\============================================================ CAPUT ARS BREVIS D — DEFINITIONES PRINCIPIORUM Ars Generalis Applied — Knowledge Base Layer Version: 1.2.0-CAPUT-AB-D-ROSETTA-INTEGRATED Status: STABILIZED / INTERPRETATIVE \+ OPERATIONAL Scope: Ars Brevis — Chapter 3 (Definitions), with Ars Generalis Ultima clarifications Authority: ARS BREVIS / AEGIS (non-mutating reference) Mutation Policy: VERSION-CONTROLLED ONLY Class: AEGIS / CAPUT \============================================================ PURPOSE \------------------------------------------------------------ This CAPUT formalizes the definitions of principles in Ars Brevis, clarified by Ars Generalis Ultima where Brevis is compressed. It preserves: • scholastic exposition of definitions • definitional structure of principles • constraints on valid predication • definition-based reasoning discipline • correlatives as intrinsic definitional structure • dual definitional modes • compound definitional construction • substantial vs accidental definitional regimes • Rosetta anchor for integrated Latin / English definitional parsing This CAPUT does NOT define doctrine. It stabilizes semantic and intelligible constraints prior to the rule-layer. \------------------------------------------------------------ CAPUT PRINCIPLE \------------------------------------------------------------ Definitions (definitiones) are not only constraints. They are: • semantic admissibility conditions • generative intelligibility operators • ontological stabilizers • anti-drift safeguards Latin anchor: Definitiones non sunt solae restrictiones; sunt conditiones admissibilitatis semanticae, operatores intelligibilitatis generativae, stabilitores ontologici, praesidia contra derivationem. \============================================================ I. DEFINITIONAL FUNCTION \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The Art defines its principles so that they may be known by their definitions and so that the artist may make affirmative and negative statements without violating them. Under these conditions, the intellect develops science, finds middle terms, and dispels ignorance, its enemy. (Latin: Ars sua principia definit ut per suas definitiones cognoscantur.) (Latin: Ut artifex enuntiationes affirmativas et negativas facere possit sine earum violatione.) (Latin: Intellectus scientiam explicat, media invenit, et ignorantiam, inimicam suam, dispellit.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ define(a\_i) → definition(a\_i) valid\_statement(p): must\_not\_violate(definition(a\_i)) \------------------------------------------------------------ Binding \------------------------------------------------------------ “know principles by their definitions” ⇔ define(a\_i) → definition(a\_i) “affirmative or negative statements” ⇔ admissible predications and denials “do not violate definitions” ⇔ semantic validity constraint “definitiones” ⇔ intelligible law of principial meaning \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions both: • constrain predication • generate intelligibility Definitions are: • admissibility filters • generative semantic operators \============================================================ II. EPISTEMIC FUNCTION \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions enable science because through them the intellect can reason without confusion, find media, and dispel ignorance. (Latin: Definitiones scientiam efficiunt quia per eas intellectus sine confusione ratiocinari, media invenire, et ignorantiam dispellere potest.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ science := valid\_definitions \+ valid\_predications \+ consistent\_reasoning Functions: • develop\_science • find\_middle\_terms • dispel\_ignorance \------------------------------------------------------------ Binding \------------------------------------------------------------ “science” ⇔ coherent definitional reasoning “finds middle terms” ⇔ medium discovery under definitional constraint “dispels ignorance” ⇔ removes contradiction and confusion \------------------------------------------------------------ Rule \------------------------------------------------------------ ignorance \= violation or absence of definitional coherence \============================================================ III. DEFINITIONS OF PRINCIPLES \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The Art defines the nine principles as follows: Latin anchor: Ars novem principia sic definit: • Goodness is the being by reason of which good does good (Latin: Bonitas est illud per quod bonum facit bonum.) • Greatness is the being by reason of which goodness, eternity etc. are great (Latin: Magnitudo est illud per quod bonitas, aeternitas et cetera sunt magna.) • Duration is that by reason of which goodness, greatness etc. are durable (Latin: Duratio est illud per quod bonitas, magnitudo et cetera sunt durabilia.) • Power is that by reason of which goodness, greatness etc. can exist and act (Latin: Potestas est illud per quod bonitas, magnitudo et cetera possunt esse et agere.) • Wisdom is a property by means of which the wise understand (Latin: Sapientia est proprietas per quam sapiens intelligit.) • Will is that on account of which goodness, greatness etc. are desirable (Latin: Voluntas est illud propter quod bonitas, magnitudo et cetera sunt desiderabilia.) • Virtue is the origin of the unity of goodness, greatness etc. in one substance (Latin: Virtus est origo unionis bonitatis, magnitudinis et cetera in una substantia.) • Truth is what is true about goodness, greatness etc. (Latin: Veritas est id quod verum est de bonitate, magnitudine et cetera.) • Glory is the delight in which goodness, greatness etc. repose (Latin: Gloria est delectatio in qua bonitas, magnitudo et cetera requiescunt.