The Six Commitments as One Architecture — Propositional Formalization
The Six Commitments as One Architecture — Propositional Formalization
Theoretical foundations: Grant C. Sterling (Eastern Illinois University). Analysis, synthesis, and instrument architecture: Dave Kelly. Prose rendering: Claude. 2026.
Purpose
This document renders the integration argument of The Six Commitments as One Architecture into propositional logic. The aim is to make the load-bearing claim formally explicit: that a single act of Stoic examination is possible only if all six commitments hold jointly, so that the negation of any one entails the impossibility of the act. The formalization treats the six commitments as the axiom set and the possibility of examination as the theorem they jointly support, in keeping with the corpus treatment of the propositional layer as an axiom-and-theorem structure.
Atomic Propositions
C1 Substance dualism holds — the rational faculty
is a distinct substance.
C2 Libertarian free will holds — assent is an
origination, not a determined output.
C5 The correspondence theory of truth holds — truth
is alignment of thought with the world.
C6 Moral realism holds — there are moral facts,
mind-independent.
C3 Ethical intuitionism holds — self-evident moral
truths are apprehended directly.
C4 Foundationalism holds — moral knowledge rests on
self-evident axioms in a traceable structure.
A There is an agent distinct from the impression
(a standing point).
G The examination is a genuine act (assent can be
withheld or given).
F The impression's claim is capable of being false.
R There is a real moral order for the claim to be
wrong about.
K The moral order is directly accessible to the agent.
S The correction is systematic — error is traceable
to its root.
E A single act of Stoic examination is possible.
Note on labeling: the commitment codes follow the corpus canonical assignment (C1 dualism, C2 free will, C3 intuitionism, C4 foundationalism, C5 correspondence, C6 moral realism). The propositions are presented in the order in which they engage during an examination, which is the order of the essay, not numerical order.
Axioms — The Role of Each Commitment
Each commitment is necessary for the function it supplies. These are the conditional claims the essay defends, one per commitment.
P1 C1 → A Dualism supplies the distinct agent.
P2 ¬C1 → ¬A Without dualism, no standing point.
P3 (A ∧ C2) → G A distinct agent plus free will
yields a genuine act.
P4 ¬C2 → ¬G Without free will, no genuine act
(only determined motion).
P5 C5 → F Correspondence makes the claim
capable of falsity.
P6 ¬C5 → ¬F Without correspondence, the claim is
at most dispreferred, never false.
P7 C6 → R Moral realism supplies the real order.
P8 ¬C6 → ¬R Without realism, nothing to be wrong
about.
P9 C3 → K Intuitionism supplies direct access.
P10 ¬C3 → ¬K Without intuitionism, the order is
unreachable.
P11 C4 → S Foundationalism makes correction
systematic.
P12 ¬C4 → ¬S Without foundationalism, error cannot
be traced to the root.
The Locks — Mutual Dependence
The essay's “locks” are the biconditional dependencies between adjacent commitments. They are stated here as the joint-necessity claims that prevent any commitment from doing its work alone.
L1 G → (C1 ∧ C2) A genuine act requires both a
locus (C1) and origination (C2).
Free will with no faculty has no
locus; a faculty with no freedom
is a fixed domain.
L2 F → (C5 ∧ C6) A falsifiable moral claim requires
both correspondence (C5) and a real
order to correspond to (C6). The hinge:
drop C6 and C5 has nothing moral to
track; drop C5 and C6 has no account
of success or failure.
L3 K → (C3 ∧ C6) Access requires both apprehension
(C3) and a real object (C6). A real
but unreachable order corrects nothing;
apprehension with no object grasps
nothing.
L4 S → (C4 ∧ C3) Systematic correction requires both
structure (C4) and the apprehended
first principles (C3) that occupy the
axiom positions.
The Constitutive Claim
Examination is possible if and only if all six functions are present. This is the definition of E in terms of the functions the commitments supply.
D1 E ↔ (A ∧ G ∧ F ∧ R ∧ K ∧ S)
Derivation — Joint Sufficiency
If all six commitments hold, the act is possible.
