Being (categorical existence)

Being, in the τ-framework, is categorical existence: an object x exists ontically iff x is the codomain of at least one register's image-functor, satisfying all six Original Rules (OR1-OR6). Being is not a primitive predicate — it is derived from set-ontology (VII.D25) and the register architecture.

Categorical invariant. x ∈ Being ⟺ ∃ Reg ∈ {E,P,D,C} : x ∈ image(Reg) ∧ x satisfies OR1-OR6.

Primary registry anchor: VII.D25

Supporting items: VII.D32, VII.D37, VII.D01

1. I.K0 — Universe Postulate
2. VII.D01 — Empirical Register defines the first readout
3. VII.D25 — Internal Set Ontology — being is set-membership in the τ-image
4. VII.D37 — OR1-OR6 narrowing rules constrain candidate beings

Being is instantiated whenever we say 'X exists' in any of the four registers: empirical existence (Reg_E — measurable), normative existence (Reg_P — ethical/legal/social), proof existence (Reg_D — theorem-proven), commitment existence (Reg_C — agent-committed). A unified ontology bridges these.

Examples:

• Empirical: 'electrons exist' (image of Reg_E containing electron-observation-types)
• Normative: 'human dignity exists' (image of Reg_P containing dignity-as-norm)
• Proof: 'prime numbers exist' (image of Reg_D containing prime-existence theorem)
• Commitment: 'promises exist' (image of Reg_C containing commitment-stances)

Register codomain: Cross-register (Being spans all four registers; an object ontically exists if it appears in any register's image)

Manuscript reference: manuscript-sources/book-07/part03/ch15-ontology.tex

Status: Planned

Related glossary entries

• MG-R01-empirical-register Empirical Register (Reg_E)
• MG-P01-or1-self-coherence OR1 Self-Coherence

Referenced by

• MG-A02-metadecode-operator MetaDecode Operator
• MG-A07-self-recognition-as-e3-operator Self-Recognition as E₃ Operator
• MG-O02-identity Identity (address persistence through change)
• MG-O03-modality Modality (necessity, possibility, contingency)
• MG-O05-mereology Mereology (parthood as colimit)
• MG-O06-universal Universal (structural position)
• MG-O07-particular Particular (instantiating source)
• MG-O12-truth-bearer Truth-bearer (proposition as section)
• MG-O13-reality Reality (recoverable kernel field)