Properties and Relations

1. Introduction

Philosophers invoke properties and relations to make sense of how the world is structured: why different things can be similar, how objects interact, and what underlies the truths we express in language and science. When we say “the apple is red” or “the planet attracts the satellite,” we seem to be attributing something repeatable—being red, attracting—to different particulars. The study of properties and relations investigates what, if anything, these repeatable features are.

This topic sits at the intersection of metaphysics and ontology. It intersects with debates about universals and particulars, substance and attribute, intrinsic and extrinsic features, and the nature of laws, causation, and modality. The central issues are not merely semantic. While some approaches treat property-talk as a convenient linguistic device, others claim that properties and relations are indispensable constituents of reality.

Historically, questions about properties and relations emerge from reflections on predication (“S is P”), beginning with ancient Greek philosophy and continuing through medieval scholasticism to modern and contemporary metaphysics. Positions range from realism about universals, which posits mind-independent repeatable entities, to nominalism, which denies such universals, to intermediate views such as trope theory and various forms of structuralism.

These debates have methodological significance. They frame how philosophers conceive of explanation: whether resemblance, causation, and law-governed regularity require a distinctive ontological category of properties and relations, or whether they can be captured purely in terms of particular things, sets, or linguistic practices. They also structure later discussions about objects, persons, social categories, and scientific kinds, which depend on how one understands “having” a property or “standing in” a relation.

This entry surveys the main concepts, historical developments, and leading positions concerning properties and relations, culminating in an overview of contemporary disputes and their broader significance.

2. Definition and Scope of Properties and Relations

Philosophers typically distinguish between properties and relations by reference to arity and dependence on multiple entities.

Basic Characterizations

• A property is commonly taken to be a way an individual thing is: being red, having mass 1 kg, being rational. These are often called monadic or one-place features.
• A relation is a way two or more things jointly are: being taller than, causing, being two meters apart. These are polyadic or many-place features, often analyzed as ordered tuples (x is larger than y).

Ontological views differ on what these entities are (universals, tropes, sets, etc.), but they largely converge on their functional role: they are posited to explain predication, similarity, classification, and structural patterns in the world.

Scope of the Category

The scope of “property” and “relation” is contested. Different theorists include or exclude:

Similarly, relations range widely:

Some philosophers expand the category to include higher-order properties and relations (properties of properties, relations between relations), while others regard this as a mere façon de parler.

Disagreement over scope often tracks broader metaphysical commitments. Sparse realists restrict properties and relations to those needed by “fundamental” science; abundant theorists allow a property or relation for every meaningful predicate. These differing conceptions of scope directly influence debates about realism, nominalism, and structuralism discussed in later sections.

3. The Core Metaphysical Questions

The metaphysics of properties and relations is structured around a cluster of interrelated questions, each generating distinct positions and arguments.

Existence and Ontological Status

A first question concerns whether properties and relations exist at all:

• Are there universals, repeatable entities shareable by multiple particulars?
• Or is talk of properties and relations reducible to particular objects, sets, or linguistic conventions?

This leads to classic contrasts between realism about universals, nominalism, and conceptualism.

Nature and Structure

A second question concerns what kind of entities properties and relations are:

• Are they abstract or concrete, dependent or independent of space-time?
• Are they universals or tropes (particularized properties)?
• Do they have quiddities—intrinsic qualitative identities—or are they exhausted by the roles they play in causal and nomic structures?

Closely related is the issue of higher-order properties and relations, and whether such entities are coherent or necessary.

Instantiation and Predication

Another central question asks how particulars have properties and stand in relations:

• What is the metaphysical relation of instantiation?
• Is predication (“a is F”) underpinned by a primitive tie, by a substratum that bears properties, or by compresence relations in a bundle?

Here, theories of objects (bundle vs. substratum) intersect with the metaphysics of properties.

Intrinsic vs. Extrinsic; Monadic vs. Relational

Philosophers also ask whether there is a principled distinction between intrinsic and extrinsic (relational) properties, and what it amounts to. This bears on questions about:

• Whether all properties are ultimately relational or structural.
• Whether relational facts can be reduced to monadic properties, or vice versa.

