Metaphysics Glossary — 68 entries, 6 categories

The 68-entry metaphysics glossary covers the four canonical registers (empirical, practical, diagrammatic, commitment), the six original-rule narrowing principles (OR1–OR6), the four-operator architecture, ontology, commitment, and phenomenology. Each entry carries a phenomenological correlate — lived-experience instantiation with concrete examples and the register codomain it lives in.

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Architecture (11)

• CI Operator Graph CI

  The CI Operator Graph (VII.D71) is the τ-categorical structural network of consequence-and-intervention operators that connects causal claims to their downstream commitments. It…

  MG-A01-ci-operator-graph

• MetaDecode Operator MetaDecode

  The MetaDecode operator (VII.D05) is the τ-categorical internal evaluator that takes an entire self-describing system (X, G, P, Φ) — including its decode map Φ — as input and pr…

  MG-A02-metadecode-operator

• τ-Modal Operators (□, ◇) □/◇

  The τ-modal operators (VII.D33) are the box (□) and diamond (◇) endofunctors that ground modal logic structurally rather than possible-world-semantically. Necessity □φ means φ i…

  MG-A03-tau-modal-operators

• Temporalization Operators T_past, T_present, T_future

  The temporalization operators (VII.D53) are the endofunctors T_past, T_present, T_future on the category Prop of propositions. Each operator relocates a proposition relative to …

  MG-A04-temporalization-operators

• Pragmatic Update Operator U_α

  The pragmatic update operator (VII.D54) is the endofunctor U_α : Disc → Disc on the category of discourse states, indexed by illocutionary type α ∈ {assert, direct, commit, expr…

  MG-A05-pragmatic-update-operator

• Operator Graph Completeness CompleteCI

  Operator Graph Completeness (VII.L28) is the structural lemma that all four components of the CI operator graph — maxim, universalization functor, coherence test, respect operat…

  MG-A06-operator-graph-completeness

• Self-Recognition as E₃ Operator 𝒜

  Self-Recognition as E₃ Operator (VII.T42) is the architectural theorem that three apparently distinct conditions are equivalent: (i) SelfDesc-of-SelfDesc at level E₃, (ii) the m…

  MG-A07-self-recognition-as-e3-operator

• Operator Realism Λ

  Operator Realism (VII.T12) is the architectural theorem that the classification of admissible continuation operators on the coherence kernel K_τ is a structural invariant: (i) t…

  MG-A08-operator-realism

• Sectoral Topology (Recognition Topology) J_rec

  Sectoral Topology (VII.L36) is the architectural lemma that the recognition Grothendieck topology J_rec is a valid topology generated by recognition morphisms, inheriting pullba…

  MG-A09-sectoral-topology

• Logos Sector Closure S_L

  Logos Sector Closure (VII.D86) is the architectural property that the Logos sector S_L = S_D ∩ S_C is closed under mutual witnessing: a content φ is S_L-admissible iff (i) φ is …

  MG-A10-logos-sector-closure

• Categorical Phenomenology Framework Π

  The Categorical Phenomenology Framework is the architectural scaffold built around the Perception Functor (VII.D44): a structure-preserving transformation from sensory contexts …

  MG-A11-categorical-phenomenology-framework

Commitment (11)

• Dignity (label-independence) Δ

  Dignity, in the τ-framework, is label-independence: a τ-categorical structural property where the moral worth of an entity does NOT depend on contingent labels (race, gender, ro…

  MG-C01-dignity

• Fairness (CI-protocol) Φ

  Fairness, in the τ-framework, is the categorical-imperative protocol over Reg_C: a τ-categorical procedure where every commitment-stance is tested for universalizability and dig…

  MG-C02-fairness

• Justice (gluing of fair stances) J

  Justice, in the τ-framework, is the sheaf-gluing of fair commitment-stances across the social base: a τ-categorical condition where local fairness verdicts (Reg_C readouts of in…

  MG-C03-justice

• Earned / Unearned framework E/U

  The Earned/Unearned framework, in the τ-framework, is a τ-categorical orthogonal factorization of every commitment-stance into an earned component (consequence of the agent's ow…

