Con-E.10 — Mereological Framework Has Known Limits for Abstract Entities#

Severity: E (Moderate) | Sphere: Se1 | Target: ax1–ax4 (PET axioms)

The PET system uses classical extensional mereology (CEM) for the parthood relation \(\leq\). CEM has well-known problems when applied to abstract entities:

  1. Extensionality: Objects with exactly the same proper parts are identical. If two possible worlds have the same physical parts but differ in moral or modal properties, CEM would identify them — which is metaphysically problematic.

  2. Unrestricted composition: Any two objects have a mereological sum. Applied to the God-world relation, this yields unintuitive entities (the sum of God’s left-hand knowledge and the Eiffel Tower is a well-defined mereological object).

  3. Application to God: Classical theology has resisted applying part-whole reasoning to God because it makes God composite, threatening aseity (self-existence) and simplicity. The PET system acknowledges this tension (ax11 vs. ax11b) but does not resolve it — it simply chooses the dipolar side.

Steel-man: Varzi (2016) documents CEM’s limitations for abstract objects. Simons (1987) develops non-extensional mereologies that avoid some of these problems but sacrifice the formal simplicity PET relies on. Brower (2008) defends divine simplicity (ax11b) against dipolar alternatives, arguing the tension with ax1 + ax3 can be resolved within classical theism.

(Source: C10 from OOv1 Critique Round 1.)