Explanatory Roles

Finally, properties and relations are evaluated by their explanatory roles:

• Do they ground resemblance and classification?
• Are they the truthmakers for generalizations and laws of nature?
• Do they underpin causal powers and modal facts (possibility, necessity, counterfactuals)?

Different answers yield competing metaphysical systems, whose development is traced historically in the next sections.

4. Historical Origins in Ancient Philosophy

Ancient philosophy introduces many of the core ideas and disputes that continue to shape theories of properties and relations.

Plato and Forms

Plato’s theory of Forms is often read as an early form of realism about properties. In dialogues such as the Phaedo and Republic, Plato posits non-sensible, eternal entities—the Beautiful itself, the Just itself—to explain:

• One-over-many: how many beautiful things are all beautiful.
• Stability: how we can have knowledge of unchanging objects despite changing appearances.

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“We are in the habit of positing a single Form for each of the many things to which we apply the same name.”

— Plato, Phaedo (100b)

Forms are paradigmatically monadic, but relational Forms (e.g., larger than) are sometimes acknowledged as well.

Aristotle’s Categories and In-Re Realism

Aristotle criticizes separate Forms and instead locates universals in re, in things themselves. In the Categories and Metaphysics, he distinguishes substance from accidents, including qualities and relations as fundamental categories of what can be said of a subject.

Aristotle treats relations as dependent on their relata and often derivative, but he nonetheless grants them ontological standing.

Hellenistic and Later Ancient Developments

Stoic philosophers shift focus toward qualified individuals and lekta (sayables), leading some interpreters to find nominalist or conceptualist tendencies in their treatment of universals. The Stoics emphasize:

• Concrete particulars as primary.
• A more deflationary attitude toward universal entities.

Neoplatonists such as Plotinus reinterpret Forms in a hierarchical emanationist framework, further elaborating the status of properties as aspects of Intellect and of sensible things.

Late antique commentators like Porphyry systematize Aristotle’s categories and raise explicit questions about universals, preparing the ground for medieval debates. Porphyry’s Isagoge famously asks whether genera and species are real entities or mere concepts, and whether they are corporeal or incorporeal, questions he explicitly leaves unresolved but that structure subsequent scholastic inquiry.

5. Medieval Scholastic Debates on Universals

Medieval scholasticism inherits ancient problems about universals and develops them into highly articulated theories of properties and relations.

Main Positions: Realism, Nominalism, Conceptualism

Scholastics generally debate the status of genera and species (e.g., humanity) as paradigmatic universals, with implications for properties more broadly.

Realists such as Aquinas adopt a moderate in re position: universals exist in things and in minds (as abstracted species), but not as separate Platonic entities. Aquinas treats properties largely as accidents inhering in substances, and relations as an accident category with special theological importance (e.g., in Trinitarian doctrine).

Scotus and Formal Distinctions

Duns Scotus introduces more refined tools to explain how properties and natures can be common yet individuated. His notion of a formal distinction aims to capture a middle ground between real and purely conceptual distinctions—for example, between a nature’s common aspect and its individual haecceity (thisness). This device is used to analyze divine attributes and creaturely properties without multiplying separate entities.

Ockham and Nominalism

William of Ockham argues vigorously against extra-mental universals. For him, only individuals exist; universals are at best mental or linguistic:

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“No universal is a substance existing outside the mind.”

— William of Ockham, Summa Logicae

Properties and relations are frequently analyzed in terms of:

• Individual things.
• Resemblance or conceptual grouping.
• Mental terms and their signification.

Ockham’s nominalism is often seen as a precursor to later deflationary approaches to properties.

Intrinsic and Extrinsic Properties; Relations to God

Medieval thinkers also refine distinctions relevant to later debates, such as intrinsic vs. extrinsic features, and the status of relations:

• Theological puzzles (e.g., the Trinity, God’s relation to creation) lead to subtle accounts of real relations vs. relations of reason (merely conceptual).
• Some scholastics treat certain relational features (e.g., “being created by God”) as asymmetrically real: real on one side, merely logical on the other.

These discussions lay the groundwork for later distinctions between internal and external relations, and between genuine and merely “Cambridge” changes.

