Conversion of Each Proposition From Formal Logic Into Stoic 500 Terminology

Claude:

I will convert each proposition from formal logic into Stoic 500 terminology, maintaining the logical structure while using Sterling's technical vocabulary.

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**1. Eudaimonia ↔ Virtue**

**Eudaimonia (happiness)** is **Telos-Achievement (471)** and consists exclusively in **Internal-Good (27)**, which is **virtue** achieved through **correct-assent (91)** and **Prohairesis-Perfection (470)**. This is the biconditional: **happiness** occurs if and only if **virtue** is present, because only **virtue** is **good (27)**, establishing **Self-Sufficiency (419)** and **Internal-Sufficiency (53)**.

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**2. Control(Virtue)**

**Virtue** belongs to the **Internal-Domain (21)** and falls within the **Sphere-of-Internals (23)**, where you possess **Internal-Authority (35)**, **Internal-Sovereignty (423)**, and **Absolute-Sovereignty (443)**. **Virtue** is produced by **Internal-Causation (422)** through **Choice-Freedom (431)** and **Libertarian-Freedom (435)**, demonstrating **Internal-Agency (421)** and establishing that **virtue** is always **Control(Virtue)** because it depends solely on **prohairesis (7)**.

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**3. Joy ↔ (Virtue ∧ Appreciation(Virtue))**

**Rational-Joy (238)**, which is **eupatheia (203)**, occurs if and only if you possess **virtue (27)** and exercise **Appreciation** through **correct-judgment (6)** recognizing that **Internal-Good (27)**. This is the biconditional: **Joy** requires both the presence of **virtue** and **Reason-Authority (451)** correctly identifying it, producing **Good-Feeling-Recognition (237)** and **Emotional-Integrity (245)**.

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**4. ¬Control(Externals)**

**Externals (22)** belong to the **External-Domain (22)** and fall within the **Sphere-of-Externals (24)**, where you possess no **Internal-Authority (35)**. **Externals** are governed by **External-Causation (407)** operating with **External-Independence (409)** and **World-Indifference (415)**, establishing **External-Limit (408)** and **Action-Limitation-Recognition (317)**. Therefore **¬Control(Externals)** because they lie outside **prohairesis (7)** entirely, as stated in **Internal-External-Distinction (33)**.

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**5. Good(Virtue)**

**Virtue** is **Internal-Good (27)**, the sole object possessing **Intrinsic-Value (31)**. This is **Moral-Truth (446)** known through **Ethical-Intuitionism (449)** and grounded in **Moral-Realism (447)**. **Good(Virtue)** is **foundational truth (450)** establishing that only **correct-judgment (6)** producing **virtuous-action (118)** constitutes **goodness (27)**, demonstrating **Final-Goodness (465)**.

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**6. Evil(Vice)**

**Vice** is **Internal-Evil (29)**, the sole object possessing genuine **badness**. **Vice** consists in **false-judgment** producing **Incorrect-Assent (92)** and **Irrational-Action (119)**, demonstrating **Desire-Error (171)** and **Aversion-Error (172)**. **Evil(Vice)** is **Moral-Truth (446)** establishing that only **vice** produced by **prohairesis (7)** through **false-valuation** constitutes **evil (29)**.

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**7. ¬Good(Externals)**

**External-Indifferents (28)** possess no **Intrinsic-Value (31)** but only **Extrinsic-Appearance (32)** of value. **Externals (22)** cannot be **good (27)** because **goodness** requires **Internal-Causation (422)** and belongs only to the **Internal-Domain (21)**. Therefore **¬Good(Externals)** is **Moral-Truth (446)** establishing **Event-Neutrality (404)** and **External-Illusion (30)**, preventing **External-Valuation** and maintaining **External-Indifference (152)**.

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**8. ¬Evil(Externals)**

**External-Indifferents (28)** possess no genuine **badness** despite **External-Illusion (30)** suggesting otherwise. **Externals (22)** cannot be **evil (29)** because **evil** requires **Internal-Causation (422)** and consists solely in **vice** within **Internal-Domain (21)**. Therefore **¬Evil(Externals)** is **Moral-Truth (446)** establishing **Event-Neutrality (404)** and **External-Futility (38)**, preventing **External-Aversion (164)** and maintaining **Aversion-Neutrality (180)**.