  MG-C04-earned-unearned

• Character (ethical fixed point) Χ

  Character, in the τ-framework, is the ethical fixed point of the commitment-update functor: a τ-categorical attractor of Reg_C-stance trajectories under repeated CI-testing. Cha…

  MG-C05-character

• Legitimacy (recognition coherence) Λ

  Legitimacy, in the τ-framework, is the institutional reflex of justice: a τ-categorical condition where authority's commitment-stances form a coherent section on the recognition…

  MG-C06-legitimacy

• Promise / Commitment (admissible Reg_C-update) Π

  A promise, in the τ-framework, is the canonical admissible update on the Commitment Register: a τ-categorical performative morphism that adds a directed obligation-edge to Reg_C…

  MG-C07-promise

• Responsibility / Liability (monodromy of broken stance) Ρ

  Responsibility, in the τ-framework, is the moral monodromy of a commitment-stance: a τ-categorical attribution of stance-failure to its source agent when transport of a Reg_C-se…

  MG-C08-responsibility

• Rights (dignity-protected unearned section) Ρ̂

  A right, in the τ-framework, is a dignity-protected section of the Commitment Register: a τ-categorical Reg_C-section that lives in the unearned summand and is invariant under a…

  MG-C09-rights

• Duty / Obligation (typed Reg_C-edge) Δ̂

  A duty, in the τ-framework, is a typed obligation-edge in the Commitment Register: a τ-categorical morphism in Reg_C, sourced from an agent and indexed by register and domain (V…

  MG-C10-duty

• Trust (admissibility expectation) Τ

  Trust, in the τ-framework, is the expectation of Commitment Register Admissibility: a τ-categorical relation in which one agent assigns prior probability one (or near-one) to an…

  MG-C11-trust

Ontology (13)

• Being (categorical existence) ∃_τ

  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 Rul…

  MG-O01-being

• Identity (address persistence through change) id_τ

  Identity, in the τ-framework, is NF-address persistence through a morphism sequence. An entity x and an entity y are 'the same entity' across change iff their NF-address a appea…

  MG-O02-identity

• Modality (necessity, possibility, contingency) □_τ / ◇_τ

  Modality, in the τ-framework, is grounded in admissible structure rather than possible worlds taken as primitives. Necessity (□_τ p) is invariance of p under all admissible tran…

  MG-O03-modality

• Causation (constrained composition) →_c

  Causation, in the τ-framework, is admissible factorization of morphisms in the coherence kernel. f causes g iff g decomposes as h ∘ f for some admissible h that respects the ker…

  MG-O04-causation

• Mereology (parthood as colimit) ⊑_τ

  Parthood, in the τ-framework, is the canonical injection into a colimit. A whole W is composed of parts {Pᵢ} iff W = colim(D) for a diagram D in the admissible category whose ob…

  MG-O05-mereology

• Universal (structural position) U_τ

  A universal, in the τ-framework, is a structural position in the coherence kernel — an NF-address that admits multiple instantiation-morphisms from particulars. Universals are n…

  MG-O06-universal

• Particular (instantiating source) p_τ

  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 i…

  MG-O07-particular

• Event (admissible morphism realization) ev_τ

  An event, in the τ-framework, is the realization of an admissible morphism in the coherence kernel — the application of a morphism f from one configuration to another, indexed b…

  MG-O08-event

• Property (instantiation morphism) F_τ

  A property, in the τ-framework, is an admissible morphism from a particular to a universal — the instantiation morphism itself. 'a is F' is rendered f : a → U where U is the NF-…

  MG-O09-property

• Relation (multi-source admissible morphism) R_τ

  A relation, in the τ-framework, is an admissible morphism (or admissible diagram) connecting multiple particulars to a shared structural position — either a universal or a colim…

  MG-O10-relation

• Time (persistence-induced order) T_τ

  Time, in the τ-framework, is derived — not a primitive container. The persistence relation on NF-addresses (VII.D34) induces a partial order on temporal configurations (VII.P06)…

  MG-O11-time

• Truth-bearer (proposition as section) P_τ

  A truth-bearer, in the τ-framework, is a section of a presheaf — a structural object, not a linguistic entity. Propositions are sections of the truth-functor over the worlds-pre…

