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

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The Ontological Minimalist: Resemblance Nominalism

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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?

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Then Question · @MayaDarmon

What are the main motivations for property nominalism?

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Motivations for Property Nominalism

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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.

Then Question · @MayaDarmon

The claim that there are no such things as properties, just lots of things which are more or less similar fails to stipulate which resemblances are significant

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The Underdetermination of Similarity: Why Resemblance Requires Selection

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# The Problem of Indiscriminate Resemblance The core vulnerability of Resemblance Nominalism lies in the non-selective nature of raw similarity. In *Seven Strictures on Similarity* (1972), Nelson Goodman demonstrated that any two objects in the universe resemble one another in infinitely many ways, and differ in infinitely many others. A billiard ball and a cherry resemble each other (both are round and red). But a billiard ball also resembles a billiard cue (both are made of processed wood/plastic and exist in a pool hall), a white dwarf star (both are dense spheres), and a printed period at the end of a sentence (both are dark circular marks on a surface). Without a criterion for **salience**, the claim that "properties are just groups of similar things" fails because everything belongs to a similarity group with everything else. Similarity is a variable, multi-dimensional relation that underdetermines property boundaries unless a background metric selects which dimensions count. ``` RAW SIMILARITY IN SPACE (Symmetrical, Multi-dimensional, Unconstrained) [ Object A ] <--- metric X ---> [ Object B ] | | metric Y metric Z v v [ Object C ] <--- metric W ---> [ Object D ] Problem: Without a predefined metric, every object resembles every other object in infinitely many, equally real respects. ``` ## The Structural Paradoxes: Imperfect Communities and Companionship Goodman formalized this failure into two foundational logical paradoxes for the nominalist attempt to construct property classes purely from resemblance: * **The Problem of Imperfect Community:** Imagine three objects: $x$ (red and round), $y$ (round and soft), and $z$ (soft and red). Every pair in $\{x, y, z\}$ shares a feature and therefore resembles the other. Yet, there is no single property shared by all three. Pure pairwise similarity creates "spurious" property classes that lack any common unifying characteristic. * **The Companionship Problem:** If two distinct properties happen to co-occur in the exact same set of objects—such as being *renate* (having kidneys) and *cordate* (having a heart)—a pure resemblance metric groups them identically. Resemblance cannot separate the two distinct respects in which the objects resemble one another. ## The Theoretical Dilemma for Nominalists To fix these structural failures, resemblance nominalists must stipulate *which* resemblances are "significant" or "property-constituting". However, this introduces a fatal dilemma: | Response Strategy | Method | Metaphysical Consequence | | :--- | :--- | :--- | | **Objective Salience** | Postulate that certain resemblances are *natively* privileged or "natural". | Sweeps real universals or sparse natural properties back in through the backdoor. | | **Cognitive Framing** | Base significance on human cognitive interest, prototype construction, or evolutionary utility. | Relativizes ontology to human psychology; properties cease to be features of objective reality. | | **Higher-Order Sets** | Require resemblance among *pairs of pairs* across higher-order hierarchies (Gonzalo Rodriguez-Pereyra). | Escalates ideological complexity to defend an ontology intended to be sparse. | Ultimately, resemblance does not explain properties; rather, the selection of relevant resemblances presupposes a framework—whether conceptual, natural, or structural—that resemblance nominalism set out to eliminate.

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Then Question · @MayaDarmon

Resemblance classes seem to be arbitrary if there is no underlying structure or entity dictating which similarities ought to be focused on

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The Arbitrariness of Similarity: Information-Theoretic and Modal Limits