6. Early Modern Transformations of Substance and Attribute

Early modern philosophy reconfigures the landscape by centering substance and attribute within new metaphysical and scientific frameworks.

Rationalist Monism and Dualism

Descartes famously proposes a dualistic ontology of thinking substance (mind) and extended substance (matter), each characterized by a principal attribute:

• Mind: thought.
• Body: extension.

Particular properties (modes) such as specific thoughts or shapes are ways that substances exist. Descartes tends to treat relations (e.g., mind–body interaction) as problematic but not fundamental; properties are primarily monadic modes of substances.

Spinoza radicalizes this scheme: there is only one infinite substance (God or Nature) with infinitely many attributes, of which thought and extension are known to us. Individual things are modes of this single substance. Properties are thus contextually reinterpreted as modes of an attribute, while relations between individuals are ultimately internal to the modes of the one substance.

Leibniz and Relational Structure

For Leibniz, reality consists of simple, non-spatial monads whose properties encode their entire history. Spatial and causal relations between bodies are derivative:

• Space is construed as an order of coexistences.
• Time as an order of successions.

Relations such as spatial distance are grounded in the coordination of monadic states; they lack independent ontological status apart from substances and their intrinsic properties. This anticipates later relational theories of space and time and raises questions about whether relations are reducible to monadic properties.

Empiricist Approaches: Locke and Hume

Locke develops a theory of primary and secondary qualities in An Essay Concerning Human Understanding. Primary qualities (shape, motion) are said to be in objects themselves, whereas secondary qualities (color, taste) are powers to produce ideas in perceivers. Thus many familiar properties are treated as dispositions or powers, relationally involving perceivers and circumstances.

Hume is often read as skeptical about robust metaphysical properties and relations. He emphasizes:

• Impressions and ideas rather than underlying qualities.
• Regularities of succession and contiguity as bases for ascribing causal relations.

Causation becomes a relation projected by the mind onto constant conjunctions, raising the possibility that at least some relations (and perhaps properties) are products of cognitive habits.

Kant and Categories

Kant reinterprets properties and relations within a transcendental framework. In the Critique of Pure Reason, he presents categories of understanding, including those of quality and relation (e.g., substance–accident, cause–effect, community). These are not properties and relations in things-in-themselves, but a priori forms under which we must conceive appearances. Kant’s stance complicates straightforward metaphysical realism about properties and relations, shifting attention to the conditions of their cognizability rather than their independent nature.

7. Analytic Philosophy and the Logic of Predication

Early analytic philosophy reframes questions about properties and relations through developments in logic, language, and the theory of predication.

Frege: Concepts and Relations

Gottlob Frege distinguishes sharply between objects and concepts (functions from objects to truth-values). Predicates in language express concepts; relational predicates express relations as functions of two or more arguments. Frege’s framework suggests:

• Properties and relations correspond to unsaturated entities (functions needing arguments).
• The structure of propositions reveals the underlying logical form of property and relation attribution.

Although Frege resists talk of “concepts as objects,” later philosophers interpret his work as supporting a kind of logical realism about properties and relations, grounded in the semantics of higher-order logic.

Russell and Moore: Universals and Relational Propositions

Bertrand Russell and G. E. Moore explicitly revive realism about universals. Russell argues that analysis of propositions such as “a is larger than b” requires us to posit relational universals in addition to monadic ones:

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“We must admit relations as real universals, not reducible to predicates of a single subject.”

— Bertrand Russell, The Principles of Mathematics

Russell’s multiple relation theory of judgment and his treatment of propositional functions further entrench properties and relations as indispensable to the ontology matching logical form.

Logical Atomism and Early Metaphysical Programs

Russell’s and early Wittgenstein’s logical atomism holds that the world consists of simple objects and their properties and relations, corresponding to simple subject–predicate and relational propositions. This picture supports:

• A correspondence between logical structure and ontological structure.
• A highly articulated inventory of properties and relations, at least at the level of logical form.

Quine and the Criteria of Ontological Commitment

Mid-20th-century analytic philosophy, especially through W. V. O. Quine, introduces tools for assessing when we are ontologically committed to properties and relations:

• Quine advocates regimenting theories into first-order logic and reading commitments from existential quantifiers.
• He is suspicious of intensional entities (meanings, properties) not required by physical theory, yet he later allows that quantification over sets and classes may be indispensable.

