Feature B — The Boundary (Draft)
Faces B0–B3: derivation, its types, and where it stops. Warrant labelled by how it was earned; the edge of what logic can derive, past which method must change; the cost of every assumption you must reach across that edge; and the consistency without which the whole closure collapses.
“Whereof one cannot speak, thereof one must be silent.” — Ludwig Wittgenstein, Tractatus 7
The second object is the typed deductive closure — the structure of warrant. Its faces hold that warrant is not a single scalar but a type (derived, inferred, posited); that the deductive type has an edge you must name rather than walk past; that crossing the edge has a cost, paid one unexplained assumption at a time; and that the whole closure must be consistent, since a single contradiction makes everything derivable and the edge meaningless. Type, edge, cost, consistency.
The Faces
Face B0 — Explicit Confidence Tiers Label what you know by how you know it.
Face B1 — Logic Where It Reaches Follow the argument as far as it goes. When it stops, name where it stops and shift methods.
Face B2 — Minimum Necessary Miracles When comparing accounts, prefer the one requiring fewer unexplained events.
Face B3 — Coherence Hold nothing that contradicts what you also hold. One contradiction unravels the whole.
Formal Statement (Concordius Framework)
The object is the deductive closure Cl(𝒫) of the primitives and its type structure. Its faces: B0 warrant is typed (deductive / convergent / testimonial — collapsing the types is an OVERCLAIM); B1 the boundary ∂Cl(𝒫) where the deductive type ends and convergence takes over; B2 the cost of exogenous inputs (minimize k by the MDL / Occam factor — each posited ‘miracle’ is a free parameter crossing ∂); and B3 consistency (by ex falso, an inconsistent closure derives everything, voiding the typing). B3 is the precondition of the other three.
Tier: derivation for B0/B2/B3; criterion for B1 (membership in Cl(𝒫) is undecidable in general).
Begin with Face B0 — Explicit Confidence Tiers →