\============================================================ CAPUT ARS BREVIS K — DE SUBIECTIS ET INSTRUMENTIS Ars Generalis Applied — Knowledge Base Layer Version: 0.2.0-CAPUT-AB-K-ROSETTA-NORMALIZED Status: STABILIZED / INTERPRETATIVE \+ OPERATIONAL (NORMALIZED) Scope: Ars Brevis — Part 9 (The Nine Subjects), with AGU-supported expansion Authority: ARS BREVIS / ARS GENERALIS ULTIMA Mutation Policy: VERSION-CONTROLLED ONLY Class: AEGIS / CAPUT \============================================================ (Latin: De Subiectis et Instrumentis) PURPOSE \------------------------------------------------------------ This CAPUT presents Subjects and Instrumentative Domain as: • L1 — Scholastic exposition • L2 — Operator form • Binding — explicit equivalence layer This artifact functions as: • interpretative key for Part IX • Rosetta bridge for subject-domain reading • anti-drift stabilization of subiecta and instrumenta It preserves: • the nine subjects as finite ontological order • principial application across subjects • subject distinction, concordance, and nobility • the instrumentative domain as operative extension • virtue / vice as generated instrumental species • mixture as epistemic access, not ontological generation \------------------------------------------------------------ CAPUT STATUS CLARIFICATION \------------------------------------------------------------ This CAPUT is a Rosetta artifact. It is not: • a runtime layer • an execution contract • a deployment artifact Proto-computational wording is retained intentionally where it helps preserve Llullian intelligibility for cross-reading and later extraction. Risk is mitigated here by framing and closure, not by erasing high-density constructions. \============================================================ PRINCIPLE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ All that exists is contained within a finite set of subjects. (Latin: Omne quod est, continetur intra finitum subiectorum numerum.) These subjects are: • ontological domains (subiecta) • fields of application for principles (A, T) • carriers of mixture (combinatio) (Latin: Haec subiecta sunt dominia ontologica (subiecta), campi applicationis pro principiis (A, T), vehicula mixtionis (combinatio).) Subjects are not generated here. Subjects are: • epistemically accessed through mixture • ontologically presupposed as a closed set • combinatorially open in expression (Latin: Subiecta non generantur hic; sunt epistemice accessa per mixturam, ontologice praesupposita ut clausum numerum, combinatorie aperta in expressione.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ SUBJECT\_SET := finite ontological domain set access(S) := via MIX(P, R) Where: P := {A, T} R := rules \------------------------------------------------------------ Binding \------------------------------------------------------------ “finite set of subjects” ⇔ closed ontological domain set “accessed through mixture” ⇔ epistemic access by principial/rule articulation “open in expression” ⇔ combinatorial extensibility of discourse \------------------------------------------------------------ REGIME LOCK \------------------------------------------------------------ L1 — Scholastic Form \------------------------------------------------------------ Principles (P) include: • A — absolute principles • T — relative principles Both are principial regimes. No operation may treat T as non-principial. (Latin: Principia (P) includunt A — principia absoluta; T — principia respectiva. Utraque sunt regimina principalia. Nulla operatio potest tractare T sicut non-principiale.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ P := {A, T} Constraint: principial(A) \= TRUE principial(T) \= TRUE \------------------------------------------------------------ Binding \------------------------------------------------------------ “both are principial” ⇔ A and T belong to the same principial order, though under distinct regimes \============================================================ I. THE NINE SUBJECTS (ORDO SUBIECTORUM) \============================================================ L1 — Scholastic Form \------------------------------------------------------------ (Latin: Ordo subiectorum novem est:) Ⅰ — B — DEUS (God) Ⅱ — C — ANGELUS (Angel) Ⅲ — D — CAELUM (Heaven) Ⅳ — E — HOMO (Man) Ⅴ — F — IMAGINATIVUM (Imaginative Power) Ⅵ — G — SENSITIVUM (Sensitive Power) Ⅶ — H — VEGETATIVUM (Vegetative Power) Ⅷ — I — ELEMENTATIVUM (Elementative Power) Ⅸ — K — INSTRUMENTATIVUM (Instrumentative Power) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ SUBJECT\_ORDER := { B: Deus, C: Angelus, D: Caelum, E: Homo, F: Imaginativum, G: Sensitivum, H: Vegetativum, I: Elementativum, K: Instrumentativum } \------------------------------------------------------------ Binding \------------------------------------------------------------ “nine subjects” ⇔ finite ordered subject set \============================================================ II. UNIVERSAL CONDITIONS (CONDITIONES) \============================================================ 1\. DEFINITIO \------------------------------------------------------------ L1 — Scholastic Form \------------------------------------------------------------ Each subject must possess a definition that distinguishes it from all others. (Latin: Unumquodque subiectum debet habere definitionem quae illud ab omnibus aliis distinguit.) All discourse must affirm or deny coherently, respecting: • principles (A, T) • rules (R) • subject definition (S) (Latin: Omnis discursus debet cohaerenter affirmare vel negare, observans principia (A, T), regulas (R), et definitionem subiecti (S).) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ For each subject s: define(s) distinguish(s, all\_other\_subjects) Constraint: valid\_discourse(s) := coherence(A, T, R, definition(s)) \------------------------------------------------------------ Binding \------------------------------------------------------------ “definition” ⇔ distinguishing subject identity “coherent affirmation/negation” ⇔ admissible discourse under subject constraint 2\. DISTINCTIO \------------------------------------------------------------ L1 — Scholastic Form \------------------------------------------------------------ Distinctions between subjects must be preserved. Example: Divine goodness ≠ Angelic goodness ≠ Human goodness (Latin: Distinctiones inter subiecta debent preservari; verbi gratia: Bonitas divina non est Bonitas angelica non est Bonitas humana.) Difference arises from: • infinity vs finitude • eternity vs temporality • ontological level \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ For principle p: instantiate(p, s₁) ≠ instantiate(p, s₂) when s₁ ≠ s₂ \------------------------------------------------------------ Binding \------------------------------------------------------------ “same principle, different subject” ⇔ subject-conditioned variation without principial collapse 3\. CONCORDANTIA \------------------------------------------------------------ L1 — Scholastic Form \------------------------------------------------------------ Subjects must not be isolated. They must maintain concordance across shared predicates. (Latin: Subiecta non debent esse isolata; debent conservare concordantiam per praedicata communia.) Example: God and Angel are concordant in spirituality. \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ For shared predicate p: concordant(s₁, s₂, p) may hold without identity(s₁, s₂) \------------------------------------------------------------ Binding \------------------------------------------------------------ “concordance” ⇔ shared predication without ontological collapse 4\. NOBILITAS ORDINIS \------------------------------------------------------------ L1 — Scholastic Form \------------------------------------------------------------ Higher subjects possess more noble principles and more perfect operations. Hierarchy: God \> Angels \> Man \> Lower faculties (Latin: Subiecta superiora habent principia nobiliora et operationes perfectiores; hierarchia: Deus, Angeli, Homo, Facultates inferiores.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ nobility\_order(subjects) := ordered hierarchy \------------------------------------------------------------ Binding \------------------------------------------------------------ “higher / lower” ⇔ ordered subject nobility and perfection \============================================================ III. ELEMENTATIVE RELATIVITY CLAUSE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Element (I) is domain-relative and scale-relative. (Latin: Elementum (I) est dominio-relativum et scalae-relativum.) ELEMENTUM is that which composes a given level. (Latin: ELEMENTUM est id quod componit datum gradum.) Thus: element ≠ absolute primitive element \= relative substrate (Latin: Elementum non est primitivum absolutum; elementum est substratum relativum.) This prevents anachronism and categorical collapse across domains. (Latin: Hoc prohibet anachronismum et collapsum categorialem trans dominia.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ element(level\_x) := relative substrate(level\_x) \------------------------------------------------------------ Binding \------------------------------------------------------------ “element” ⇔ compositional substrate relative to level and domain \============================================================ IV. ONTOLOGICAL CASCADES \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Subjects form a cascade: Elementative → Vegetative → Sensitive → Imaginative → Human (Latin: Subiecta formant cascadem: Elementativum, Vegetativum, Sensitivum, Imaginativum, Homo.) Each higher subject integrates lower ones and operates at greater generality. (Latin: Unumquodque subiectum superius integrat inferiora et operatur in maiori generalitate.