This yields a tension: analytic methods make reference to properties and relations precise, but they also underpin deflationary or nominalist readings that dispense with them when possible.

Linguistic Turn and Beyond

Later analytic philosophers explore whether properties and relations are:

• Semantic correlates of predicates (e.g., in some forms of higher-order logic).
• Mere logical devices for regimenting discourse.
• Or robust metaphysical entities correlated with the best explanatory theories.

This period lays the groundwork for contemporary debates about truthmakers, natural properties, and structural realism, all of which presuppose or challenge the idea that properties and relations mirror the logical structure of our language.

8. Realism about Properties and Relations

Realism in this context is the view that properties and relations exist as mind-independent entities that can be shared or instantiated by many particulars.

Universals Realism

Most classical realists hold that properties and relations are universals—repeatable entities wholly present in each of their instances. When two electrons both have charge −e, they instantiate the same universal negative charge.

Realists typically argue that universals:

• Explain resemblance: Similar objects share a common property, rather than merely resembling each other.
• Ground classification and kinds: Natural kinds like electron or gold are unified by shared property-sets.
• Serve as truthmakers: General and predicative claims (e.g., “All Fs are G”) are made true by universals instantiated in the world.
• Underwrite laws of nature: Some realists, such as D. M. Armstrong, propose that laws are relations between universals (e.g., N(F, G)).

Sparse vs. Abundant Realism

A key division is between:

Sparse realists (e.g., Armstrong, David Lewis on natural properties) aim to avoid ontological proliferation by tying universals to the roles they play in basic physics and lawlike explanation. Abundant realists are more liberal, often motivated by logical or semantic considerations.

Realism about Relations

Realists increasingly emphasize relations as on a par with, or even more fundamental than, monadic properties. Russellian realists insist that many facts are irreducibly relational (spatial, causal, ordering relations) and cannot be analyzed solely in terms of intrinsic monadic features. Contemporary structural realists (discussed later) extend this idea, sometimes claiming that relational structure is ontologically primary.

Objections and Challenges

Standard criticisms include:

• The one-over-many problem: how one universal can be wholly present in multiple places without being a mere set or mere abstraction.
• Epistemic access: how we perceive or know universals, given that we interact causally with particulars.
• Metaphysical cost: some argue universals are an unnecessary addition to a parsimonious ontology.
• Coextensive universals: distinguishing properties that are necessarily coextensive (e.g., “creature with a heart” vs. “creature with kidneys”) raises individuation puzzles.

Realists respond by refining accounts of instantiation, positing primitive grasp of universals, appealing to explanatory indispensability, or restricting universals to those featuring in best scientific theory.

9. Nominalist and Conceptualist Alternatives

Nominalism and conceptualism deny or downplay the existence of mind-independent universals, offering alternative accounts of property and relation talk.

Varieties of Nominalism

Nominalists agree that only particulars (and sometimes sets or classes) exist, but they differ in how they reconstruct predicates and resemblance.

Predicate nominalists treat “is red” as a mere word applied to things, without ontological correlates. Class nominalists identify a property with the set of all things to which the predicate applies. Critics note that such accounts struggle to distinguish natural from gerrymandered properties and may reintroduce universals via set membership.

Resemblance nominalism explains property ascriptions by networks of similarity among particulars: two things are both red because they resemble paradigmatic red things. However, this raises concerns about:

• Resemblance regress: resemblance itself appears to be a relational property; if that needs explanation, a regress of higher-order resemblances threatens.
• The need to distinguish “good” resemblances from accidental ones.

Trope-Theoretic Nominalism

Some nominalists accept tropes (particularized properties) as the only qualitative entities. On this view, there are no universals; similarity among objects is explained by resemblance among tropes, not by shared universals. Trope theory is often classified as a realist nominalism or as an intermediate position, and is treated in detail in the next section.

Conceptualism

Conceptualists maintain that universality resides only in thought or language:

• Universals are features of concepts, not of extra-mental reality.
• Similarity and classification reflect the way our cognitive faculties group particulars.