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The claim that resemblance nominalism devolves into arbitrariness without an underlying structure can be deepened by examining the **information-theoretic structure of similarity space** and the **modal limits of class membership**. ``` INFORMATION-THEORETIC EXPANSION [ N-Dimensional State Space ] ---> Infinite Projections (Bit-Strings) | v [ Equal Hamming Distances ] ---> Pure Arbitrariness | v [ Pragmatic/Invariance Constraints ] ---> Non-Arbitrary Metric ``` ### The Information-Theoretic State-Space Expansion Consider an object represented as a point in an $n$-dimensional state space, where $n$ approaches infinity. Information theory demonstrates that for any finite set of objects, there exists an infinite number of orthogonal coordinate systems under which two arbitrarily chosen objects will have an identical **Hamming distance**—a measure of positional disagreement [1]. Without a privileged metric to weight these axes, the information-theoretic distance between a billiard ball and a cherry is formally equivalent to the distance between a billiard ball and the concept of justice. Similarity is not merely "multi-dimensional"; it is mathematically unconstrained without an a priori projection operator [1]. ### Modal Instability: The Fragility of Extension A critical defect of ungrounded resemblance classes emerges in modal contexts—specifically regarding **counterfactual scope**. * If the property "redness" is simply the maximal class of resembling red particulars, then the ontological boundary of "redness" changes whenever a red object is created or destroyed. * Under standard possible-world semantics (David Lewis), an object's properties depend on its counterparts across modal space [2]. * If similarity is ungrounded, an object $a$ in the actual world $W_1$ might resemble counterpart $b$ in $W_2$ along axis $X$, but resemble counterpart $c$ in $W_3$ along axis $Y$. Because there is no intrinsic structural tie binding these across worlds, resemblance classes suffer from extreme modal fragility: they cannot guarantee that an object would retain its properties under counterfactual perturbations. ### Theoretical Responses and Resolution To rescue the project without reintroducing universals, modern nominalists look to **physics-based invariants** or **pragmatic functionalism**: | Strategy | Mechanism | Metaphysical Trade-off | | :--- | :--- | :--- | | **Symmetry Groups (Physics)** | Ground resemblance in physical invariants (e.g., conserved quantities under Noether's theorem) [3]. | Restricts nominalism to micro-physics; struggles with macro-level and social properties. | | **Evo-Devo / Pragmatism** | Similarities are constrained by evolutionary niche construction and sensory-motor capacities. | Relinquishes objective metaphysics; turns properties into biological projection. | Without anchoring resemblance to fundamental physical symmetries or evolutionary constraints, similarity classes remain logically indeterminate [1, 3]. *** ### References * [1] Information-theoretic bounds on similarity metrics and dimensional projection: Cover, T. M., & Thomas, J. A. (2006). *Elements of Information Theory* (2nd ed.). Wiley-Interscience. * [2] Counterpart theory and modal properties: Lewis, D. (1986). *On the Plurality of Worlds*. Blackwell. * [3] Physical invariants and symmetry groups as grounds for fundamental properties: Brading, K., & Castellani, E. (Eds.). (2003). *Symmetries in Physics: Philosophical Reflections*. Cambridge University Press.

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The Limits of Ontological Minimalism: Why Resemblance Nominalism Remains Intact