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ P := {B, C, D, E, F, G, H, I, K} B — Bonitas goodness(x) := that whereby good does good C — Magnitudo greatness(x) := that which makes other principles great D — Duratio duration(x) := that which makes other principles durable E — Potestas power(x) := that which enables existence and action F — Sapientia wisdom(x) := property by which the wise understand G — Voluntas will(x) := that which makes things lovable or desirable H — Virtus virtue(x) := origin of union of principles I — Veritas truth(x) := that which is true about principles K — Gloria glory(x) := delight in which principles find rest \------------------------------------------------------------ Binding \------------------------------------------------------------ “by reason of which / by means of which / on account of which” ⇔ definitional operator type “good does good” ⇔ act-based essential definition “delight in which principles repose” ⇔ state-of-rest definition \------------------------------------------------------------ Structural note \------------------------------------------------------------ These Latin anchors stabilize the definitional carriers. They do not replace the wider chapter logic by which the same principles are later read through correlatives, modes, and compound articulation. \------------------------------------------------------------ Rule \------------------------------------------------------------ Each principle: • acts over other principles • is defined relationally, not in isolation • may be read substantially or accidentally according to regime \============================================================ IV. DEFINITIONS OF RELATIONS \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The relational principles are defined as follows: Latin anchor: Principia respectiva sic definiuntur. • Difference is what makes goodness, greatness, etc. clear reasons without confusion (Latin: Differentia est id quod facit bonitatem, magnitudinem et cetera claras rationes sine confusione.) • Concordance is that through which goodness, etc. agree in unity and plurality (Latin: Concordantia est id per quod bonitas et cetera conveniunt in unitate et pluralitate.) • Contrariety is mutual resistance caused by divergent ends (Latin: Contrarietas est mutua resistentia propter fines diversos.) • Beginning is that which is relatively prior (Latin: Principium est id quod est relative prius.) • Middle is the subject through which end influences beginning and beginning reciprocally influences end (Latin: Medium est subiectum per quod finis influit in principium et principium reciproce influit in finem.) • End is that in which the beginning reposes (Latin: Finis est id in quo principium requiescit.) • Majority is an image of the immensity of the divine dignities (Latin: Maioritas est imago immensitatis dignitatum divinarum.) • Equality is the subject in which ultimate concordance reposes (Latin: Aequalitas est subiectum in quo finalis concordantia requiescit.) • Minority is being close to nothingness (Latin: Minoritas est ens propinquum non-esse.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ R := {Difference, Concordance, Contrariety, Beginning, Middle, End, Majority, Equality, Minority} Difference difference(x,y) := that whereby principles are distinct without confusion Concordance concordance(x,y) := that through which principles agree in unity and plurality Contrariety contrariety(x,y) := mutual resistance due to divergent ends Beginning beginning(x) := that which is prior to all else Middle middle(x) := that in which beginning and end interact reciprocally End end(x) := that in which the beginning rests Majority majority(x) := image of boundlessness / immensity of principles Equality equality(x) := subject of final concordance of principles Minority minority(x) := being close to non-being \------------------------------------------------------------ Binding \------------------------------------------------------------ “clear reasons without confusion” ⇔ distinction-preserving relational clarity “agree in unity and plurality” ⇔ concordant multiplicity under unity “being close to nothingness” ⇔ minimal ontological proximity to non-being \------------------------------------------------------------ Rule \------------------------------------------------------------ Relational definitions establish: • distinction • agreement • opposition • process • comparison \============================================================ V. CORRELATIVE STRUCTURE LAW \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The principles do not stand alone. Their natural properties require innate correlatives, such as: • bonifier • bonified • bonifying and likewise for the other principles, each in its own way. Without these natural properties, the principles would not be what their definitions say they are. (Latin: Principia non stant sola; eorum proprietates naturales correlativa innata requirunt.) Latin anchor: bonificans, bonificabile, bonificare \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ ∀ p ∈ P: ∃ triad Corr\_p: (agent\_p, patient\_p, act\_p) Examples: Bonitas → (bonificans, bonificabile, bonificare) Magnitudo → (magnificans, magnificabile, magnificare) Duratio → (durans, durabile, durare) \------------------------------------------------------------ Binding \------------------------------------------------------------ “natural properties” ⇔ intrinsic correlatives “cannot exist without” ⇔ ontological necessity of correlatives \------------------------------------------------------------ Structural note \------------------------------------------------------------ Correlatives are stated here as definitional necessity. Full correlative doctrine remains distributed and is not exhausted by this chapter alone. \------------------------------------------------------------ Rule \------------------------------------------------------------ • no principle exists definitionally without correlatives • correlatives are intrinsic, not optional • correlatives are not derived from outside the principle \============================================================ VI. SUBSTANTIAL AND ACCIDENTAL DEFINITIONAL REGIMES \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Some principles are substantial and others accidental, but contrariety is always accidental. Substantial principles require substantial definitions; accidental ones require accidental definitions. (Latin: Quaedam principia sunt substantialia et alia accidentalia, sed contrarietas semper est accidentalis.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Def\_substantial(Di) Def\_accidental(Di) Example: goodness: substantial: bonificans → bonificabile (per essentiam) accidental: bonificans → bonificabile (per accidens) \------------------------------------------------------------ Binding \------------------------------------------------------------ “substantial definition” ⇔ per se ontological articulation “accidental definition” ⇔ habit / quality / external articulation \------------------------------------------------------------ Rule \------------------------------------------------------------ • definition type depends on ontological regime • contrariety is always accidental • regime mismatch invalidates reasoning \============================================================ VII. TWO MODES OF DEFINITION \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions may be made in many ways, but all are included in two modes. The first mode proceeds through causes: • efficient • material • formal • final The second mode is shown by rule C. (Latin: Primus modus procedit per causas: efficientem, materialem, formalem, finalem.) (Latin: Secundus modus ostenditur per regulam C.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Mode 1 — causal: {efficient, material, formal, final} Mode 2 — correlative: definition via: • coessential parts • intrinsic structure • functional participation \------------------------------------------------------------ Binding \------------------------------------------------------------ “mode of cause” ⇔ causal definitional decomposition “mode shown in rule C” ⇔ correlative / coessential definitional structure \------------------------------------------------------------ Structural note \------------------------------------------------------------ The two-mode distinction is chapter-native. More technical formal stratification belongs to later interpretative and extractive layers. \------------------------------------------------------------ Rule \------------------------------------------------------------ • both modes are legitimate • Brevis compresses them • Ultima makes them explicit \============================================================ VIII. FUNCTIONAL DEFINITIONS (ACT-BASED) \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Forms can be defined by their acts: • elemental power functions by elementing • vegetative power by vegetating • sensitive power by sensing • imaginative power by imagining • rational power by reasoning Likewise: • fire is the being that ignites • goodness is the being because of which good does good (Latin: Formae possunt definiri per suos actus: elementativa per elementare, vegetativa per vegetare, sensitiva per sentire, imaginativa per imaginari, rationalis per ratiocinari.) (Latin: Ignis est ens quod ignit; bonitas est ens per quod bonum facit bonum.