The economy beneath the ladder · what you can afford

Resource Arithmetic

The seven modalities say what is possible, preferable, permitted, durable, revisable, known, and forceable. None of them say what any of it costs. This is the economy the ladder runs on: a ledger where value is never created from nothing, where some things are spent and others reused, and — the part that ties it all together — where a repair like deliberating or escalating is only worth invoking if its value beats its price. It is also where continual learning lives, because finite model capacity is just another conserved resource, and forgetting is the tradeoff you pay to reclaim it.

IThe algebra

A ledger records, for each account, how much of each resource it holds. The only primitive is a transfer that moves an amount between two accounts, and it can never move more than an account holds (the affine floor — no overdraft). There is no "mint": spending is a transfer to a sink, refilling is a transfer from a treasury. Because everything is a transfer in a closed system, the grand total of every resource is conserved by construction — value is never created from nothing. That is your "currency invariant," and it is the same conservation the σ-lattice and CRDTs rely on: independent transactions on disjoint accounts commute.

Linear vs reusable — the of-course modality

Not everything depletes. Linear logic draws the line exactly where this rung needs it: ordinary resources are used once (no duplication, no silent discard), but a resource marked with the ! "of-course" modality may be copied freely. That single distinction is the bridge to continual learning.

Continual learning falls straight out of this. Capacity is a conserved resource: learning a task moves capacity from free to committed (plasticity spent on stability), and consolidation mints reusable ! knowledge that costs nothing to reuse. Forgetting moves capacity back to free — but it must release the knowledge with it. You cannot keep the knowledge and reclaim its capacity, and that impossibility is the stability–plasticity dilemma, stated as a conservation law.

Pricing the repair — Type II rationality

Every rung has a repair: reconcile, contrary-to-duty, escalate, deliberate. None of them are free. The resource rung makes the decision to invoke one explicit — a repair is worth invoking only when its expected value exceeds its cost and you can afford it. The epistemic rung detects a known-unknown; this rung decides whether closing it is rational. That is exactly what bounded-rationality theory calls maximizing utility net of the cost of deliberating.

IIThe laws

Eight for the economy, three for the bridges. The highlighted cross-check is the linear-vs-reusable split: spending depletes, but using a ! resource does not.

IIIThe laws, checked

Each law against random ledgers in your browser — same engine that ships in box-and-box.

IVType sketch

// a closed ledger: accounts → resources → amounts, plus a kind per resource
interface Ledger { bal: Record<Account, Record<Resource, number>>; kind: Record<Resource, "depletable"|"reusable"|"capacity">; }

function transfer(L, res, from, to, amt): Ledger | INFEASIBLE; // the only primitive; conserves Σ
const spend  = (L,a,res,amt) => transfer(L,res,a,SINK,amt);     // consume → sink
const refill = (L,a,res,amt) => transfer(L,res,TREASURY,a,amt); // accrue ← treasury
function feasible(L, a, cost): boolean;                        // the alethic gate; else 0̲
function use(L, a, res): { ok, L };                            // depletes — unless res is `!` reusable

// continual learning
const allocate    = (L,task,amt) => ...; // free → committed (plasticity → stability)
const consolidate = (L,task) => ...;     // mint reusable `!` knowledge
const forget      = (L,task) => ...;     // reclaim capacity — and release the knowledge

// price the repair (Type II)
function repair(L, a, {resource, value, cost}): { decision: "invoke"|"skip"|"cannot-afford", L };

VWorked example

An affordability gate; a Type-II decision over three unknowns (one worth resolving, one not, one unaffordable); and continual learning as conserved capacity — learn two tasks, reuse the knowledge for free, then forget one to reclaim its capacity. Runs live.

VIStanding on

Resources as things used exactly once — no duplication, no discard — is Girard's linear logic (1987), with the ! "of-course" modality marking what may be freely copied. Treating the cost of deciding as part of the decision is I. J. Good's "Type II" rationality and Russell & Wefald's metareasoning (1989). The multi-agent companion this rung points at — bidding, prices, allocation — is market-based control (Clearwater 1996; Wellman's market-oriented programming), which belongs next to the strategic rung rather than here. And the continual-learning reading — capacity as a finite resource split between stability and plasticity — is the central dilemma of lifelong learning, here recast as a conservation law. The logic is established; the contribution is the executable synthesis, and the move of pricing the ladder's own repairs.