Relation and Identity: A Survey of Substance and Process Accounts

¶I. The Problem

What is a relation? Is it a fundamental feature of reality, or a projection of our conceptual schemes? Does identity rest on intrinsic properties, or is it constituted by relational structure? How does something remain itself through change?

These questions are ancient. They arise wherever we try to say what reality is. Aristotle distinguished relatives — things that are what they are only in relation to something else. Russell fought against Bradley’s regress, which threatened to make relations incoherent. Leibniz grounded identity in indistinguishability across all properties and relations. Whitehead inverted the entire tradition: things are not primary; relations are. Nāgārjuna, writing seventeen centuries before Whitehead, argued that nothing has intrinsic nature — all entities arise through dependent origination, through relations to other entities.

This survey examines two contrasting metaphysical traditions: the substance tradition, which takes entities as primary and relations as dependent on them, and the process tradition, which inverts the priority and treats relations (and their continuous becoming) as constitutive of entities. These traditions address the core questions from different angles: What makes something one thing rather than many? What preserves identity through change? How do relations bind their terms together without infinite regress?

The tension between these traditions is not a historical curiosity. It reflects a real difficulty in metaphysics — the difficulty of saying what entities are and how they relate. This survey aims to clarify that tension and show how contemporary accounts (process philosophy, dependent origination, category theory, and relational ontologies) offer resources for moving past the classical impasse.

¶II. The Substance Tradition: Aristotle, Russell, and the Problem of Dependence

¶A. Aristotle’s relatives

Aristotle defines a relative (pros ti, “said of something in relation”) in Categories 7.6: “A relative is that which is said to be what it is of or than something else.” A relative is what it is IN VIRTUE OF being related. A parent is relative (parent of a child), a master is relative (master of a slave), a larger thing is relative (larger than something else). A relative differs from non-relative qualities: “pale” is not said of something else — a thing can be pale all by itself. But “parent” cannot be conceived except in relation. The parent IS what it is only by standing in the relation to the child.

This has two consequences. First: relations are real. They are among the genera (kinds of being) Aristotle distinguishes, not illusions or secondary projections of substance. Second: relations are dependent. A relation depends on its relata (the things related). The parent depends on the child: there is no parent without a child. Yet the dependence is not one-way — the child too is relative to the parent (as offspring). Each term depends on the relation to the other term.

For Aristotle, however, substance (primary being, ousia) is what truly exists. Relations are real, but they are secondary — ontologically dependent on substances. A substance like a human being persists even when its relations change. Socrates remains Socrates whether or not he is a father (Xanthippe might have remained barren). The substance has an identity independent of its accidental relations.

This raises a question the substance tradition never fully resolves: if relations are real but dependent on substances, and substances can change relations while remaining themselves, what grounds identity through relational change? Aristotle appeals to the form (eidos), the stable structural principle that persists. But how does form itself persist, especially through substantial change (death, transformation)? The question becomes harder in the modern period.

¶B. Russell’s defense of relations as primitive

Bertrand Russell (1903) faces the problem that Bradley raised: the regress of relations. Bradley (1893) argues that if a relation between A and B is itself a thing, then the binding of the relation to A and to B must itself be a relation, creating an infinite chain. To escape the regress, Bradley concludes that relations are not real — they are appearances, ways our mind organizes experience, not genuine features of reality.

Russell rejects Bradley’s conclusion. Relations are real, and primitive. They are not reducible to properties of their terms. Consider “A to the left of B.” This is not a property of A alone, nor of B alone, nor even of A and a property of B — it is a fact about A and B together. The relation is a fundamental building block. Russell writes (1903, § 99): “Relations are not adjectives, and therefore cannot be subsumed under the category of qualities.” A relation is a kind of thing, but it is not like the substances Aristotle discusses — it is not an individual, but rather a universal that holds between individuals.

Russell’s move is to posit relations as logical primitives. We do not have to justify relations by deriving them from something more fundamental. They are part of the ground floor of logic. This resolves the regress, because the binding of the relation to its terms is not a further relation that needs binding — it is constitutive. The relation just is the connection between the terms, without a second-order relation needed to mediate it.

