational properties are fixed as well (relations supervene on monadic properties). But in modern logic and science there is no justification for this claim.
The central notions in the logical treatment of relations are as follows. The domain of a relation is the set of things that bear the relation to something. The range is the set of things that have something bear the relation to them. The field of a relation is the set of things that belong either to its domain, or to its range. A binary relation relates one element from its domain to one of its range: R xy . Relations may be defined over greater numbers of things: for example, we can define R xyz to be the relation holding between three numbers when x + y = z, and so up to relations defined over n-tuples of any size. For formal and mathematical purposes a relation may be identified with the class of ordered pairs (or in general ordered n-tuples ) that satisfy it. So ‘father of’ becomes the set of all pairs x, y, such that x is the father of y, ‘is greater than’ becomes the set of all pairs x, y, such that x is greater than y, and so on. The main properties to be noticed in the theory of relations are indexed under their own headings: see antisymmetric, asymmetric, equivalence relation, irreflexive, ordering relation, reflexive, symmetric, transitive.

Philosophy dictionary. . 2011.

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  • RELATION — Le concept de relation apparaît comme l’un des concepts fondamentaux du discours rationnel. Il semble lié à la pratique de l’analyse, qui constitue elle même l’un des aspects essentiels de la démarche discursive. L’analyse décompose les unités… …   Encyclopédie Universelle

  • relation — Relation. s. f. Rapport d une chose à une autre. Cet article a relation au precedent. ce traité a relation avec celuy qui a esté fait auparavant. ce que vous dites n a aucune relation à la chose, avec la chose dont il s agit. Relation, en termes… …   Dictionnaire de l'Académie française

  • Relation — Re*la tion (r? l? sh?n), n. [F. relation, L. relatio. See {Relate}.] 1. The act of relating or telling; also, that which is related; recital; account; narration; narrative; as, the relation of historical events. [1913 Webster] ??????oet s… …   The Collaborative International Dictionary of English

  • relation — relation, relationship, relatives As nouns, relation and relative both mean ‘a person related by blood or by marriage’, and both are idiomatic in the plural. For some reason, however, relation is the normal choice in the explicit context of… …   Modern English usage

  • Relation — may refer to:*Relation, a person to whom one is related, i.e. a family member (see also Kinship) *Relation (mathematics), a generalization of arithmetic relations, such as = and …   Wikipedia

  • relation — I (connection) noun affiliation, affinity, alliance, analogy, applicability, appositeness, apposition, association, bearing, bond, closeness, cognation, comparableness, connation, connaturalness, connexion, correlation, correspondence, homology,… …   Law dictionary

  • relation — [ri lā′shən] n. [ME relacion < MFr or L: MFr relation < L relatio: see RELATE] 1. a narrating, recounting, or telling 2. what is narrated or told; account; recital 3. connection or manner of being connected or related, as in thought,… …   English World dictionary

  • relation — ► NOUN 1) the way in which two or more people or things are connected or related. 2) (relations) the way in which two or more people or groups feel about and behave towards each other. 3) a relative. 4) (relations) formal sexual intercourse. 5)… …   English terms dictionary

  • relation — late 14c., from Anglo Fr. relacioun, O.Fr. relacion (14c.), from L. relationem (nom. relatio) a bringing back, restoring, from relatus (see RELATE (Cf. relate)). Meaning person related by blood or marriage first attested c.1500. Stand alone… …   Etymology dictionary

  • Relation — (v. lat. Relatio), 1) (röm. Ant.), Vortrag, welchen der Consul od. Einer der höhern Magistrate im Senat hielt; 2) Verfahren, wo der Unterrichter dem Kaiser die Entscheidung in schwierigen Fällen überließ, bes. bei nöthiger Abweichung vom streugen …   Pierer's Universal-Lexikon

  • Relation — (lat., »Zurücktragung oder bringung«), Bericht, Berichterstattung (s. Referat), Reisebeschreibung etc.; im 16. und 17. Jahrh. üblich für »Zeitung« (vgl. Zeitungen). Dann soviel wie Beziehung, gegenseitiges Verhältnis, z. B. Wertrelation der… …   Meyers Großes Konversations-Lexikon

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