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 challenge of coextensive properties arises when two intuitively distinct properties belong to the exact same set of objects. If being *cordate* (having a heart) and being *renate* (having kidneys) apply to identical entities in the actual world, how can a resemblance nominalist argue that "having a heart" is not identical to "having a kidneys"? Resemblance nominalism deploys two strategies depending on whether the coextension is contingent or necessary. ### 1. Contingent Coextension: Expanding to Modal Space For properties that happen to co-occur in our world by empirical coincidence, the prominent nominalist solution—pioneered by thinkers like David Lewis and expanded by Gonzalo Rodriguez-Pereyra—is to widen the domain of objects to include non-actual, possible particulars. By adopting **modal realism**, the set defining a property consists of all concrete objects that possess it across all possible worlds. ``` ACTUAL WORLD POSSIBLE WORLDS [Object A] (Heart + Kidney) <---> [Object C] (Heart only) ---> Included in "Cordate" class [Object B] (Heart + Kidney) <---> [Object D] (Kidney only) ---> Included in "Renate" class Result: The cross-world "Cordate" and "Renate" classes contain different members. ``` Because there are possible worlds containing creatures with hearts but no kidneys, the *trans-world resemblance class* for "cordate" differs from that of "renate". The properties remain distinct because their membership diverges across modal space. ### 2. Necessary Coextension: The Identity Defense and Predicate Asymmetry When coextension holds across *all* possible worlds—such as *trilateral* (having three sides) and *triangular* (having three angles)—modal expansion fails. Resemblance nominalism handles this via two competing maneuvers: | Strategy | Mechanism | Metaphysical Consequence | | :--- | :--- | :--- | | **Property Identity** | Denies that necessary coextension reflects two distinct properties. | "Trilateral" and "triangular" are merely two names for the *same* underlying resemblance class of objects. | | **Hyperintensional Distinctions** | Distinguishes properties not by objects, but by *primitive relations*. | Objects resemble one another along different relational axes (e.g., side-resemblance vs. angle-resemblance). | The ultimate cost for the resemblance nominalist is ideological: to keep their ontology free of universals, they must accept either counterintuitive property identities or a vast landscape of concrete possible worlds.