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**9. Emotion ↔ Belief(Value(Externals))**

**Pathos (202)**, which is **pathological-emotion**, occurs if and only if you assent to **impressions** attributing **value** to **External-Indifferents (28)**. This is **Emotional-Cause-Recognition (206)**: **Emotion** arises from **Assent (2)** to **false-judgment (6)** that **externals (22)** possess **Intrinsic-Value (31)**. The biconditional establishes that **Pathos-Recognition (202)** requires identifying **Belief(Value(Externals))** as the **Emotional-Trigger (205)** producing **External-Desire (163)** or **External-Aversion (164)**.

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**10. ¬Value(Externals)**

**External-Indifferents (28)** possess no **Intrinsic-Value (31)**. This is **Moral-Truth (446)** grounded in **Moral-Realism (447)** and known through **Ethical-Intuitionism (449)**. **¬Value(Externals)** establishes **External-Indifference (152)** and **Event-Neutrality (404)**, preventing **External-Illusion (30)** and maintaining **Domain-Clarity (49)**. Only **Internal-Good (27)** possesses genuine **value**.

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**11. ¬Emotion ↔ ¬Belief(Value(Externals))**

**Passion-Freedom (250)**, which is **apatheia**, occurs if and only if you withhold **assent (2)** from **impressions** attributing **value** to **externals (22)**. This biconditional establishes that **Emotional-Freedom (244)** requires **Cognitive-Purity (99)** achieved through **Assent-Withholding (87)** toward all **External-Valuation**. When **¬Belief(Value(Externals))** is maintained through **External-Indifference (152)**, then **Emotional-Neutrality (242)** and **Emotional-Equanimity (236)** result, producing **¬Emotion** in the sense of **¬Pathos**.

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**12. Virtue → ¬Belief(Value(Externals))**

**Virtue (27)** necessarily entails **External-Indifference (152)** because **virtue** consists in **correct-judgment (6)** which recognizes **Moral-Truth (446)** that **¬Value(Externals)**. Therefore **Virtue → ¬Belief(Value(Externals))** through **Value-Detection (66)** and **Internal-External-Test (68)**, establishing that **Prohairesis-Perfection (470)** requires **Emotional-Purification (211)** removing all **External-Valuation**, demonstrated through **Character-Purity (299)**.

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**13. Joy → ¬Belief(Value(Externals))**

**Rational-Joy (238)**, which is **eupatheia (203)**, requires **Internal-Orientation (158)** and **External-Indifference (152)**. Therefore **Joy → ¬Belief(Value(Externals))** because genuine **joy** arises from **appreciation** of **Internal-Good (27)** which is incompatible with **External-Desire (163)**. This demonstrates **Good-Feeling-Recognition (237)** distinguishing **eupatheia (203)** from **pathos (202)** through **Emotional-Content-Extraction (207)**.

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**14. ∴ Eudaimonia ↔ (¬Belief(Value(Externals)) ∧ Virtue)**

Therefore **Telos-Achievement (471)**, which is **eudaimonia (happiness)**, occurs if and only if you achieve both **Virtue (27)** through **Prohairesis-Perfection (470)** AND **¬Belief(Value(Externals))** through **External-Indifference (152)**. This biconditional establishes that **Final-Goodness (465)** and **Final-Freedom (464)** require both positive achievement of **Internal-Good (27)** through **correct-assent (91)** and negative elimination of **External-Valuation** through **Desire-Elimination (159)** and **Aversion-Transfer (160)**. This is the **Teleological-Completion (467)** demonstrating **Self-Sufficiency (419)** and **Internal-Sufficiency (53)**, producing **guaranteed happiness** through **Sage-Structure (468)** and **Sage-Invulnerability (469)**.

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**Complete conversion achieved using Stoic 500 terminology while preserving logical structure.**