But Russell’s solution creates a different problem: which relations are real, and which are not? Some relations seem to be purely in the mind — “A is entertaining to B” depends on B’s psychology, not on A’s nature. Russell distinguishes internal relations (relations that depend essentially on the nature of their terms, like “A is larger than B”) from external relations (where the terms could be otherwise related or unrelated). But this distinction itself is unclear. The tension in Russell — how to distinguish genuine relations from projections — will echo through the rest of the survey.

¶C. Leibniz and the identity of indiscernibles

Gottfried Leibniz approaches identity from a different angle. His principle of the identity of indiscernibles states: if two things share all their properties and relations, they are the same thing. Contrapositive: distinct things must differ in at least one property or relation.

This principle has profound consequences. It means identity is not primitive or irreducible — it is grounded in properties and relations. Two objects are the same object if and only if they share all properties and relations. If they differ in any respect, they are distinct.

Leibniz introduces a subtlety: the property of location (or more precisely, a haecceity — a “thisness” specific to an individual thing) can differ. Two atoms might be indistinguishable in every universal property, yet differ in their position in the universe. So Leibniz concludes there are no two indistinguishable things in a finite universe; the universe’s structure ensures diversity. But the principle establishes that identity and difference reduce to difference in properties or relations — there is no bare identity, no “self-identity” apart from some ground.

This entails a strong relationalism: an entity’s identity is exhausted by its properties and its relational nexus. Change a relation, and you change the entity. Remove an entity from all its relations, and you dissolve its identity. Identity is not something over and above the total constellation of properties and relations; it just is that constellation.

¶D. Kripke and rigid designation

Saul Kripke (1980) challenges the Leibnizian picture. In Naming and Necessity, Kripke argues that names are rigid designators — they refer to the same object across all possible worlds, even when the object’s properties differ. The name “Socrates” refers to Socrates even in a possible world where Socrates is not a philosopher (though this would contradict his actual essence). The identity of Socrates is not fully determined by his properties; it depends on the actual causal history of how he came to exist.

Kripke introduces essential properties (like origin — Socrates must have arisen from these particular parents) and contingent properties (like having a beard). This distinction matters for identity: Socrates could have lacked a beard; he could not have arisen from different parents. Identity is grounded partially in essential properties, which are often relational (the parents’ identities are relations), but it is not reducible to any conjunction of observable properties.

This challenges the Leibnizian picture: if identity rests on the actual causal history of an entity’s genesis, then properties and relations at a given moment are not sufficient to determine identity. The very same observable state might realize different identities in different causal histories. Identity depends on which properties are essential — which ones an entity could not lack and remain itself — and essence is determined by actual origin, not by what observable properties happen to coincide.

¶E. Geach on relative identity

Peter Geach (1967) cuts through the impasse: “Identity is not the same for all things.” We can say “A is the same F as B” — the same ship, the same person, the same artwork — without saying “A is the same G as B.” The Ship of Theseus, repaired plank by plank, remains the same ship, but not the same collection of original matter. A person remains the same person through cellular replacement, but not the same body.

Geach dissolves the classical problem of identity by making it relational: identity-in-respect-of-a-sortal (a category). There is no bare “is identical” in the world — only identity relative to a kind. You cannot meaningfully ask “is this the same thing?” without specifying the sortal. “The same what?” becomes the essential question.

Geach’s insight is profound: identity is not a pure logical predicate, fixed independently of context. It is always identity-under-a-description, relative to a sortal category. This means identity is not one relation, but many relations, each sortal-specific. The Ship of Theseus is the same ship (sortal: ship) but arguably not the same hunk of wood (sortal: material object). Identity becomes a family of relations indexed by kinds.

¶III. The Process Tradition: From Whitehead to Nāgārjuna

The substance tradition treats things (substances, objects) as primary and relations as dependent on them. The process tradition inverts this: relations and processes are primary; things are derivative or emergent.

¶A. Whitehead: actual occasions and internal relations

Alfred North Whitehead’s Process and Reality (1929) is the most systematic philosophical framework for prioritizing relations. For Whitehead, the fundamental unit of reality is not a substance or even a particle, but an actual occasion — a discrete “drop of experience” of becoming.