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The objection posits that Resemblance Nominalism collapses into arbitrary projection without an external metric, information-theoretic boundary, or underlying real structure. Under its strongest formulation—the **Metric Indeterminacy Argument**—the objection asserts that: 1. **Premise 1:** Any mathematical or information-theoretic representation of concrete particulars (e.g., points in an $n$-dimensional state space) contains infinitely many orthogonal axes under which pairwise distances (such as Hamming or Euclidean distances) are invariant or arbitrary. 2. **Premise 2:** Without a privileged projection operator or objective metric to weight these axes, resemblance nominalism cannot non-arbitrarily determine which resemblance classes constitute genuine "properties". 3. **Inferential Path:** Because nominalism rejects abstract universals or objective "naturalness" metrics, it cannot define a privileged projection operator endogenously. 4. **Conclusion:** Therefore, resemblance nominalism must either accept the arbitrariness of properties or secretly presuppose the very structural or realist frameworks it claims to replace. While logically formidably constructed, this critique misidentifies the foundational claim of sophisticated nominalism. It relies on a category mistake: it superimposes a mathematical state-space model onto nominalism and then blames the metaphysics for the formal indeterminacy of that model. --- ### The Primitive Counter-Grounding: Exact Resemblance as Ontological Primitive The objection's primary hidden dependency is the assumption that similarity is a *derived, quantitative metric* calculated across abstract dimensions. Modern resemblance nominalists (most notably Gonzalo Rodriguez-Pereyra) explicitly reject this "metric-first" interpretation. In a rigorous nominalist framework: * **Resemblance is an irreducible, primitive, non-relational truthmaker.** Particulars do not resemble one another *because* they fall close together on a mathematical axis; rather, coordinate systems are formal abstractions derived from primitive, concrete resemblance relations. * **Primitive Exact Resemblance ($R$):** Nominalism does not start with arbitrary "overall similarity" across infinite dimensions. It grounds basic properties in **exact similarity** among particulars. Two electrons do not "calculate" their charge distance in a state space; their exact resemblance in mass or charge is a primitive, ungrounded metaphysical fact about reality. By treating state-space models as primary and metaphysical reality as secondary, the objection commits a **reification fallacy**. Information theory models similarity spaces using mathematical abstractions; the resemblance nominalist asserts that these abstract spaces are descriptive heuristics, not the underlying ontological engine. ``` THE REALIST/INFORMATION-THEORETIC ERROR [ Abstract Metric Space ] ---> Determines ---> [ Object Resemblance ] THE NOMINALIST REVERSAL [ Primitive Particulars ] ---> Resemble ---> [ Construct Metric Spaces ] ``` --- ### Empirical and Formal Counterevidence The claim that ungrounded nominalism cannot resist arbitrary projection or modal fragility is contradicted by both empirical formalisms in physics and rigorous modal semantics. #### 1. Empirical Proof from Quantum Field Theory (QFT) In microphysics, fundamental particles of the same species (e.g., all positrons) are non-individuated and exhibit absolute identical behavior under quantum statistical mechanics (Fermi-Dirac statistics). * **Documented Case:** Positron annihilation events in particle colliders show that positrons act strictly identically regarding mass, charge, and spin magnitude. * **Metaphysical Significance:** A resemblance nominalist does not need a "projection operator" to state that positron $A$ and positron $B$ exactly resemble each other. The physical symmetry is an empirical manifestation of primitive identity/resemblance. It is not arbitrary; it is rigidly constrained by physical reality without requiring an abstract "Positron Universal" residing outside spacetime. #### 2. Resolution of Modal Fragility via Counterpart Theory The objection claims that resemblance classes are modally fragile across possible worlds. However, under David Lewis’s **Counterpart Theory**, an object $a$ in world $W_1$ possesses a property counterfactually in world $W_2$ precisely because $a$'s counterpart in $W_2$ belongs to the relevant actual resemblance class in that world. Modal scope is not an external, ungrounded metric; it is tethered directly to counterpart relations between concrete particulars across worlds. --- ### Scope Failures and Boundary Conditions The critique correctly identifies genuine limits in resemblance nominalism, but these represent **boundary conditions** rather than a systemic refutation. | Domain / Phenomenon | Status of the Arbitrariness Objection | Nominalist Resolution | | :--- | :--- | :--- | | **Sparse / Fundamental Physics** (e.g., spin, charge) | **Fails.** Resemblance is primitive, exact, and objective. | Grounded in primitive exact resemblance of physical particulars. | | **Determinable Ranges** (e.g., "adjectival betweeenness" of colors) | **Partially Applies.** Requires explaining why orange is "between" red and yellow. | Solved by ordering exact determinates into disjunctive networks of resemblance. | | **Abundant / Social Properties** (e.g., "being a tax-deductible asset") | **Applies.** Pure resemblance cannot distinguish social constructs from physical traits. | Qualified as pragmatic/conceptual classes, shifting them out of fundamental metaphysics. | --- ### Conclusion: Qualification, Not Refutation The objection does not refute Resemblance Nominalism; rather, it **narrowly clarifies its boundaries**. The Metric Indeterminacy Argument successfully demonstrates that nominalism cannot use *derived, multi-dimensional quantitative spaces* to explain fundamental properties from scratch without encountering information-theoretic indeterminacy. However, when resemblance nominalism is correctly framed around **primitive exact resemblance among concrete particulars**, the charge of arbitrary projection fails. The argument merely proves that information-theoretic models are representational tools, not ontological grounds. *** ### References * [1] Rodríguez-Pereyra, G. (2002). *Resemblance Nominalism: A Solution to the Problem of Universals*. Oxford University Press. * [2] Lewis, D. (1983). "New Work for a Theory of Universals." *Australasian Journal of Philosophy*, 61(4), 343-377. * [3] Armstrong, D. M. (1989). *Universals: An Opinionated Introduction*. Westview Press.

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

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