Medieval conceptualists and some modern philosophers (e.g., aspects of Kantianism) stress that the mind supplies the general forms under which we represent objects. Contemporary conceptualists sometimes link properties to cognitive or linguistic practices, or to inferential roles in reasoning.

Motivations and Objections

Motivations for nominalist and conceptualist positions include:

• Ontological parsimony (Ockham’s razor).
• Alignment with empiricism or physicalism.
• Suspicion of abstract or non-spatiotemporal entities.

Critics argue that these views face difficulties accounting for:

• Laws of nature and counterfactuals without positing property-types.
• The apparent objectivity of resemblance and natural kinds.
• Distinctions among coextensive predicates without appealing to more than linguistic or conceptual facts.

Debate continues over whether nominalist and conceptualist strategies can fully capture the explanatory roles traditionally assigned to properties and relations.

10. Trope Theory and Particularized Properties

Trope theory proposes that the basic qualitative constituents of reality are not universals but tropes: particularized property-instances.

Core Idea

On this view, when a tomato is red, what exists is:

• The tomato (a particular).
• A specific redness trope located in that tomato.

Another tomato’s redness is a numerically distinct redness trope. Similarity between tomatoes is grounded not in a shared universal but in resemblance among their redness tropes.

Tropes are usually taken to be:

• Particular (non-repeatable).
• Concrete (spatiotemporally located).
• Simple or at least not composed of universals.

Relations can be treated analogously as relational tropes, particularized instances of relating (this specific being-two-meters-apart trope between A and B).

Bundles and Object Constitution

Many trope theorists adopt a bundle theory of objects: objects are collections or “bundles” of compresent tropes (color trope, shape trope, mass trope, etc.). The compresence relation itself may be:

• Another relational trope.
• Or a primitive tie that groups tropes into a single object.

Alternative versions treat tropes as modifications of an underlying substratum, preserving a substratum–property distinction within a trope framework.

Advantages Claimed

Proponents argue that trope theory:

• Avoids the puzzle of multipresence associated with universals (each trope is in one place only).
• Offers a concrete, empirically friendly ontology.
• Provides fine-grained causal explanations, since causal powers attach to specific tropes.
• Serves as a compromise between realism (tropes are real qualitative entities) and nominalism (no universals).

Standard Objections

Critics raise several issues:

• Similarity regress: to explain why some tropes resemble each other more than others, one might need higher-order resemblance tropes, generating a regress.
• Compresence problem: explaining what unites tropes into a single object can seem to require further tropes or relations, again threatening regress or circularity.
• Individuation: qualitatively identical tropes must be numerically distinct; specifying a robust criterion of individuation may be difficult without appeal to substrata or spatiotemporal positions.
• Relational tropes: some question whether there can be particularized instances of relations without presupposing more fundamental relational structure.

Despite these challenges, trope theory remains a significant alternative framework for understanding properties and relations, influencing contemporary discussions of objects, causation, and laws.

11. Intrinsic versus Extrinsic Properties

The distinction between intrinsic and extrinsic (or relational) properties is central to understanding how objects are in themselves versus how they are in relation to other things.

Basic Characterizations

• An intrinsic property is often described as a property an object has in itself, independent of its environment or relations. Examples frequently cited include mass, shape, and charge (though even these are controversial in modern physics).
• An extrinsic property (or relational property) depends on how the object stands with respect to other entities, times, or circumstances—for instance, being two meters from a tree, being admired by someone, or being a citizen of a particular state.

Analytic Criteria

Philosophers have proposed various formal criteria to nail down this intuitive contrast:

David Lewis and others introduce the idea that intrinsic properties are those that do not imply the existence of distinct contingent objects. However, formulating this precisely without circular appeals to “relations” is technically complex.

Mixed and Contextual Cases

Many properties appear mixed or context-sensitive:

• Dispositions (fragility, solubility) seem partly intrinsic but also defined in terms of how an object would behave under certain conditions.
• Social or institutional properties (being a professor, owning a car) are typically regarded as paradigmatically extrinsic.

Some philosophers argue that the intrinsic–extrinsic divide is not fundamental, or that many properties cannot be neatly classified. Others treat it as indispensable for analyzing:

• Causation (intrinsic features as causal bases).
• Personal identity and persistence.
• Ethics (distinguishing intrinsic value from relational value).

