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.
G. E. Moore introduced the distinction between internal and external relations.
F. H. Bradley formulated a regress argument to defend the claim that relations do not exist.
The nature of relations was reconceptualized following various academic developments in the 19th century, such as the formulation of the logic of relations by Augustus De Morgan.
Gottfried Wilhelm Leibniz held that relations do not have fundamental reality and described the world instead as a collection of unconnected monads.
In logic and philosophy, a property is a characteristic of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiated, and often in more than one object. It differs from the logical/mathematical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities can in some sense have some of the same properties is the basis of the problem of universals.
Property dualism: the exemplification of two kinds of property by one kind of substance