Relations (philosophy)

Symbolism in logic to express relations — In logic, relations are commonly represented by uppercase letters while lowercase letters are used for the relata.

Relations are ways in which several entities stand to each other. They usually connect distinct entities but some associate an entity with itself. The adicity of a relation is the number of entities it connects. The direction of a relation is the order in which the elements are related to each other. The converse of a relation carries the same information and has the opposite direction, like the contrast between "two is less than five" and "five is greater than two". Both relations and properties express features in reality with a key difference being that relations apply to several entities while properties belong to a single entity.

Many types of relations are discussed in the academic literature. Internal relations, like resemblance, depend only on the monadic properties of the relata. They contrast with external relations, like spatial relations, which express characteristics that go beyond what their relata are like. Formal relations, like identity, involve abstract and topic-neutral ideas while material relations, like loving, have concrete and substantial contents. Logical relations are relations between propositions while causal relations connect concrete events. Symmetric, transitive, and reflexive relations are distinguished by their structural features.

Metaphysical difficulties like the question of where relations are located lie at the center of discussions of their ontological status. Eliminativism is the thesis that relations are mental abstractions that are not a part of external reality. A less radical position is reductionism, which claims that relations can be explained in terms of other entities, like monadic properties, and are not a substantial addition to reality. According to realists, relations have mind-independent existence. A strong form of realism is relationalism, which states that all of reality is relational at its most basic level. Historically, eliminativism and reductionism were the dominant views. This only changed toward the end of the 19th century, when various developments in the fields of mathematics, logic, and science prompted a more realist outlook.