Let's discuss the idea that there are no such things as properties, just lots of things which are more or less similar

How do two distinct physical objects—such as a ripe tomato and a stop sign—share the exact same feature, such as being "red"? In metaphysics, the standard *realist* response posits the existence of **universals**: abstract, repeatable entities that exist over and above individual things and are instantiated by them. The thesis you have introduced is the core commitment of **Resemblance Nominalism**, an elegant alternative within *nominalism* (the denial of abstract entities). It claims that the fundamental furniture of the world consists solely of concrete particulars; properties do not exist as independent metaphysical items. Instead, an object is "red" simply because it resembles a set of other concrete, red objects. ``` THE METAPHYSICAL DIVIDE REALISM RESEMBLE NOMINALISM (Universals exist) (Only particulars exist) [ Universal ] [ Object A ] / \ \ resembles [ Object A ] [ Object B ] [ Object B ] ``` ### Mechanisms and Logical Architecture To understand how this operates, consider how a resemblance nominalist constructs what we ordinary speakers call "properties": 1. **Primitive Resemblance:** Resemblance is treated as an irreducible, primitive relation. Objects do not resemble one another *because* they share a property; rather, we say they share a property *because* they resemble one another. 2. **Equivalence Classes:** A "property" is reinterpreted as a maximal group of particulars that resemble each other to a requisite degree. 3. **Paretian / Paradigm Models:** Some versions select paradigm instances (e.g., a standard reference meter or a ideal sample of red) and define membership in a property class by an object’s degree of similarity to those paradigms. ### The Core Debates: Russell’s Regress and Coextension Despite its intuitive appeal, Resemblance Nominalism faces two classical objections in analytic metaphysics: * **Russell’s Regress:** Formulated by Bertrand Russell in *The Problems of Philosophy* (1912), this argument asserts that if you eliminate properties by invoking a relation of *resemblance*, you must explain what all individual acts of resemblance have in common. They must resemble each other, requiring a higher-order resemblance relation, triggering an infinite regress. Russell argued this proves that at least *one* universal—the relation of resemblance itself—must exist. Modern nominalists, such as Gonzalo Rodriguez-Pereyra, counter that resemblance is a multigrade relation that applies directly to particulars without constituting a repeatable universal. * **The Problem of Coextensive Properties:** If two distinct properties belong to the exact same set of objects in the actual world (for example, *renate* [having kidneys] and *cordate* [having a heart]), resemblance nominalism risks treating them as identical because the set of resembling objects is identical. Resolving this often forces nominalists to extend their scope to *possible* objects across modal space, importing heavy cosmological commitments to preserve a lean ontology. ### Broad Implications Resemblance Nominalism aligns closely with cognitive science theories of categorization, such as **prototype theory**, where human concepts are structured around similarity to central exemplars rather than strict, necessary-and-sufficient features. Economically, it offers a sparse ontology—reducing the universe to concrete entities and their concrete relationships—though critics argue that it merely sweeps metaphysical complexity under the rug of "primitive similarity". ## Follow-up questions 1. How does resemblance nominalism handle cases where two distinct properties happen to be possessed by the exact same set of objects? 2. Does Bertrand Russell’s regress argument successfully force the resemblance nominalist to accept at least one universal? 3. How do modern prototype theories in cognitive psychology mirror or challenge the philosophical assumptions of resemblance nominalism?

The charge that Resemblance Nominalism turns all qualitative features into **extrinsic properties**—qualities an entity possesses in virtue of its relations to *other* things—represents one of the most counterintuitive tension points in contemporary metaphysics. ### The Intuition of Intrinsicality Intuitively, an isolated sphere in a vacant universe would still be round; its shape is an **intrinsic property** (determined solely by the object itself). Under standard Resemblance Nominalism, however, an object $a$ is round because it belongs to a maximal class of mutually resembling particulars. This creates an immediate conceptual paradox: $$\text{Object } a \text{ is round} \iff \text{Resembles}(a, b, c, \dots)$$ If $a$'s qualitative nature is constituted by its primitive resemblance relations to distinct entities $b$ and $c$, then $a$'s "roundness" depends on the existence and character of things outside itself. Were all other objects erased, the resemblance relations would collapse, apparently stripping $a$ of its qualities. ``` INTRINSIC REALISM EXTRINSIC RESEMBLE NOMINALISM (Quality grounded locally) (Quality grounded relationally) [ Object A ] [ Object A ] | / \ Instantiates: Roundness Resembles Resembles | / \ (Inherent) [ Object B ] [ Object C ] ``` ### Truthmakers vs. Identity: The Nominalist Counter-Strategy To resist this threat of global extrinsicality, modern proponents like Gonzalo Rodríguez-Pereyra draw a crucial distinction between **metaphysical truthmakers** and **intrinsic natures**: 1. **Internal Relations:** Resemblance is an *internal relation*—a relation that supervenes entirely on the intrinsic natures of its relata. It obtains *because* of how the particulars are in themselves, without needing an external "bridge" or third-party universal. 2. **Modal Scope:** To prevent a lonely object from losing its properties, nominalists extend the resemblance class across modal space. Object $a$ remains round even if alone in the actual world because it retains primitive resemblance to *possibilia*—merely possible round particulars in other counterfactual worlds. ### Comparative Trade-Offs | Metaphysical Framework | Primary Explanation of "a is Red" | Ontological Cost | Handing of Intrinsicality | | :--- | :--- | :--- | :--- | | **Realism (Universals)** | $a$ instantiates the universal *Redness*. | Abstract, repeatable entities. | Preserved directly (local instantiation). | | **Trope Theory** | $a$ possesses a particular, unrepeatable trope ($red_1$). | Abstract particulars (tropes). | Preserved directly (local trope). | | **Resemblance Nominalism** | $a$ primitives-resembles all other actual/possible red particulars. | Concrete possibilia / Counterfactual worlds. | Preserved indirectly via internal relations across modal space. | By relocating the grounding of qualities to cross-world resemblance networks, Resemblance Nominalism saves its sparse baseline ontology, but at the cost of requiring an expansive framework of possible worlds to keep basic physical qualities intrinsic. *** ## References * **Armstrong, D. M.** (1978). *Universals and Scientific Realism*. Cambridge University Press. * **Lewis, D.** (1986). *On the Plurality of Worlds*. Blackwell. * **Rodríguez-Pereyra, G.** (2002). *Resemblance Nominalism: A Solution to the Problem of Universals*. Oxford University Press.

