Particular (instantiating source)
A particular, in the τ-framework, is an NF-addressable object that figures as the source of instantiation morphisms targeting universals — and whose identity through change is its address persistence. Particulars are not bare substrata bearing properties from outside; they are loci in the coherence kernel from which property-instantiations originate. Particularity is dual to universality: same NF-addresses, opposite morphism-direction.
τ-Definition
A particular, in the τ-framework, is an NF-addressable object that figures as the source of instantiation morphisms targeting universals — and whose identity through change is its address persistence. Particulars are not bare substrata bearing properties from outside; they are loci in the coherence kernel from which property-instantiations originate. Particularity is dual to universality: same NF-addresses, opposite morphism-direction.
Categorical invariant. p is particular ⟺ p ∈ NF-Addr ∧ ∃ f ∈ AdmMor : src(f) = p ∧ tgt(f) is universal.
Primary registry anchor:
VII.D34
τ-Derivation Chain
-
VII.D25— Internal Set Ontology — particulars are NF-addressable. -
VII.D34— Identity as Address Persistence — particulars retain identity through morphism sequences via address persistence. -
VII.D36— Abstract Object as Structural Position — particulars (concrete and abstract) are positions in structures. -
VII.D40— Non-Dualistic Platonism — particulars and universals share one ontology; particulars are sources, universals are codomains.
Lean modules referenced:
TauLib.BookVII.Meta.Registers
Phenomenological Correlate
A particular is instantiated whenever we identify 'this' — this stone, this person, this proof, this commitment. The grammatical subject of an instantiation claim ('this apple is red') points to a particular: the source of the redness-instantiation morphism. Particularity is local — anchored to an NF-address — but it is not bare; it inherits all the structure encoded in its outgoing admissible morphisms.
Examples:
- Empirical: this apple — an NF-address in the perceptual category whose outgoing morphisms instantiate redness, sweetness, sphericity, and so on (in Reg_E).
- Personal: this person — an NF-address whose persistence through biographical morphism sequences gives personal identity (VII.D34) and whose instantiation-morphisms populate normative profiles (in Reg_P).
- Proof-theoretic: this proof — an NF-address whose outgoing morphisms target the theorem and the lemmas it instantiates (in Reg_D).
- Commitment-theoretic: this promise — an NF-address whose outgoing morphisms instantiate the promised-act and the obligation-stance (in Reg_C).
Register codomain: Cross-register (every register supplies particulars; particularity is the source-side of instantiation in any register).
Manuscript reference: manuscript-sources/book-07/part02/ch26.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookVII.Meta.Registers
Lean kind: structure
Lean symbol: Tau.BookVII.Meta.Registers.IdentityAsAddressPersistence