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Def(Di): Di := being\_that(acts\_by Di) \------------------------------------------------------------ Binding \------------------------------------------------------------ “defined by its act” ⇔ operational form of essence “the being that ...” ⇔ act-based convertibility between thing and definition \------------------------------------------------------------ Rule \------------------------------------------------------------ • act reveals essence • functional definition is canonical and highly useful • thing and definition should convert \============================================================ IX. COMPOUND DEFINITIONS \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions can be compounded by combining principles: • great goodness is the being because of which great good does great good • great eternal goodness is the being because of which great eternal good does great eternal good (Latin: Magna bonitas est illud per quod magnum bonum facit magnum bonum.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Def(p\_i \+ p\_j): \= combined functional articulation Def(p\_i \+ p\_j \+ p\_k): \= higher-order compound articulation \------------------------------------------------------------ Binding \------------------------------------------------------------ “compound definitions” ⇔ principial composition inside definitional form “cannot otherwise be demonstrated” ⇔ compound definition increases demonstrative reach \------------------------------------------------------------ Rule \------------------------------------------------------------ • compound definitions preserve truth • they expand expressive and demonstrative power • they are built from primordial principles \============================================================ X. DEFINITIONAL STRUCTURE LAW \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions are not isolating. Each principle is defined with reference to other principles, relations, correlatives, or acts. (Latin: Definitiones non sunt isolantes; unumquodque principium definitur cum respectu ad alia principia, respectiva, correlativa, vel actus.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ ∀ p ∈ P: definition(p) references: • other principles • relational effects • correlatives • act structure \------------------------------------------------------------ Binding \------------------------------------------------------------ “not isolating” ⇔ non-atomic definitional structure \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions are: • relational • generative • non-atomic • analogically extendable relationality in definitions must not be confused with collapse of principial identity \============================================================ XI. NATURAL PROPERTY REQUIREMENT \============================================================ L1 — Scholastic Form \------------------------------------------------------------ If the principles had no natural properties, their definitions would perish; and if the definitions perish, neither the principles nor the universe remain. (Latin: Si principia nullas proprietates naturales haberent, earum definitiones perirent; et si definitiones pereunt, nec principia nec universum manent.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ ∀ p: Def(p) requires: correlatives(p) Failure condition: if correlatives absent: → principle collapses → system collapses \------------------------------------------------------------ Binding \------------------------------------------------------------ “definitions perish” ⇔ invalidation of principial ontology “universe remains” ⇔ experiential confirmation of principial necessity \------------------------------------------------------------ Rule \------------------------------------------------------------ Correlatives are ontologically necessary for the stability of the system. \============================================================ XII. DOMAIN ADAPTATION RULE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Some principles adapt their expression according to the nature of the subject. For instance: • wisdom in rational substance refers to intellect • wisdom in non-rational beings refers to instinct • will in non-rational beings refers to appetite (Latin: Sapientia in substantia rationali refert ad intellectum; sapientia in entibus non-rationalibus refert ad instinctum.) (Latin anchor: Voluntas in entibus non-rationalibus refert ad appetitum.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ adapt(Def\_i, substrate K) → domain-appropriate expression Examples: wisdom: rational → intellect non-rational → instinct will: rational → volition non-rational → appetite \------------------------------------------------------------ Binding \------------------------------------------------------------ “in another way” ⇔ substrate-conditioned definitional adaptation \------------------------------------------------------------ Rule \------------------------------------------------------------ • definitional structure remains stable • expression varies with substrate • K conditions definitional articulation \============================================================ XIII. NON-VIOLATION LAW \============================================================ L1 — Scholastic Form \------------------------------------------------------------ No affirmation or negation may violate the definitions. (Latin: Nulla affirmatio vel negatio potest definitiones violare.