If Resemblance Nominalism must construct an object’s qualitative nature out of similarity relations to other entities, it generates a cascade of theoretical and structural consequences. To resolve the Extrinsicality Dilemma, nominalists traditionally rely on two strategies: either grounding resemblance in **modal realism** (the existence of concrete parallel worlds) or accepting **primitive internal relations** (relations that hold solely by virtue of the intrinsic natures of their relata). Tracing the implications reveals how this metaphysical choice dictates commitments across physics, epistemology, and formal logic. ``` THE EXTRINSICALITY FORK | +----------------------+----------------------+ | | [ Strategy A: Modal Realism ] [ Strategy B: Primitivism ] | | Requires concrete possibilia Resemblance holds as an across possible worlds. un-grounded brute fact. | | Implication: Massive expansion Implication: Explanation stops; of universe's baseline ontology. semantic circularity looms. ``` --- ## 1. Conceptual Implications: The Modal Explosion and Inflationary Ontology If an isolated object $a$ retains its shape only because it resembles other possible objects, the nominalist must explain what these non-actual entities are. * **Immediate Consequence:** To maintain that shape is an intrinsic feature without instantiating an abstract universal, the nominalist must accept David Lewis’s **Modal Realism**—the thesis that unactualized possible worlds exist as concrete, physical spatio-temporal systems [1]. * **The Conceptual Paradox:** The central motivation for nominalism is *ontological parsimony* (Ockham’s Razor): eliminating abstract entities like universals to keep the universe simple. However, saving nominalism from the Extrinsicality Dilemma requires accepting an infinite number of concrete alternative universes. * **Evaluation:** This represents a logical consequence within the framework. The nominalist trade-off replaces *qualitative* dishonesty (inventing abstract universals) with *quantitative* inflation (inventing concrete worlds). --- ## 2. Uncomfortable Implications: Explanatory Inversion and Semantic Circularity In classical metaphysics, an object’s relations depend on its intrinsic nature: a billiard ball collides *because* it has mass and momentum. Resemblance Nominalism flips this order of explanation. | Dimension | Standard Realism / Trope Theory | Resemblance Nominalism | | :--- | :--- | :--- | | **Direction of Grounding** | $a$ has a property $\rightarrow$ $a$ resembles $b$. | $a$ resembles $b$ $\rightarrow$ $a$ has a property. | | **Explanatory Basis** | **Local:** Intrinsic nature grounds the relation. | **Relational:** Similarity network grounds the nature. | | **Philosophical Risk** | Ontological bloat (abstract entities). | Explanatory circularity / Brute facts. | * **The Counterintuitive Conclusion:** If resemblance is primitive, we cannot say two electrons repel because they share the intrinsic property of negative charge. Rather, their "charge" is constituted by the global resemblance class of all negative particulars. * **The Threat of Circularity:** If the nominalist counters that resemblance is an *internal relation* (holding solely because of how the relata are "in themselves"), a severe semantic tension arises. If the relata are "a certain way in themselves," they possess intrinsic qualitative natures. But if those intrinsic natures are themselves reducible to resemblance relations, the theory becomes conceptually circular. --- ## 3. Second-Order Implications for Physicalism and the Sciences The tension between extrinsicality and intrinsicality directly impacts contemporary philosophy of science, particularly **Ontic Structural Realism (OSR)** and quantum mechanics [2]. ``` PHYSICAL FOUNDATIONS IN TENSION Quantum Entanglement Resemblance Nominalism (State determined holistically) (Grounded in discrete particulars) \ / \ / Tension: Is fundamental reality relational structures or discrete, primitive objects? ``` * **Alignment with Relational Physics:** Modern quantum mechanics demonstrates that fundamental particles lack definite intrinsic properties independent of their measurement context or entangling relations. The relational architecture of Resemblance Nominalism fits neatly with quantum holism, where an entity's physical state is defined via structural relations rather than isolated intrinsic essences [2]. * **Disruption of Local Physicalism:** Conversely, standard physicalism assumes *micro-physical intrinsicality*—that the physical world is built bottom-up from local micro-entities with inherent physical constants (like mass and spin). If Resemblance Nominalism is true, a single fundamental particle cannot possess its mass in isolation. Its physical identity depends on the global configuration of the universe (or multiverse), challenging traditional bottom-up physical reductionism [3]. --- ## Direct Logical Map of Implications 1. **If** an object's properties are defined by similarity relations to other objects... 2. **Then** an isolated object's properties depend on counterfactual or possible entities... 3. **Which requires** an ontology of possible worlds (Modal Realism) to avoid property collapse... 4. **Resulting in** an inflationary ontology that undermines nominalism's original goal of parsimony. --- ## References * **[1] Lewis, D.** (1986). *On the Plurality of Worlds*. Blackwell. * **[2] Ladyman, J., & Ross, D.** (2007). *Every Thing Must Go: Metaphysics Naturalized*. Oxford University Press. * **[3] Rodríguez-Pereyra, G.** (2002). *Resemblance Nominalism: A Solution to the Problem of Universals*. Oxford University Press.