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?

While the denial of universals is often framed as mere ontological thrift, the deepest motivations for property nominalism extend far beyond basic parsimony. They stem from profound epistemological, causal, and semantic pressures that challenge the coherence of realist metaphysics. ``` MOTIVATIONS FOR PROPERTY NOMINALISM EPISTEMIC ACCESSIBILITY CAUSAL CLOSURE (How can we know abstracta?) (Abstract objects cannot act) \ / \ / v v [ NOMINALIST ONTOLOGICAL FRAMEWORK ] | v NATURALISTIC ADEQUACY (Eliminates abstract mystery) ``` ### The Epistemic and Causal Imperatives The primary driver for nominalism is the **Epistemic Access Problem**, famously articulated by Paul Benacerraf against mathematical platonism and adapted widely across metaphysics. If universals are non-spatiotemporal, abstract entities, they lack causal efficacy. How, then, can physical organisms operating within a spatiotemporal realm interact with or acquire knowledge of them? Realism creates an unbridgeable explanatory gap between the abstract realm of properties and human cognitive mechanisms. Nominalism resolves this by anchoring all truth-makers in concrete, epistemically accessible particulars. Closely tied to this is the principle of **Causal Closure** in physicalism: only entities capable of entering into causal networks are explanatory. Abstract universals do no work in empirical science. A physician diagnoses a condition based on concrete cellular structures and biochemical cascades, not by appealing to an abstract "disease universal." By refusing to multiply entities beyond necessity—a strict application of *Ockham's Razor*—nominalism keeps ontology aligned with naturalistic science. ### The Semantic and Mereological Puzzles of Realism Nominalism is also motivated by internal paradoxes within realist frameworks, particularly regarding instantiation: * **The Problem of Spatial Location:** Realists must claim that a single universal (e.g., "whiteness") is fully present in a snowflake in Canada and a swan in Australia simultaneously. Nominalists argue that this violates fundamental mereological intuitions—the principle that an entity cannot be wholly present in two disjoint spatial locations at once. * **Bradley's Regress:** Formulated by F.H. Bradley, if an object $a$ instantiates a universal $F$, there must be a tie or relation of *instantiation* holding them together. But if instantiation is itself a relational universal, it requires a higher-order relation to connect it to $a$ and $F$, triggering a vicious infinite regress. Nominalism avoids this by refusing to treat instantiation as an extra entity in the universe. By grounding state-affairs entirely in concrete particulars, nominalism preserves a unified, naturalistic worldview free from abstract, causally inert entities.