1. C1 ∧ C2 ∧ C3 ∧ C4 ∧ C5 ∧ C6 assumption 2. C1 1, ∧E 3. A 2, P1, →E 4. C2 1, ∧E 5. A ∧ C2 3, 4, ∧I 6. G 5, P3, →E 7. C5 1, ∧E 8. F 7, P5, →E 9. C6 1, ∧E 10. R 9, P7, →E 11. C3 1, ∧E 12. K 11, P9, →E 13. C4 1, ∧E 14. S 13, P11, →E 15. A ∧ G ∧ F ∧ R ∧ K ∧ S 3,6,8,10,12,14, ∧I 16. E 15, D1, ↔E Conclusion: (C1 ∧ C2 ∧ C3 ∧ C4 ∧ C5 ∧ C6) → E
Derivation — Joint Necessity (the Load-Bearing Result)
The negation of any single commitment entails that examination is impossible. The case for C6 is shown in full because C6 is doubly load-bearing — it appears in both L2 and L3 — and the remaining cases follow the same one-line pattern.
General schema, for any commitment Cn whose function is X
with axiom (¬Cn → ¬X):
1. ¬Cn assumption
2. ¬X 1, the relevant negative axiom, →E
3. ¬(A∧G∧F∧R∧K∧S) 2, ∧ introduction of a false conjunct
4. ¬E 3, D1, ↔E (contrapositive)
Thus ¬Cn → ¬E for each of the six.
Worked case — C6 (moral realism):
1. ¬C6 assumption
2. ¬R 1, P8, →E
3. ¬(A∧G∧F∧R∧K∧S) 2, a false conjunct falsifies the conjunction
4. ¬E 3, D1, ↔E
(¬C6 also falsifies F via L2 and K via L3 — the
same conclusion is reached by three independent
routes, which is why C6 is the most load-bearing
of the six.)
By the schema:
¬C1 → ¬E (P2: ¬C1 → ¬A)
¬C2 → ¬E (P4: ¬C2 → ¬G)
¬C3 → ¬E (P10: ¬C3 → ¬K)
¬C4 → ¬E (P12: ¬C4 → ¬S)
¬C5 → ¬E (P6: ¬C5 → ¬F)
¬C6 → ¬E (P8: ¬C6 → ¬R)
The Architecture Theorem
Combining joint sufficiency with joint necessity yields the formal statement of the integration thesis: examination is possible exactly when all six commitments hold, and the failure of any one is sufficient for its impossibility.
T1 E ↔ (C1 ∧ C2 ∧ C3 ∧ C4 ∧ C5 ∧ C6)
Corollary (contrapositive, the “standing or falling
together” result):
T2 ¬(C1 ∧ C2 ∧ C3 ∧ C4 ∧ C5 ∧ C6) → ¬E
equivalently
(¬C1 ∨ ¬C2 ∨ ¬C3 ∨ ¬C4 ∨ ¬C5 ∨ ¬C6) → ¬E
That is: deny any one commitment, and the act of Stoic
examination is no longer possible. The six cannot be
adopted singly or traded away one at a time, because
each is a conjunct of the single condition under which
examination is so much as possible.
Note on the Formalization
Two points of interpretation. First, the necessity axioms P2, P4, P6, P8, P10, P12 carry the weight of the argument; they assert that each function genuinely fails in the absence of its commitment, which is the substantive philosophical claim the essay defends case by case. The formal apparatus does not establish those conditionals; it displays what follows once they are granted. Second, D1 is constitutive rather than empirical: it defines what an act of examination is by the functions it requires, which is why the biconditional is warranted rather than a mere material conditional. The theorem T1 is therefore as strong as the six necessity axioms and the constitutive definition together — which is the precise sense in which the corpus claims the commitments form one architecture rather than a list.
Theoretical foundations: Grant C. Sterling (Eastern Illinois University). Analysis, synthesis, and instrument architecture: Dave Kelly. Prose rendering: Claude. 2026.
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