Source
Achille Varzi, “Mereology”, Stanford Encyclopedia of Philosophy, LIT-124 (revision of 27 June 2026), read in full in NOTE-163, §§2.1–5.
What was actually shown
The core is contested (§2.1). Each axiom of Core Mereology has dissenters. Against Reflexivity: Kearns’s time-travel and fractal cases. Against Transitivity: functional or “φ-part” readings, multilocation and Frege’s Etna argument. Against Antisymmetry: Thomson’s statue and clay, the Net of Indra, perichoresis, time-travel walls and structured propositions. Antisymmetry “can hardly be regarded as constitutive of the basic meaning of ‘part’”. The section ends with Donnelly’s (2011: 246) doubt that “any useful core mereology” is common to all plausible theories. M is “the common starting point of all standard theories” (§2.2), a claim about what is standard.
Equivocation removes some objections, not all. Most ordinary-language objections to Reflexivity and Transitivity equivocate between “part” and a restricted “φ-part” (Simons 1987: 107f). The genuine threats are metaphysical: time travel, multilocation and structured propositions.
Beyond the core (§§3–4). Supplementation is “a minimal but substantive addition”, with Brentano’s accidents, Fine’s singletons, Whitehead’s boundary-free regions and coincidence cases against it. Extensionality needs Antisymmetry as well as Strong Supplementation, so a non-antisymmetric theory can keep Strong Supplementation without extensionality (Cotnoir and Bacon 2012). Composition principles: restricted ones give only sufficient conditions and, made biconditional, face the sorites; universalism is defended by Lewis’s argument from vagueness and charged with ontological exuberance. The Special Composition Question has no agreed answer.
Interaction effects. The additions interact in ways easy to miss. Supplementation with Reflexivity and Transitivity entails Antisymmetry. Supplementation with products for overlappers entails Strong Supplementation and so extensionality. How a sum is defined changes which theory an unrestricted-sum axiom produces (THEORY-493).
What could have come out otherwise. Some principle could have had no serious dissent. The survey finds none.
What this does not say
- That the core is false. It says no axiom is safe as a meaning postulate. The entry still builds on M.
- That every principle is equally contested. The entry calls bounds for overlapping things, (P.11ξ) with ξ = O, “rather uncontroversial” (§4.1), so its own headline in §4.5 overstates its treatment.
- That the survey is neutral. Varzi is a known extensionalist, and §3.2 and §4.5 give the extensionalist replies the last word, though the objections are reported fairly.
- That the biological or systems senses of “part” are covered. Note 1 excludes the systems-theory and ecological senses of “mereology”, and note 18 quantum part–whole formalisms.
- That a restricted part relation is a rival to parthood. A φ-part (a functional part, a component, a body part for moral purposes) need not be transitive even when P is. The entry treats such relations as restrictions.
Connections
- The record’s mereology topic. NOTE-163 recommends reading the biological-individuality works (LIT-005, LIT-049, LIT-157, LIT-188, LIT-142) as answering a restricted “which collectives count as individuals of a kind” question, not the Special Composition Question about P. A THEORY on biological individuation would need to decide which it is.
- Register (LIT-138, THEORY-540) proposes exactly such a restriction: a moral body-part relation that is not the transitive closure of ordinary parthood.
- Lewis (LIT-1015, THEORY-452) holds a de dicto account of vague parthood, on which, as §5 reports, the axioms need no revision.
- Mutual dependence. The non-wellfounded mereologies of §2.1 parallel Morganti’s symmetric ontological dependence (LIT-173), which is about dependence, not parthood.