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

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.