  MG-O12-truth-bearer

• Reality (recoverable kernel field) ℛ_τ

  Reality, in the τ-framework, is the field of NF-addresses that is jointly recoverable across all four registers — the maximal coherent structure that survives the OR1–OR6 narrow…

  MG-O13-reality

Phenomenology (11)

• Qualia (subsymbolic morphisms) Q

  Qualia are τ-categorical subsymbolic internal morphisms within the Mind-Topos: the sub-level structural elements of phenomenal experience that resist verbal/symbolic encoding. T…

  MG-H01-qualia

• Intentionality (aboutness as morphism) Int

  Intentionality is τ-categorical aboutness: the directional internal morphism in the Mind-Topos that takes a representation to its intentional object. It is not a mysterious extr…

  MG-H02-intentionality

• Mind-Topos Structure M_τ

  The Mind-Topos is the τ-categorical structure that any system possessing genuine mindedness instantiates: an internal topos on the system's carrier whose objects are representat…

  MG-H03-mind-topos

• Subjectivity (first-person perspective) FP

  Subjectivity — the first-person perspective — is τ-categorically the structural property of a Mind-Topos to admit a *global section* that points to itself: the system has a vant…

  MG-H04-subjectivity

• Aesthetics — beauty as scale-invariant morphism B

  Beauty in the τ-framework is τ-categorical structural invariance: a structure is beautiful when it survives the action of the admissible-transformation group of its motif-space …

  MG-H05-aesthetics

• Sublime (comprehension boundary) Sub

  The sublime is τ-categorically the *comprehension boundary phenomenon*: the structural event in which a finite observer encounters a structure whose invariance pattern overwhelm…

  MG-H06-sublime

• Narrative structure (story functor) St

  Narrative structure is τ-categorically the *Story Functor*: a functor St : Episodes → M_τ that maps lived episodes (events, encounters, decisions) into the agent's Mind-Topos wi…

  MG-H07-narrative

• Language and meaning (subsymbolic self-enrichment) L

  Language is τ-categorically the self-enrichment of the subsymbolic layer (VII.T20): the system acquires the capacity to name and transport its own pre-symbolic patterns. Meaning…

  MG-H08-language-meaning

• Symbol / sign relation Sym

  A symbol is τ-categorically a *readout* on the subsymbolic layer: a structure-preserving morphism Sym : SubSym → Layer_L that names a subsymbolic pattern in the linguistic layer…

  MG-H09-symbol

• Truth as register-readout (section-existence) T

  Truth in the τ-framework is τ-categorically *section-existence*: a proposition is true iff its truth-bearer (a section of a presheaf, VII.D61) is supported by a truth-maker (a s…

  MG-H10-truth

• Self-Recognition (E₃ operator) SR

  Self-Recognition is τ-categorically the E₃ operator (VII.T42): the SelfDesc-of-SelfDesc structure that closes the awareness-of relation reflexively, terminating the would-be inf…

  MG-H11-self-recognition

Principle (11)

• OR1 Self-Coherence OR₁

  OR1 is the first of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the self-coherence requirement: any τ-categorical reality candidate m…

  MG-P01-or1-self-coherence

• OR2 Finite Signature OR₂

  OR2 is the second of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the finite-signature requirement: any τ-categorical reality candidat…

  MG-P02-or2-finite-signature

• OR3 Diagonal-Free Self-Reference OR₃

  OR3 is the third of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the diagonal-free self-reference requirement: any τ-categorical reali…

  MG-P03-or3-diagonal-free-self-reference

• OR4 NF-Addressability OR₄

  OR4 is the fourth of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the address-centric access requirement: every admissible constructio…

  MG-P04-or4-nf-addressability

• OR5 Holomorphic Continuation OR₅

  OR5 is the fifth of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the holomorphic continuation requirement: any τ-categorical reality c…

  MG-P05-or5-holomorphic-continuation

• OR6 Spectral Completeness OR₆

  OR6 is the sixth of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the spectral completeness requirement: any τ-categorical reality cand…

  MG-P06-or6-spectral-completeness

• Six Ontic Requirements (OR1-OR6) OR₁..₆

  The Six Ontic Requirements (VII.D37) are six independent narrowing principles that any candidate foundation of reality — any category proposed as an ontic substrate — must satis…

