nucleation

CLAIM-106: Pragmatic fidelity is a graded, potentially asymmetric property of transport, not an equivalence relation; equivalence is its zero-distortion limit

2 min read

Properties15
StatusActive
Version3
Rolethesis
Warrantinterpretive
Tagsphilosophy-of-language, mathematics
Linepragmatic-transport
Workswhat-survives-translation
GroundsCASE-015 — The telephone game
SupportsCLAIM-056 — Local transport errors in a reconstruction chain are bounded by the per-step discrepancies weighted by the sensitivity of the later reconstructions, so the same local error can be damped, accumulated or amplified, and local similarity can coexist with large global drift; the bound measures departure from a reference transport, not whether the act survives, CLAIM-101 — Translation is a context-conditioned transport process that preserves selected structures of communicative meaning to varying degrees while introducing distortions that may accumulate, attenuate or amplify under composition, CLAIM-128 — No single ranking of translations holds across tasks: where distortion profiles trade off, only a task's priorities rank them, and the theory of fidelity fixes no weighting, CLAIM-246 — Sharing a kind is symmetric and blind to which work is the source, so the October thesis cannot say a translation is of its original, against the line's own directed, graded fidelity and identity through descent
Objects toCLAIM-067 — If a transport exactly intertwines a generating set of communicative operations, it preserves every trajectory composed from them
Objected byCLAIM-218 — The task-paired risk difference the record uses in place of Blackwell's order, D_Q = sup_q |R_q(U) − R_τ(q)(V)|, is a different quantity: it reduces each risk set to one number, needs the losses of paired tasks on one scale, and its absolute value counts improvement as distortion
SupersedesCLAIM-067 — If a transport exactly intertwines a generating set of communicative operations, it preserves every trajectory composed from them
ComplementsCLAIM-210 — Sharing a kind and being a rendering are different relations: kind-sharing is symmetric and says what is to be preserved, while fidelity belongs to a transport from a given source, so an utterance of the same kind made independently of the source shares its kind and has no fidelity to it, CLAIM-259 — For report fidelity, the decision term should be the positive part of the risk increase on the same decision problem, with losses in [0, 1] and a stated prior; so restated it is directed, counts no improvement as loss, and vanishes for every problem and prior exactly when the rendering is at least as informative as the source in Blackwell's order
UsesTERM-015 — fidelity, as graded, directed transport distortion, TERM-008 — transport
Cited as “rests on” byCLAIM-242 — The use-level counterpart of Saussure's value is an utterance's contrast with the alternatives its speaker could have used in context; values do not cross between languages, which is why fidelity is graded transport through an anchored correspondence rather than identity of value

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The claim

U20: “I think presenting this as an equivalence might be too constraining. I agree that there should be some transport map that at least gets to within some eps, but that’s just a similarity constraint, not an equivalence. This is why the game ‘telephone’ works.” A50: “I think this is an important correction.” A52’s thesis: “Pragmatic fidelity is therefore a graded, potentially asymmetric property of transport, rather than fundamentally an equivalence relation.”

Two consequences A50 drew: “There is no requirement that the transport be invertible or symmetric”, and “similarity is not transitive” (CLAIM-056). Manuscript §6: the transport (TERM-008) “is intentionally directed: compression and interpretation need not be invertible”; §12: “stochastic transport generalizes exact equivalence to graded fidelity”.

What it does not say

That equivalence is useless: “We can still recover equivalence as a special case—for example, zero distortion under a suitably separating observation family.” Nor which distortion measure to use (QUESTION-017). Nor that A86’s D_Q realizes it: D_Q is symmetric (CLAIM-218), and a directed term is proposed in CLAIM-259.

Note of 2026-10-28: promoted

The status review of this date promoted this claim (ADR-057). CASE-015 and the terms it uses are Active, and no judgement data in the record show fidelity verdicts behaving as an equivalence. CLAIM-218, its one objection, is aimed at the measure: “It does not say CLAIM-106 is false.” That is conceded above, in what the claim does not say. The directed repair, CLAIM-259, stays Proposed.

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