Relation (philosophy)
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.
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.
[27] A closely associated contrast is that properties belong to entities or inhere in them while relations are not found in the relata but stand between them.
[28] Both are often used to describe and explain repeating patterns in the world[12] and many of the ontological distinctions applied to properties also affect relations.
[33] Various types of relations are distinguished in the academic literature based on their ontological status, the domains they apply to, and the structures they form.
[39] Another definition is defended by philosophers like Armstrong, who hold that a relation is internal if it is necessitated by the properties or the intrinsic features of the relata.
[40] David K. Lewis provides a slightly different formulation by claiming that internal relations supervene on the intrinsic properties of their elements.
[44] According to a common view, internal relations do not form part of reality on the most fundamental level since they supervene on their relata.
[68] Both relationalists and substantivalists accept regular statements about spatiotemporal relations, for example, that "the two towers of the Golden Gate Bridge are 4,200 feet apart".
[69] In classical physics, space and time are understood as independent dimensions that are absolute and can be measured and analyzed separately from each other.
In modern physics, space and time are seen as interdependent dimensions that form a unified continuum whose curvature is affected by the presence of mass and energy.
Strong realists advance a more robust view and see relations as part of the fundamental ontological inventory of reality.
[96] A further argument against reductionism comes from modern physics and holds that the non-relational properties it discusses are not sufficient to explain all phenomena.
In its widest sense, it states that all of reality is relational at its most fundamental level and denies the existence of non-relational properties.
[107] According to philosopher Randal Dipert, the world is made up of relations that form the structure of a mathematical graph and the concrete entities in it are subgraphs.
[110] In the philosophy of space and time, relationalism is the view that spacetime is not a substance, as substantivalists claim, but a network of spatiotemporal relations between individual physical phenomena.
[112] In the philosophy of sociology, relationalism is an approach that investigates wide social phenomena by studying the relations between interactants.
Examples are seeing society as the totality of interactions between people or understanding the world of art in terms of the relations between artists, producers, audiences, and critics.
[120] This approach was exemplified by Peter Abelard and William Ockham, who explained relations in terms of non-relational qualities possessed by the relata.
[121] Some scholastic philosophers, like Peter Auriol, rejected relations and held instead that they are merely mental associations of entities not found outside the mind.
[122] A different approach was followed by Albert the Great and John Duns Scotus, who understood relations as a distinct and irreducible type of entity.
[121] Thomas Aquinas defended a middle position by holding that some relations have a substantial foundation in reality, like being a father, while others merely exist on the verbal level, like being moved by.
This implies that relations lack a proper ontological status and only exist in the mind as a form of mental comparison.
[125] Gottfried Wilhelm Leibniz rejected the fundamental reality of relations based on the claim that they would lack a proper location in this case.
These ontological difficulties prompted Leibniz to propose his monadology, according to which reality is made up of windowless and unconnected monads.
For example, Aristotelian logic restricts itself to propositions in a subject-predicate form in which the predicate expresses qualities or attributes of a single entity in the subject position.
[132] An important early development in this regard was the formulation of the logic of relations by Augustus De Morgan in the 19th century.
[136] Various early analytic philosophers, like Moore and Bertrand Russell, rejected Bradley's monist idealism and the associated theory of relations.
[137] Moore based his rejection of Bradley's doctrine on the claim that it is not in tune with common sense, which favors a pluralistic ontology with genuine relations.
[140] A further approach is found in Ludwig Wittgenstein's early philosophy, where he stated that objects can form connections with each other without requiring any additional elements.
