The Logical Dependencies in Core Stoicism Grant C. Sterling, ISF

 

The Logical Dependencies in Core Stoicism

Grant C. Sterling, ISF September 19, 2005. Dependency map: Dave Kelly, 2026. Prose rendering: Claude.

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Sterling’s own labels distinguish three types of propositions: theorems (Th) — foundational postulates not argued for within this document; derived propositions (numbered without Th) — conclusions derived from prior propositions; and one special proposition (2*) — a claim to be proven later in the document. The dependency structure follows his own “Ergo” and “By X” citations.

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Foundational Theorems

Not derived from anything within this document; jointly required by the derived propositions that follow.

• Th 1 — Everyone wants happiness.
• Th 2 — If you want happiness it would be irrational to accept incomplete happiness if complete happiness is available.
• Th 3 — All unhappiness is caused by desire for an outcome that does not result.
• Th 6 — The only things in our control are beliefs and will.
• Th 7 — Desires are caused by beliefs about good and evil.
• Th 10 — The only thing actually good is virtue; the only thing actually evil is vice.
• Th 16 — If you desire something and achieve it you get a positive feeling.
• Th 18 — Some positive feelings do not result from desires.
• Th 20 — The universe is governed by Nature, Providence, or God.
• Th 21 — That which is Natural or governed by Providence is exactly as it should be.
• Th 24 — An act of will must have content — the result at which one aims.
• Th 25 — Some things are appropriate objects to aim at, though not genuinely good.
• Th 26 — Such objects include life, health, pleasure, knowledge, justice, truth-telling.
• Th 27 — Virtue consists of rational acts of will; vice of irrational acts of will.

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Derived Propositions

Each derived proposition states what it depends on.

2* — Complete happiness is possible. [To be proven — resolved at the document’s conclusion when the threads are tied together.]

4 — Desiring things out of your control makes you subject to possible unhappiness. [From Th 3]

5 — Desiring things out of your control is irrational, if it is possible to control your desires. [From 4, 2*, Th 2]

8 — Desires are in our control. [From Th 6, Th 7]

9 — Desiring things out of our control is irrational. [From 5, 8]

11 — Virtue and vice are in our control. [From Th 10 — virtue and vice are acts of will; from Th 6 — will is in our control]

12 — Externals are never good or evil. [From Th 10, 11]

13 — Desiring things out of our control involves false judgment. [From 9, 12]

14 — If we value only virtue we will judge truly and be immune to all unhappiness. [From 12, 13]

15 — If we truly judge that virtue is good, we will desire it. [From Th 10, Th 7]

17 — If we correctly judge and correctly will, we will have appropriate positive feelings. [From 15, Th 16]

19 — Positive feelings not resulting from desire are not irrational or inappropriate. [From Th 18 — they do not involve false value judgment]

22 — If you regard all aspects of the world as exactly as they should be, you receive appropriate positive feelings. [From Th 21]

23 — The Stoic will have positive feelings in at least three ways: appreciation of his own virtue, physical and sensory pleasures, and appreciation of the world as it is. [From 17, 19, 22]

28 — Any act that aims at an external object of desire is not virtuous, since all desires for externals are irrational. [From 9, Th 27]

29 — Virtue consists of pursuit of appropriate objects of aim, not pursuit of external objects of desire. Such virtuous acts give good feelings and never produce unhappiness. [From Th 25, Th 26, 28, 17]

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The Critical Dependency Chain

The spine of the document. Three chains converge at 13 and 14.

Th 3 → 4 → 5 (with 2*, Th 2) → [requires 8] → 9 → 13 → 14

Th 6 + Th 7 → 8

Th 10 → 11 → 12 → 13

Everything in Sections Three and Four is downstream of 14.

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The Most Load-Bearing Theorem

Sterling identifies it himself in the closing note: Theorem 7. Denying it collapses 8, 9, 13, 14, 28, and 29 simultaneously — destroying both the unhappiness argument and the virtue argument. Theorem 7 is the structural keystone. Everything that makes the system action-guiding rather than merely metaphysical runs through it.

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The Isolable Section

Sterling also notes that Theorems 20 and 21 can be denied without serious damage to the virtue and unhappiness arguments. Section Three’s Providence strand — 20, 21, 22, 23 — is structurally separable. It adds a third route to positive feelings but is not load-bearing for the core ethical conclusions at 14 and 29.

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Dependency map: Dave Kelly, 2026. Source: Core Stoicism, Grant C. Sterling, ISF September 19, 2005. Prose rendering: Claude.