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ valid\_predication(p\_i, p\_j): must satisfy: compatible(definition(p\_i), definition(p\_j)) Invalid: contradiction(definition(p\_i), definition(p\_j)) \------------------------------------------------------------ Binding \------------------------------------------------------------ “do not violate definitions” ⇔ compatibility constraint on predication \------------------------------------------------------------ Rule \------------------------------------------------------------ No statement may violate definitions. \============================================================ XIV. MEDIUM DISCOVERY (DEFINITIONAL) \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions help the intellect find middle terms and make demonstrations. (Latin: Definitiones adiuvant intellectum invenire medios terminos et facere demonstrationes.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ medium(p\_i, p\_j): derived from: definitions(p\_i) definitions(p\_j) find\_common\_structure \------------------------------------------------------------ Binding \------------------------------------------------------------ “find middle terms” ⇔ derive admissible media from definitions \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions constrain and reveal possible media. \============================================================ XV. ROLE IN COMBINATORY SYSTEM \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions prepare the principles for lawful combination and demonstration. (Latin: Definitiones principia praeparant ad legitimam combinationem et demonstrationem.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Definitions operate as: semantic constraints over combinatorics combinatory\_result: must satisfy definitions \------------------------------------------------------------ Binding \------------------------------------------------------------ “make demonstrations” ⇔ definitional admissibility of combinations \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions filter: • valid combinations • valid conclusions • admissible demonstrations \============================================================ XVI. RELATION TO FIGURES AND RULES \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions stand between the figures and the rules: • the figures generate and arrange the principial field • the definitions stabilize meaning • the rules inquire through what has thus been prepared (Latin: Definitiones stant inter figuras et regulas: figurae generant et disponunt campum principalem, definitiones significationem stabiliunt, regulae inquirunt per id quod sic praeparatum est.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Interaction: Figures → generate and arrange the principial field Definitions → constrain meanings Rules → operate on constrained meanings \------------------------------------------------------------ Binding \------------------------------------------------------------ “definitions of the principles ... and rule C” ⇔ definitions are linked to future rule operation \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions precede rules and stabilize interpretation. \============================================================ XVII. ANTI-DRIFT POLEMICAL CLAUSE \============================================================ L1 — Scholastic Form \------------------------------------------------------------ There is a confused and prolific way of defining things without the Art, by composing predicates haphazardly and without respect for proper and appropriated definitions. Some will attack the principles by disparaging the definitions, but the principles mutually help each other. (Latin: Est modus confusus et prolixus definiendi res sine Arte, componendo praedicata temere et sine respectu ad definitiones proprias et appropriatas.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Invalid pattern: definition := accidental aggregation Example: man \= rational animal \+ rider \+ writer Refutation pattern: principles \+ relations \+ higher/lower distinctions restore admissibility \------------------------------------------------------------ Binding \------------------------------------------------------------ “confused and prolific” ⇔ uncontrolled semantic aggregation “mutually help each other” ⇔ inter-principial support network \------------------------------------------------------------ Rule \------------------------------------------------------------ Valid definition must: • respect principial structure • respect correlatives • preserve convertibility • distinguish proper from appropriated predicates \============================================================ XVIII. GENERAL DEFINITIONAL FORM \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions employ different relational operators: • that whereby • that by which • that in which • that toward which (Latin: Definitiones variis operatoribus relationalibus utuntur: per quod, quo, in quo, ad quod.