Relation to Monadic vs. Polyadic Distinctions

The intrinsic–extrinsic distinction is not identical to the monadic–relational distinction:

• Intrinsic properties are monadic but not all monadic properties are intrinsic (e.g., “being the only object in the universe” is monadic but extrinsic).
• Extrinsic properties are typically relational but may be expressible by monadic predicates that encode relational conditions.

Debate continues over whether the intrinsic–extrinsic distinction tracks a deep metaphysical difference or primarily reflects conceptual and explanatory interests.

12. Bundle and Substratum Theories of Objects

Theories of objects often turn on how properties and relations compose or characterize individual things. Two influential approaches are bundle theories and substratum theories.

Bundle Theories

Bundle theorists claim that an object is nothing over and above a bundle of compresent properties (and perhaps relations). On this view:

• There is no underlying “bare particular” that has properties; the object simply is the complex of properties.
• Identity of objects is determined by their qualitative profile.

Some bundle theories employ universals as bundle constituents; others use tropes. A trope-bundle theory may hold, for example, that a particular electron is just a bundle of charge, spin, and mass tropes.

Advantages cited include:

• Avoiding mysterious substrata with no intrinsic character.
• Aligning with empiricist intuitions that all we ever find are properties.

Challenges include:

• The problem of change: if an object just is its bundle of properties, how can it survive gain or loss of properties?
• Indiscernibles: qualitatively identical bundles appear indistinguishable, raising worries about how to account for distinct but qualitatively identical objects.

Substratum Theories

Substratum theorists posit an underlying bearer or subject (substratum) that has properties but is not identical with them. The object is constituted by:

• A substratum (often characterized as a bare particular or basic substance).
• Properties inhering in that substratum.

This approach aims to:

• Provide a principle of unity tying diverse properties together.
• Explain persistence through change: the same substratum underlies different property instantiations over time.

Objections focus on the obscurity and possible redundancy of substrata:

• Bare particulars are sometimes accused of being “something of which nothing can be said,” raising questions about intelligibility.
• Critics argue that the instantiation relation between objects and properties may suffice to account for unity, making substrata unnecessary.

Comparative Overview

Different combinations with universals, tropes, and relational structures yield a variety of hybrid views, but all are attempts to articulate how properties and relations give rise to—or are borne by—individual objects.

13. Relational Ontology and Structuralism

Relational ontology and structuralism emphasize the primacy of relations and structures over intrinsically characterized objects and properties.

Relational Ontology

Relational ontologists claim that relations are at least as fundamental as, and sometimes more fundamental than, monadic properties. In some strong versions:

• Objects are constituted by the network of relations in which they stand.
• There may be no fully non-relational or purely intrinsic properties.

Examples include:

• Relational theories of space and time, where spatiotemporal relations are fundamental.
• Social ontologies where persons or roles are defined by relational positions (e.g., parent, citizen).

Ontic Structural Realism

A prominent contemporary form of structuralism, especially in the philosophy of science, is Ontic Structural Realism (OSR). OSR holds that:

• The world’s basic ontology consists of structures—networks of relations.
• Objects are often regarded as nodes or placeholders within structures, lacking independent intrinsic natures.

Supporters cite modern physics (e.g., quantum entanglement, gauge theories) as suggesting that relational structure is more fundamental than independently existing particles with intrinsic properties.

Criticisms and Challenges

Critics raise several concerns:

• The relata problem: relations seem to require things that are related; a purely relational ontology risks circularity if relata are themselves constituted solely by relations.
• Qualitative content worry: structure alone may not capture the “what-it-is-like” or quiddistic character of properties; different properties could occupy the same structural role.
• Self-defeat: some argue that specifying structures presupposes intrinsic features (e.g., metric values), undermining radical structuralism.

Moderate structuralists respond by allowing some thin intrinsic features or by refining what counts as “structural.” Debates continue over whether relations and structures can be ontologically fundamental without presupposing more traditional properties or substrata.

14. Properties, Relations, and Laws of Nature

Theories of laws of nature often rely on specific conceptions of properties and relations to explain regularities, counterfactuals, and causal structure.