An actual occasion comes into being (concrescence) through integrating prehensions (grasps) of prior occasions. A prehension is an internal relation — a taking-into-account of another occasion. An occasion does not first exist and then relate to others; the occasion is constituted by its prehensions of other occasions. The relations ARE the occasion. Whitehead writes: “Each actual entity is a nexus of prehensions… There is no coherence unless there is something by reason of which the diverse elements are coherent” (1929, Part II, Ch. I). That “something” is not external to the prehensions; it is the binding of prehensions themselves — the actual occasion.

This means relations are internal relations — they constitute their relata. Change a relation, and you change the things themselves. For Whitehead, there are no external relations in the classical Aristotelian sense. The being of a thing just is its network of prehensions. A person is not an independently existing entity that happens to be related to parents, friends, and community. The person is constituted by their prehensions: their grasping of their parents’ presence, their appropriation of cultural influences, their responsive engagement with the world around them. Sever these relations, and you do not have a person in isolation — you have a mere abstraction, a logical remainder.

Whitehead’s internal relations resolve Bradley’s regress, but not through Russell’s move (making relations primitive in a logical sense). Rather, internal relations don’t need binding because they are constitutive — the relation and its relata are mutually defining. There is no third thing that must bind them together; the relation just is that binding. The unity of an actual occasion is the integration of its prehensions; there is no further adhesive required.

¶B. William James: relations in experience

William James (1912) approaches relations from radical empiricism — the doctrine that relations are as much matters of direct experience as the terms they relate. James writes: “The relations between things, conjunctive as well as disjunctive, are just as much matters of direct particular experience… as the things themselves” (Essays in Radical Empiricism, 1912, p. 42).

James rejects the assumption that relations are somehow less real or more abstract than their terms. The “and” between two thoughts is as real as the thoughts themselves. When you experience a transition from one thought to another, you experience the relation. The relation is not inferred from the terms; it is given in experience.

This has a profound consequence: if relations are directly experienced, they are not secondary phenomena, not abstractions layered over a primary realm of substances. They are immediate facts about the world. When you see that one person is taller than another, you do not first see two separate humans and then infer the relation “taller than.” You perceive the relation directly. It is part of the experienced fact.

¶C. Peirce: Thirdness and triadic relations

Charles Sanders Peirce introduces a crucial distinction: dyadic relations (relations between two things) versus triadic relations (relations among three things). A dyadic relation like “A is taller than B” can be reduced to a property: “A has a degree of height that exceeds B’s degree of height.” But a triadic relation like “A is between B and C” cannot be reduced to dyadic relations without loss. You cannot decompose “A is between B and C” into pairs; the position of A (the middle term) is only defined by the joint presence of B and C.

Peirce calls this irreducible triadic structure “Thirdness” — it is a category of mediation and continuity. A sign (Firstness) refers to an object (Secondness) through an interpretant (Thirdness). The interpretant is not a fourth thing; it is the medium through which the sign-object relation becomes meaningful. This triadic structure is irreducibly three-part; you cannot decompose it into dyadic relations without loss.

Peirce’s insight applies broadly to predication and meaning-making. When a subject stands in a relation to an object through a predicate, the structure is not dyadic. “Socrates is wise” is not reducible to a binary relation between Socrates and wisdom. The predicate “wise” mediates — it interprets wisdom as a property of Socrates in a particular context. Remove the predicate (the interpretant), and you have no meaningful relation between the subject and object, only bare juxtaposition.

¶D. Nāgārjuna: dependent origination and emptiness

Nāgārjuna (c. 150 CE) develops a relational metaphysics in the Mūlamadhyamakakārikā (Fundamental Verses on the Middle Way). The core principle is dependent origination (pratītyasamutpāda): “When this is, that is; when this is not, that is not; when this ceases, that ceases.”

Dependent origination means nothing has intrinsic nature (svabhāva, literally “own-being”). Nothing exists independently. Everything exists only in relation to other things. A part is only a “part” in relation to a whole. A subject only exists in relation to objects, just as objects only exist in relation to subjects. The distinction between subject and object, knower and known, is relational, not intrinsic. It is not given in advance by the nature of things, but emerges through dependent origination.

