Relations.
Many things. Different ways of being one.
A rich family of philosophical, logical, metaphysical, and semantic relations helps us understand the relationship between the one and the many—or between a general category and the particulars that fall under it.
These relations are not interchangeable. Some concern classes and members, others universals and particulars, general and specific categories, or wholes and parts.
Twenty ways to relate.
These relations emerge from different philosophical traditions and theories. Several are competing analyses of closely related phenomena, rather than simply synonyms.
On smaller screens, scroll the table sideways to read the examples.
| Relation or distinction | What it expresses | Example |
|---|---|---|
| Set membership | An element belongs to a collection. | Socrates ∈ the set of humans. |
| Instantiation | A particular is an instance of a kind or universal. | Socrates instantiates humanity. |
| Exemplification | An entity possesses or manifests a property. | This apple exemplifies redness. |
| Universal–particular | Something repeatable or general relates to individual instances. | Humanity ↔ individual humans. |
| Type–token | A repeatable type has particular occurrences or tokens. | The word “tree” ↔ each printed occurrence. |
| Predication | A general predicate is attributed to a subject. | “Socrates is human.” |
| Concept–object / falling under | An object satisfies or falls under a concept. | Socrates falls under the concept human. |
| Genus–species | A general kind is differentiated into more specific kinds. | Animal → mammal → human. |
| Subsumption / subclass inclusion | One class is included within another. | All squares are rectangles. |
| Determinable–determinate | A general property is specified in a particular way. | Color → red → scarlet. |
| Mereology | A whole stands in a parthood relation to its constituents. | A tree ↔ its branches. |
| Composition / aggregation | Multiple constituents jointly constitute a whole. | Individual musicians → orchestra. |
| Participation (methexis) | Particulars participate in general Forms, in Platonic metaphysics. | Beautiful things participate in Beauty. |
| Essence–accident | A property belongs to something essentially or contingently. | Being human vs. being sunburned. |
| Abstraction–concretization | Generality is extracted from, or given particular realization in, instances. | Particular triangles → triangularity. |
| Intension–extension | A concept’s meaning or conditions of application versus what it applies to. | “Prime number” ↔ its defining condition and the primes. |
| Resemblance / family resemblance | Items are grouped through shared or overlapping similarities. | Different activities called “games.” |
| Prototype–instance | An instance is more or less typical of a category. | A robin is a more typical bird than a penguin. |
| Grounding / ontological dependence | One fact or entity depends metaphysically on others. | A set’s existence grounded in its members, on some accounts. |
| Realization / implementation | An abstract role or functional specification is fulfilled by something concrete. | A computational function realized by circuitry. |
Different relations. Different levels.
One useful way to organize these relations is to identify what kinds of things are being related. The same object can be regarded as a particular, a bearer of properties, a member of a collection, or a composed whole.
A particular and what it falls under.
Membership, instantiation, exemplification, predication, and falling under a concept.
This apple exemplifies scarlet.
A category and a broader category.
Subsumption, genus–species, determination, and conceptual implication.
Scarlet is a determinate of red.
A part and what it helps make.
Parthood, composition, aggregation, and sometimes collective membership.
A branch is part of a tree.
How does a multiplicity become a unity?
Several additional frameworks help clarify what it means to understand many things as one.
Distributive versus collective predication
A statement may apply to each member individually or only to the members together. “The students are tall” is distributive; “the students form a circle” is collective. Properties of a collective do not necessarily belong to its members.
Identity versus similarity
A class may be defined by necessary and sufficient membership conditions, whereas a category understood through family resemblance may have no single feature shared by every member. This leads toward Wittgenstein, resemblance nominalism, prototype theory, and fuzzy classification.
Extensional versus intensional individuation
Two classes can have exactly the same members while the concepts specifying them differ in meaning. Identity of extension need not imply identity of intension. This becomes particularly important in modal logic and philosophy of language.
Essential versus accidental classification
Socrates’ being human may be regarded as essential, while his being seated is accidental. Both can define classes, but they classify him in fundamentally different ways: what something is, and what happens to be true of it.
Constitution versus classification
An orchestra can be considered an organization constituted by musicians, a collective to which musicians belong, or a classifying concept that applies to certain groups. Those interpretations have different identity and persistence conditions.
What unifies the many?
The field can also be organized around the source of unity: what makes these things belong together?
On smaller screens, scroll the table sideways to read both columns.
| Principle of unity | Corresponding relation or theory |
|---|---|
| Having a common property | Exemplification, instantiation |
| Falling under a common concept | Predication, concept–object |
| Sharing a common essence | Essential predication, genus–species |
| Belonging to the same collection | Set membership |
| Being parts of one whole | Mereology, composition |
| Being manifestations of one type | Type–token |
| Sharing sufficient similarities | Resemblance, prototype theory |
| Participating in one Form | Platonic participation |
| Being specifications of something general | Determinable–determinate |
| Depending on a common explanatory basis | Grounding, realization |
| Being organized into a functional unity | Organization, collective constitution |
Five ways of understanding unity
- Extensional unity
- Unity through collection.
- Intensional unity
- Unity through conceptual content.
- Qualitative unity
- Unity through shared properties.
- Mereological unity
- Unity through composition.
- Structural or functional unity
- Unity through organization and relations.
Paths for further investigation
Aristotle’s said-of/present-in distinction, Frege’s falling-under relation, Plato’s participation relation, genus–differentia, exemplification, and collective versus distributive predication offer useful starting frameworks. Together, they open up much of the classical and contemporary problem of the One and the Many.