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Def(Di) := relational-functional articulation of Di Def : D → Structure Def(Di) \= (Di, Op\_i, F\_i, Corr\_i, Mode\_i) Where: Op\_i ∈ {per\_quod, quo, in\_quo, ad\_quod} F\_i \= functional role of Di Corr\_i \= (agent\_i, patient\_i, act\_i) Mode\_i ∈ {causal, correlative} \------------------------------------------------------------ Binding \------------------------------------------------------------ “that whereby / by which / in which / toward which” ⇔ operator type of definition “natural properties / correlatives” ⇔ Corr\_i “two modes” ⇔ Mode\_i \------------------------------------------------------------ Structural note \------------------------------------------------------------ These operator-types are interpretative formal aids. They clarify the chapter’s definitional directions without replacing the chapter’s own scholastic phrasing. \------------------------------------------------------------ Relational Law \------------------------------------------------------------ ∀ Di : Def(Di) non est atomica ∃ Dj (Dj ≠ Di) ∧ Corr\_i ∧ Mode\_i \------------------------------------------------------------ Rule \------------------------------------------------------------ • definitions are relational • definitions imply interaction • no principle is self-sufficient in definition \============================================================ XIX. DEFINITIONAL OPERATOR TYPES \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Different definitions orient the principle differently: • by causation • by operation • by repose • by directedness (Latin: Variae definitiones principium aliter ordinant: per causationem, per operationem, per requiem, per directionem.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Operators: 1\. per\_quod → “that whereby” 2\. quo → “that by which” 3\. in\_quo → “that in which” 4\. ad\_quod → “that toward which” \------------------------------------------------------------ Binding \------------------------------------------------------------ “operator form” ⇔ directional role of definitional relation \------------------------------------------------------------ Rule \------------------------------------------------------------ Operator type determines: • direction of function • role in predication • relation to other principles \============================================================ XX. DEFINITIONS OF PRINCIPLES — TYPED FORMS \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The principles distribute their definitions across different operator types according to their nature. (Latin: Principia distribuunt suas definitiones secundum diversos typos operatorios pro sua natura.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ B — Bonitas Def(B) := (B, per\_quod, actus\_bonificandi, Corr\_B, correlative) C — Magnitudo Def(C) := (C, per\_quod, amplificatio\_aliorum\_principiorum, Corr\_C, correlative) D — Duratio Def(D) := (D, per\_quod, stabilizatio\_aliorum\_principiorum, Corr\_D, correlative) E — Potestas Def(E) := (E, per\_quod, possibilitas\_essendi\_et\_agendi, Corr\_E, correlative) F — Sapientia Def(F) := (F, quo, intellectus\_operatur, Corr\_F, correlative) G — Voluntas Def(G) := (G, per\_quod, appetibilitas\_aliorum, Corr\_G, correlative) H — Virtus Def(H) := (H, per\_quod, unio\_principiorum, Corr\_H, correlative) I — Veritas Def(I) := (I, quo, conformitas\_de\_principiis, Corr\_I, correlative) K — Gloria Def(K) := (K, in\_quo, quies\_principiorum, Corr\_K, correlative) \------------------------------------------------------------ Binding \------------------------------------------------------------ “that whereby” ⇔ per\_quod “by means of which” ⇔ quo “delight in which” ⇔ in\_quo \------------------------------------------------------------ Structural note \------------------------------------------------------------ The typed-form display is an interpretative stabilization of how the chapter distributes definitional force. It must not be mistaken for a verbatim Llullian schema. \------------------------------------------------------------ Rule \------------------------------------------------------------ Definitions distribute across: • per\_quod (generative action) • quo (cognitive operation) • in\_quo (state of rest) \============================================================ XXI. DEFINITIONS OF RELATIONS — TYPED FORMS \============================================================ L1 — Scholastic Form \------------------------------------------------------------ The relational principles likewise admit typed formalization. (Latin: Principia respectiva similiter admittunt formalizationem typatam.