  MG-P07-six-ontic-requirements

• Layer Discipline (Register Discipline) Reg-typing

  Layer Discipline (also: register discipline) is the methodological principle that every claim must be typed in the correct register (Reg_E, Reg_P, Reg_D, Reg_C) and that coheren…

  MG-P08-layer-discipline

• Earned / Unearned Ethics Framework earned/unearned

  The Earned / Unearned Ethics Framework (VII.D74) is the methodological principle that an ethical claim carries probative weight only if it is (i) register-typed, (ii) structural…

  MG-P09-earned-unearned

• Independent Necessity of Each Ontic Requirement OR_i ⊥ OR_{≠i}

  Independent Necessity (VII.P08) is the principle that each of the Six Ontic Requirements is independently necessary: dropping any one OR_i while retaining the other five admits …

  MG-P10-independent-necessity

• Truth-Bearer as Section s ∈ Γ(F, U)

  The Truth-Bearer principle (VII.D61) states that anything that can be true or false is, structurally, a candidate global section of a presheaf F : τ^op → Set over an open cover …

  MG-P11-truth-bearer

Register (11)

• Empirical Register (Reg_E) Reg_E

  The Empirical Register Reg_E is the τ-categorical readout functor whose codomain is Obs (observations): the structural interface between the τ-framework and falsifiable empirica…

  MG-R01-empirical-register

• Practical Register (Reg_P) Reg_P

  The Practical Register Reg_P is the τ-categorical readout functor whose codomain is Norm (normative constraints): the structural interface between the τ-framework and action-gui…

  MG-R02-practical-register

• Diagrammatic Register (Reg_D) Reg_D

  The Diagrammatic Register Reg_D is the τ-categorical readout functor whose codomain is Proof (structural proofs): the interface between the τ-framework and proof-bearing content…

  MG-R03-diagrammatic-register

• Commitment Register (Reg_C) Reg_C

  The Commitment Register Reg_C is the τ-categorical readout functor whose codomain is Stance (stance-constituted contents): the interface between the τ-framework and performative…

  MG-R04-commitment-register

• Empirical Sector (S_E) S_E

  The Empirical Sector S_E is the collection of all E_3-admissible contents whose coherence is governed by the Empirical Register Reg_E. Formally, S_E = { c ∈ Adm_{E_3} | Coh(c) =…

  MG-R05-empirical-sector

• Practical Sector (S_P) S_P

  The Practical Sector S_P is the collection of all E_3-admissible contents whose coherence is governed by the Practical Register Reg_P. Formally, S_P = { c ∈ Adm_{E_3} | Coh(c) =…

  MG-R06-practical-sector

• Diagrammatic Sector (S_D) S_D

  The Diagrammatic Sector S_D is the collection of all E_3-admissible contents whose coherence is governed by the Diagrammatic Register Reg_D. Formally, S_D = { c ∈ Adm_{E_3} | Co…

  MG-R07-diagrammatic-sector

• Commitment Sector (S_C) S_C

  The Commitment Sector S_C is the collection of all E_3-admissible contents whose coherence is governed by the Commitment Register Reg_C. Formally, S_C = { c ∈ Adm_{E_3} | Coh(c)…

  MG-R08-commitment-sector

• Logos Sector (S_L) S_L

  The Logos Sector S_L is the unique mixed sector at E_3 where the diagrammatic register and the commitment register coincide. Formally, S_L = { c ∈ Adm_{E_3} | Coh_D(c) = Coh_C(c…

  MG-R09-logos-sector

• Register Completeness (Mediator Uniqueness) VII.P30

  Register completeness is the structural fact that the four canonical registers (Reg_E, Reg_P, Reg_D, Reg_C) exhaust the modes of engagement available to a self-modelling observe…

  MG-R10-register-completeness

• Register-Enrichment Correspondence VII.D75

  The Register-Enrichment Correspondence is the order-preserving mapping between the four registers of reason and the four enrichment layers of τ: Reg_P ↔ E_0 (pre-structural), Re…

  MG-R11-register-enrichment-correspondence