This is emptiness (śūnyatā) — not the absence of things, but the absence of intrinsic self-nature. A thing is empty of svabhāva while being fully real in its relational dependence. The world is neither a fixed plenum of self-identical substances nor a void. It is a network of mutually dependent entities, each arising in relation to the others. Nāgārjuna systematically refutes the four possibilities: things cannot arise from themselves (which would require intrinsic nature), from other things alone (which would be arbitrary causation), from both (combining contradictions), or from neither (which leaves nothing to explain). Things arise only through dependent origination — the mutual causation of all entities.

This radical relationalism has a striking consequence: identity and distinction are not intrinsic features but relational designations. The same physical event has different identities relative to different contexts — it is a “cause” relative to its effects, a “cause-and-effect” relative to its originating conditions, an “outcome” relative to its causes. Identity is context-dependent. This does not make it arbitrary, but it means we cannot point to some intrinsic essence and say “that is what makes this entity what it is.” What makes an entity what it is, is its role in the network of dependent origination.

¶E. Simondon: individuation and process

Gilbert Simondon (2005) articulates a process ontology centered on individuation — the process through which an individual comes to be. The standard hylomorphic model (form imposed on matter) misses what individuation actually is. Individuation is not the stamping of a form on pre-existing matter. It is a process of differentiation from a pre-individual field, a process where both the individual and the environment are constituted.

Simondon writes: “The individual does not precede the process of individuation. The individual is what results from the process.” A crystal does not pre-exist and then acquire a crystalline form. The crystal individuates through a process of phase transition, and the process constitutes both the crystal and the surrounding medium. Identity is not achieved at a moment; it is maintained through the continuity of a process.

This has profound implications for understanding identity through change. You cannot understand an entity’s identity by looking at a snapshot at a single moment in time. The snapshot shows the current state, but not the identity. Identity lies in the continuity of the process through which the entity came to be and continues to become. A person is not her body at age 25, nor at age 50. The person is the process through which she individuated from a pre-individual field (her parents, her culture, the material world), differentiated herself through choices and experiences, and maintained identity through a continuous transformation. The continuity of her process of becoming is what makes her a single individual across time.

This dissolves the classical problem of the Ship of Theseus. The ship maintains identity not because some essential feature persists unchanged, but because its individuation process is continuous. As planks are replaced, the shipwright’s ongoing work, the ship’s operational role in use, the continuity of its maritime history — these processes constitute the ship’s identity. A ship identical in every observable respect but created yesterday by accident rather than built over years of continuous modification is not the same ship, because it lacks the individuation history.

¶F. Karen Barad: intra-action and agential cuts

Karen Barad (2007) develops a framework of intra-action (not interaction) influenced by quantum mechanics and process philosophy. Interaction assumes pre-existing entities that then relate to each other. Intra-action denies this assumption. Entities do not exist independently and then interact. Rather, entities emerge through relations, through intra-actions. The boundaries between “this” and “that” are not given in advance but are enacted through relational practices.

Barad writes: “The notion of intra-action recognizes that distinct agencies do not precede, but rather emerge through, their encounter” (2007, p. 178). When an electron and a photon encounter each other in a measurement apparatus, they do not pre-exist as fully formed entities that then relate. The electron and the photon emerge through their intra-action. What we call “the electron” is not a pre-existing thing; it is an effect of the measurement apparatus and the apparatus’s relation to other apparatus configurations. The boundaries of the electron (what counts as this electron and not that electron) are not determined by nature alone; they are enacted through the relational practices of measurement and observation.

This insight extends beyond quantum physics. In any relational network — whether of people in a community, organisms in an ecosystem, or information in a system — the entities do not pre-exist and then relate. The entities emerge through their intra-actions, through being linked to, referenced by, encountered by other entities. The boundaries of an entity are enacted through relational practices, not inscribed in advance.

¶G. Category theory: morphisms as primary

In pure mathematics, category theory inverts the traditional object-first orientation of set theory. In a category, morphisms (arrows, relations between objects) are the primary data, and objects are secondary. The axioms of a category specify how morphisms compose; objects are just things that morphisms compose to and from. An object is characterized not by its internal structure but by what maps to it and from it.

The Yoneda lemma — one of the deepest theorems in category theory — states that an object is completely determined by its morphisms. You can recover everything about an object from knowing all the arrows pointing to it and from it. This is the mathematical articulation of a relational metaphysics: an entity is what it is through its relations. There is no hidden nature of an object apart from its relational interactions. To fully specify an object in a category is to specify the complete network of relations in which it participates.