Governing vs. Humean Views

Many non-Humean accounts treat laws as involving robust connections between properties:

• D. M. Armstrong’s theory sees laws as relations of necessitation between universals (e.g., N(F, G)), where F and G are property-universals. The law holds in virtue of a real relation that “governs” particular instances.
• Other modal realists posit that properties have essential roles: a property’s identity includes the nomic and causal roles it necessarily plays.

By contrast, Humean views such as David Lewis’s Best System Analysis regard laws as:

• Features of the best systematization of the total distribution of particular events and their qualitative properties.
• Supervenient on the mosaic of local, categorical properties and spatiotemporal relations, without irreducible nomic relations.

Dispositional and Categorical Properties

A major fault line concerns whether properties are essentially dispositional or categorical:

Dispositional essentialists claim that laws follow from the essences of properties: for example, the property of negative charge essentially confers attraction to positive charge. Laws thus express necessary relations built into property identities.

Categoricalists tend to regard properties as having qualitative natures that could, in principle, play different nomic roles (“quiddities”). Laws then relate these properties externally, whether or not such relations are necessary.

Role of Relations

Relational structure figures prominently:

• Spatiotemporal relations define the arena in which local property-instances are arranged, crucial for Humean mosaics.
• Laws often concern relational properties such as distances, forces, and field strengths at points or regions.
• Some views treat laws themselves as higher-order relations among properties, events, or universals.

Debates over whether such nomic relations are fundamental or reducible to patterns among categorical properties affect assessments of realism about properties and relations.

Explanatory and Epistemic Considerations

Philosophers also consider:

• Whether positing universals or dispositional essences improves explanations of counterfactuals and causal dependence.
• How our empirical access to laws and properties (via scientific practice) constrains metaphysical theorizing.

These issues keep the metaphysics of properties and relations closely tied to the philosophy of science and theories of modality.

15. Interdisciplinary Connections in Science, Religion, and Politics

Properties and relations figure prominently beyond core metaphysics, shaping concepts and debates in several disciplines.

Science

In physics, fundamental quantities such as mass, charge, spin, and field values are standardly treated as properties, while spatiotemporal and entanglement relations are central to theory. This has motivated:

• Structural realism, emphasizing relational structure over intrinsic particle properties.
• Reconsideration of whether traditional intrinsic–extrinsic distinctions hold at quantum scales, given non-local correlations.

In biology, classification into species and higher taxa invokes properties and relations (e.g., genetic similarity, reproductive relations). Discussions of natural kinds intersect with debates about whether such biological categories correspond to real property clusters or are pragmatic groupings.

In cognitive science and AI, mental states are often characterized functionally, in terms of relations among inputs, internal states, and outputs. Functional properties raise questions about whether they can be reduced to lower-level physical properties or whether they constitute distinct, higher-level relational properties.

Religion

In theology, divine attributes (omniscience, omnipotence, goodness) are typically understood as properties of God. Classical theists often hold these to be:

• Necessary and essential properties.
• Sometimes identified with God’s essence, leading to debates about the distinctions among attributes.

The doctrine of the Trinity involves intricate intra-divine relations (Father, Son, Spirit) that are said to be real relations without implying three separate substances. The relation between God and creation raises questions about extrinsic vs. intrinsic divine properties and about whether God can change in relational respects without undergoing intrinsic change.

Process and relational theologies emphasize dynamic relations between God and the world, sometimes prioritizing relational over static property attributions.

Politics and Social Ontology

In political philosophy and social ontology, many central categories are explicitly relational:

• Power, authority, and status are defined by networks of social and institutional relations.
• Properties like being a citizen, being married, owning property, or being a refugee depend on legal and normative structures.

Debates about race, gender, and other identity categories often turn on whether these are:

• Intrinsic properties of individuals.
• Socially constructed relational properties arising from institutions, norms, and power relations.

Analyses of structural injustice focus on relational patterns (e.g., patterns of domination, dependence, exclusion), aligning with broader structuralist approaches that understand social phenomena in terms of webs of relations rather than isolated individuals with fixed intrinsic properties.