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ cascade := ascending integration order \------------------------------------------------------------ Binding \------------------------------------------------------------ “cascade” ⇔ hierarchical inclusion without flattening \============================================================ V. SUBJECT ACCESS THROUGH MIXTURE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Subjects are structurally closed and combinatorially explorable. (Latin: Subiecta sunt structuraliter clausa et combinatorie explorabilia.) Knowledge of subjects proceeds through mixture: Knowledge(S) := MIX(P, R) This operation is epistemic (access), not ontological generation. (Latin: Cognitio(S) := MIX(P, R); haec operatio est epistemica (accessus), non generatio ontologica.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ access(S) := MIX(P, R) Constraint: access ≠ generate\_being \------------------------------------------------------------ Binding \------------------------------------------------------------ “know subject through mixture” ⇔ epistemic approach to already-given ontological domains \============================================================ VI. THE NINTH SUBJECT — INSTRUMENTATIVE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ INSTRUMENTUM is that by which a subject operates within a principial configuration. (Latin: INSTRUMENTUM est id per quod subiectum operatur intra configurationem principalem.) Two regimes appear: 1\. natural instruments (organs, faculties) 2\. moral instruments (virtues, vices, habits) (Latin: Duo regimina: instrumenta naturalia (organa, facultates) et instrumenta moralia (virtutes, vitia, habitus).) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ INSTRUMENTUM := operative mediator within subject Regimes: NATURAL MORAL \------------------------------------------------------------ Binding \------------------------------------------------------------ “instrument” ⇔ operative means within subject-conditioned action \============================================================ VII. MORAL INSTRUMENTS \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Virtues and vices are not principles and not subjects. They are generated instrumental species. (Latin: Virtutes et vitia non sunt principia, non sunt subiecta; sunt species instrumentales generatae.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ virtue\_or\_vice := generated\_instrumental\_species \------------------------------------------------------------ Binding \------------------------------------------------------------ “generated instrumental species” ⇔ derived moral forms, not foundational ontological domains \============================================================ VIII. CONFIGURATION LAW \============================================================ L1 — Scholastic Form \------------------------------------------------------------ INSTRUMENTUM MORALE is MIX(P, R) as instantiated in S. Thus: Justice \= structured mixture Avarice \= structured privative mixture (Latin: INSTRUMENTUM MORALE est MIX(P, R) prout instantiatur in S; iustitia est mixtura structurata, avaritia est mixtura structurata privativa.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ INSTRUMENTUM\_MORALE := instantiate(MIX(P, R), S) \------------------------------------------------------------ Binding \------------------------------------------------------------ “justice / avarice” ⇔ subject-instantiated moral configurations \============================================================ IX. DUAL REGIME (VIRTUE / VICE) \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Virtue arises when mixture aligns with goodness, truth, and end, preserves concordance, and orders faculties properly. (Latin: VIRTUS oritur cum mixtura congruit cum bonitate, veritate, fine, conservat concordantiam, facultates recte ordinat.) Vice arises when mixture is privative or disordered, misuses contrariety or minority, and corrupts finality. (Latin: VITIUM oritur cum mixtura est privativa vel inordinata, abutitur contrarietate vel minoritate, corrumpit finalitatem; ergo vitium est mixtura privativa vel inordinata.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ virtue := ordered\_mixture vice := privative\_or\_disordered\_mixture \------------------------------------------------------------ Binding \------------------------------------------------------------ “virtue / vice” ⇔ two moral regimes of instantiated mixture \============================================================ X. CORRELATIVE STRUCTURE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ All instruments retain correlatives. Justice: justifier / justifiable / justifying Avarice: avaricer / avariced / avaricing (Latin: Omnia instrumenta retinent correlativa: iustitia iustificantem, iustificabile, iustificare; avaritia avaricantem, avaricabile, avaricare.) Privative correlatives do not possess full principial integrity but mirror the structure of positive correlatives. (Latin: Correlativa privativa non habent plenam integritatem principalem, sed speculantur structuram correlativorum positivorum.