Face B3: Coherence (Draft)
Hold nothing that contradicts what you also hold. One contradiction unravels the whole.
A body of commitments must not assert a thing and its negation. This is not fastidiousness: from a contradiction, everything follows — so a single unreconciled contradiction does not stay local, it makes every claim derivable and every warrant worthless. The discipline is to hunt one’s own contradictions and, when one is found, to hold the matter open until it is reconciled — treating the contradiction as a defect regardless of which side turns out right.
It is tempting to treat a contradiction between two of your beliefs as a small, contained problem — a tension to be lived with, filed in a different drawer. It is not contained. From a contradiction, anything whatever can be derived; a single live contradiction does not sit quietly in its corner, it silently licenses every conclusion you might want and so voids the worth of all of them. A closure with a contradiction in it has no edge — everything is “derivable,” which is the same as nothing being warranted.
So coherence is the precondition that makes the rest of the Boundary mean anything: the typing of warrants (C0) and the edge of derivation (C1) are only meaningful inside a consistent closure. The discipline is active, not passive — not merely “avoid contradicting yourself” but go looking for your own contradictions, and when you find one, refuse the convenient resolution. A found contradiction is a defect to be repaired, not a side to be chosen; until it is genuinely reconciled, the matter stays open.
In practice:
You believe two things that have never been in the same room — a principle you apply at work and its opposite you apply at home, each comfortable in its own context. The honest move is not to keep the rooms separate. It is to put the two beliefs on the same table on purpose, and accept that one of them, or your understanding of both, has to give.
Formal Statement (Concordius Framework)
The deductive closure Cl(𝒫) of one’s primitives (see B1) must be consistent: there is no claim C with both C and ¬C in Cl(𝒫). The requirement is not optional, because of ex falso quodlibet — from a contradiction, every proposition is derivable, so an inconsistent closure satisfies Cl(𝒫) = the whole language. Warrant-typing (C0) then collapses: every claim becomes trivially “deductive,” and the distinction between derived, inferred, and posited — the entire point of the Boundary — is destroyed. Coherence is therefore the precondition of the Boundary’s other three faces, not a peer to them. It is the CONTRADICTION check of the corpus’s own TruthChecker raised to a feature, and it recurs at the meta-level in the Mirror: the self-application (D0) must itself be consistent.
Tier: derivation — ex falso is theorem-grade; coherence is the consistency requirement without which the typed closure is meaningless.