16. Current Debates and Unresolved Problems

Contemporary metaphysics features a range of ongoing disputes about properties and relations, many drawing on advances in logic, science, and meta-ontology.

Naturalness and Eligibility

Following David Lewis, many philosophers discuss natural or elite properties—those that carve nature at its joints and underpin objective similarity, laws, and causation. Key questions include:

• Whether naturalness is a primitive feature of some properties.
• How to distinguish natural properties from merely gerrymandered or disjunctive ones.
• Whether naturalness supports a sparse realism or can be reconstructed within a nominalist framework.

Grounding and Metaphysical Structure

The notion of grounding—a relation of metaphysical dependence—interacts with properties and relations:

• Are properties fundamental entities, or do they themselves depend on more basic structural facts?
• Can all relational facts be grounded in intrinsic facts, or are some relations fundamental?

Debates about metaphysical structure consider whether properties and relations form hierarchies (e.g., base-level physical properties grounding higher-level mental or social properties) and how precisely to formalize such hierarchies.

Quiddities and Identity of Properties

The question of quiddities remains contentious. Some argue properties have primitive identities beyond their roles in laws; others deny this, claiming that properties are wholly determined by their causal–nomic roles. Issues include:

• Whether distinct possible worlds could share all structural and nomic facts yet differ in which properties occupy those roles.
• How to interpret modal claims about property identity and cross-world comparison.

Intrinsicality and Externalism

Advances in physics and philosophy of mind have prompted reconsideration of the intrinsic–extrinsic distinction:

• Externalist theories in semantics and mental content suggest many mental “properties” are partly environment-dependent.
• Quantum entanglement challenges the idea of wholly independent, intrinsic states of particles, encouraging relational or holistic views.

Some philosophers propose that intrinsicality is an artifact of classical intuitions and that a fundamentally relational understanding of properties is required.

Structural Realism and Objecthood

Ontic structural realism continues to be debated, especially regarding:

• Whether structures can exist without objects or intrinsic property-contents.
• How to formally represent structures in ways that avoid collapse into traditional object–property ontologies.

No consensus has emerged on whether structuralism can stand as a self-sufficient metaphysics.

Methodological and Meta-Ontological Questions

Finally, there is disagreement about how to settle questions about properties and relations:

• Some appeal to explanatory indispensability and fit with best science.
• Others emphasize conceptual analysis, linguistic data, or logical regimentation.
• Meta-ontological deflationists question whether disputes about properties and relations are substantive or largely verbal.

These unresolved issues ensure that the metaphysics of properties and relations remains an active and evolving area of research.

17. Legacy and Historical Significance

Debates about properties and relations have had a lasting impact on the development of metaphysics, logic, theology, and the sciences.

Historically, reflections on predication in ancient philosophy led to the formulation of categories (substance, quality, relation) that still structure ontological thinking. Medieval disputes over universals shaped scholastic methodology and introduced distinctions (e.g., between real and conceptual relations) that continue to inform contemporary views.

Early modern reconceptions of substance and attribute under rationalism and empiricism influenced the transition from Aristotelian to mechanistic and then field-based scientific ontologies, reframing how properties and relations are tied to space, time, and causation. Kant’s emphasis on categories of quality and relation as conditions of experience redirected attention to the interplay between ontology and cognition.

In analytic philosophy, formal work on logic and language turned properties and relations into central tools for semantic and metaphysical analysis, prompting sophisticated theories of universals, predication, and ontological commitment. These developments laid the foundation for current research programs, including truthmaker theory, grounding, and structural realism.

The legacy extends beyond metaphysics narrowly construed. In theology, the treatment of divine attributes and intra-divine relations has drawn heavily on metaphysical notions of property and relation. In political theory and social ontology, the idea of relational properties has underpinned analyses of power, identity, and social structure, contributing to contemporary understandings of structural injustice and social construction.

Across these domains, the enduring significance of the topic lies in its role as a framework for explanation. How philosophers and theorists conceive of properties and relations shapes accounts of similarity, causation, law, objecthood, and structure. As scientific and social theories evolve, they continually generate new questions about what kinds of properties and relations they implicitly posit, ensuring that this area of inquiry remains central to philosophical reflection.