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ For each instrument i: correlatives(i) := {agent, patient, act} \------------------------------------------------------------ Binding \------------------------------------------------------------ “retain correlatives” ⇔ instrumenta preserve correlative articulation \============================================================ XI. FACULTY COUPLING \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Virtue: higher faculties govern lower. Vice: lower faculties disorder the governance of higher. (Latin: Virtus: facultates superiores regunt inferiores; vitium: facultates inferiores inordinant regimen superiorum.) Example: avarice: imagination and sensitivity disorder intellect and will (Latin: Exempli gratia, avaritia: imaginatio et sensitivum inordinant intellectum et voluntatem.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ virtue := ordered faculty hierarchy vice := inverted/disordered faculty hierarchy \------------------------------------------------------------ Binding \------------------------------------------------------------ “faculty coupling” ⇔ moral form as ordered or disordered governance \============================================================ XII. NUMERICAL STRUCTURE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Moral instruments comprise approximately 36 species. Their correspondence to the 36 dyads of Figure 3 is analogical. (Latin: Instrumenta moralia circiter 36 species habent; correspondentia est ad 36 dyades Figurae Tertiae.) Numerical correspondence is analogical, not strictly bijective. \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ moral\_species ≈ 36 relation\_to\_figure3 := analogical \------------------------------------------------------------ Binding \------------------------------------------------------------ “36 species” ⇔ bounded numerical analogy, not strict identity \============================================================ XIII. PROCEDURAL NATURE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Virtues and vices are habitual configurations, dynamically expressible through operations. Thus: ethics \= applied combinatorial discipline (Latin: Virtutes et vitia sunt configurationes habituales, dynamice expressibiles per operationes; ergo ethica est disciplina combinatoria applicata.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ ethics := applied mixture in moral regime \------------------------------------------------------------ Binding \------------------------------------------------------------ “habitual configurations” ⇔ dynamic moral forms under repeated operation \============================================================ XIV. META-MIXTURE CLAUSE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ After explicit mixture, further implicit mixtures are allowed. MIX\* := extension over implicit or peregrine principles within principial constraints (A, T). (Latin: Post mixturam explicitam, ulteriores mixturae implicitae permittuntur; MIX\* est extensio super principia implicita vel peregrina intra constraintes principales (A, T).) This allows extended reasoning and discovery of new media. (Latin: Hoc permittit rationem extensam et inventionem novorum mediorum.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ MIX\* := constrained extension of mixture \------------------------------------------------------------ Binding \------------------------------------------------------------ “implicit mixtures” ⇔ lawful extension beyond explicit combinations \============================================================ XV. FUNCTION \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Subjects contain all being, are distinguished by definition, unified by concordance, and ordered by nobility. (Latin: Subiecta continent omne ens, distinguuntur per definitionem, uniuntur per concordantiam, ordinantur per nobilitatem.) Instrumentative extends operation into morality, generates virtues and vices, and binds action to principial structure. (Latin: Instrumentativum extendit operationem in moralitatem, generat virtutes et vitia, ligat actionem ad structuram principalem.) The Art becomes general through subjects, operative through instruments, generative through mixture. (Latin: Ars fit generalis per subiecta, operativa per instrumenta, generativa per mixturam.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ CAPUT K governs: • finite subject ontology • principial application across subjects • instrumentative extension • moral generated species • epistemic access through mixture \------------------------------------------------------------ CLOSURE CLARIFICATION \------------------------------------------------------------ This CAPUT preserves: • subject ontology without runtime conversion • instrumentality without executable activation • moral generation as Rosetta-explicit articulation It is written to stabilize reading, not to serve as deployment logic. \============================================================ END CAPUT ARS BREVIS K — DE SUBIECTIS ET INSTRUMENTIS \============================================================