¶IV. Toward a Relational Metaphysics

The traditions reviewed in this survey — substance and process, Eastern and Western — converge on a shared insight: relation and identity are intertwined in ways that resist reduction. No account that makes things purely primary (Aristotle’s substance) fully captures the phenomenon of relational dependence. No account that dismisses relations as appearances (Bradley) can account for their manifest role in constituting what things are.

Contemporary philosophy has moved toward relational ontologies that take these insights seriously. Whitehead, category theory, and dependent origination all propose that entities are what they are through their relations, not in spite of them. Identity persists not through an unchanging essence but through the continuity of relational structure and process.

¶Resolving Bradley’s Regress

The core problem remains: if a relation is a thing, how does it bind to its terms without an infinite regress of further relations? Russell’s answer — that relations are logical primitives requiring no further mediation — works but leaves the question of which relations are genuine and which are projective.

Whitehead’s answer is deeper: internal relations don’t need mediation because they are constitutive. The binding just is the integration of the relation into the relata. This dissolves the regress not by stipulation but by reconceiving what relations are. Relations are not things that stand between other things waiting for adhesive. Relations are the ongoing constitution of the things themselves.

Nāgārjuna reaches the same conclusion from a different angle: because nothing has intrinsic self-nature, there is no regress problem. There are no pre-formed things waiting to be bound together. Things arise through dependent origination — through relations. The relation and the relata come into being together, not sequentially. This is not mysticism; it is ontological clarity about the structure of dependence.

¶Identity Through Relational Change

The classical problem of identity — how something remains itself through change — dissolves once identity is understood as relational and processual rather than substantial. Leibniz showed that identity is grounded in indistinguishability across all properties and relations. Kripke showed that identity also depends on actual causal history. Geach showed that identity is always sortal-relative. Simondon showed that identity is the continuity of an individuation process.

These insights are not contradictory; they are complementary. An entity’s identity is multiply grounded:

1. Relational differentiation: An entity is distinguished from every other entity by its unique constellation of relations.
2. Essential properties and causal history: Among an entity’s properties and relations, some are essential (constitutive of what it is) and some are contingent. Essential properties are often relational and are grounded in the actual genesis of the entity.
3. Sortal identity: Identity is never bare; it is always identity-under-a-description, relative to a kind. “Same ship” and “same matter” pick out different continuities.
4. Individuation process: Identity is the continuity of a process of becoming, not a static property. An entity remains itself as long as its process of differentiation from the pre-individual and integration with the environment continues.

¶The Triadic Structure

Peirce’s insight about triadic relations is crucial for understanding predication, signification, and meaning. Most relations in natural language and thought are not dyadic. When we say “Socrates is wise,” we express not a dyadic fact but a triadic one: a subject, a predicate (the mediating term), and an object or property. The predicate interprets the property for the subject in a particular context.

This triadic structure is irreducible. It appears in Peirce’s semiotics (sign-object-interpretant), in Russell’s later work on judgment, in contemporary linguistics (argument-predicate-complement), and in dependent origination (where cause, effect, and causal conditions form an irreducible three-fold). It deserves to be recognized as a fundamental structure of reality, not reduced to dyadic relations.

¶Implications

These insights — that relations are constitutive, that identity is processual and relational, that triadic structures are irreducible — lead to a reorientation of metaphysics. Instead of asking “What are the fundamental things?” (Aristotle’s question), we ask “What are the fundamental relations and processes through which entities come to be?” Instead of looking for intrinsic essences, we examine relational signatures and patterns of individuation. Instead of treating change as anomalous (accidental relations that come and go), we recognize it as the normal state of affairs — the continuous process through which entities maintain identity while becoming.

This is not a flight from ontology into phenomenology or pragmatism. It is a different ontology, one that takes relations and process as primary without denying the reality of entities. Things are real. They have determinate natures. But their natures are relational, not intrinsic; processual, not static; multiple, not singular.

¶See also

• Thing — the most general category, understood through relations
• Dependence — the condition of existing only through relations to other entities
• Identity — continuity through relational change
• Change — transformation as the normal state of relational entities
• Related philosophical traditions: Process philosophy, Metaphysics, Ontology