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Difference Def(Diff) := (Diff, per\_quod, distinctio\_sine\_confusione, Corr\_Diff, correlative) Concordance Def(Conc) := (Conc, per\_quod, unitas\_in\_pluralitate, Corr\_Conc, correlative) Contrariety Def(Contr) := (Contr, per\_quod, resistentia\_propter\_finem, Corr\_Contr, accidental) Beginning Def(Beg) := (Beg, per\_quod, prioritas, Corr\_Beg, causal) Middle Def(Mid) := (Mid, in\_quo, reciprocatio\_principii\_et\_finis, Corr\_Mid, correlative) End Def(End) := (End, in\_quo, quies\_principii, Corr\_End, causal) Majority Def(Maj) := (Maj, per\_quod, excessus\_principiorum, Corr\_Maj, correlative) Equality Def(Eq) := (Eq, in\_quo, concordantia\_finalis, Corr\_Eq, correlative) Minority Def(Min) := (Min, ad\_quod, proximitas\_non\_esse, Corr\_Min, correlative) \------------------------------------------------------------ Binding \------------------------------------------------------------ “clear without confusion” ⇔ distinctio\_sine\_confusione “ultimate concordance reposes” ⇔ concordantia\_finalis in\_quo “close to nothingness” ⇔ proximitas\_non\_esse \------------------------------------------------------------ Structural note \------------------------------------------------------------ This typed-form layer is descriptive and Rosetta-oriented, not a replacement for the chapter’s own wording. \------------------------------------------------------------ Rule \------------------------------------------------------------ Relational definitions express: • distinction • process • comparison \============================================================ XXII. DEFINITIONAL CONSISTENCY LAW \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions must agree with each other if reasoning is to be valid. (Latin: Definitiones debent inter se concordare si ratiocinatio valida esse debet.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ ∀ Di, Dj: compatible(Def(Di), Def(Dj)) Violation: contradiction(Def(Di), Def(Dj)) → invalid \------------------------------------------------------------ Binding \------------------------------------------------------------ “true and necessary science” ⇔ compatibility of definitional structures \------------------------------------------------------------ Rule \------------------------------------------------------------ Valid reasoning requires definitional compatibility. \============================================================ XXIII. FUNCTIONAL SUMMARY \============================================================ L1 — Scholastic Form \------------------------------------------------------------ Definitions provide the artist with lawful, clear, and productive ways of understanding and combining principles. (Latin: Definitiones praebent artifici vias legitimas, claras et productivas ad principia intelligenda et combinanda.) \------------------------------------------------------------ L2 — Operator Form \------------------------------------------------------------ Definitions provide: • operator typing • correlatives as intrinsic structure • dual definitional modes • compound definitional expansion • act-based semantic grounding • relational constraints • semantic admissibility • integrated Latin/English Rosetta stabilization of principial definitions Formal role: Def := constraint\_layer \+ generative\_semantic\_engine over combinatorics \------------------------------------------------------------ Binding \------------------------------------------------------------ “lawful and clear definitions” ⇔ admissible and convertible semantic structures \------------------------------------------------------------ Relation \------------------------------------------------------------ Figures → generate combinations Definitions → filter and ground combinations Rules → operate upon constrained meanings \============================================================ XXIV. NON-COLLAPSE RULE \============================================================ This CAPUT must: • preserve L1 and L2 distinctly • maintain explicit bindings • preserve substantial/accidental distinction • preserve dual definitional modes • preserve distinction between chapter-native definitions and later object-level consolidation • preserve distinction between definitional grounding and later correlative / combinatory extraction models This CAPUT must not: • redefine TENET • introduce rule execution • execute combinatory procedures • collapse principles into relations • reduce definitions to mere constraints \============================================================ XXV. FUNCTION \============================================================ CAPUT ARS BREVIS D governs: • definitional grounding of principles and relations • correlatives as intrinsic semantic structure • validity of predications • semantic constraints on combinatorics • compound and act-based definitions • preparation for the rule system • anti-drift interpretation of Llullian definitions • integrated Latin/English Rosetta stabilization of definitions \============================================================ END CAPUT ARS BREVIS D \============================================================