The claim
This is the record’s reply of 2026-10-10 to CLAIM-236. It is decisive and checkable: it is read off the form of CLAIM-111’s criterion, and the arithmetic below is the objection’s own, re-derived.
CLAIM-111’s criterion is P_o(z | c_o, u_o) ≈ P_t(τ_z(z) | c_t, u_t), “where τ_z maps corresponding latent communicative frames across linguistic environments”. Each side is a listener’s posterior over situations: on the left a source-language listener’s, given the source utterance; on the right a target-language listener’s, given the rendering. On the rational-speech-act model of THEORY-172, each listener’s posterior is computed with that listener’s own language’s alternatives. The criterion then compares the two posteriors through τ_z, which maps situations, not utterances. Nothing in it maps one language’s alternatives onto the other’s, and nothing needs to. The objection asked for “a rule for when a target form with different alternatives counts as matching”. The criterion is that rule: a target form matches when its posterior matches.
The worked case, re-derived
The objection’s case: two meanings, m₁ and m₂, with a uniform prior; the speaker’s rationality α = 1, and no costs. The pragmatic speaker chooses an utterance u for meaning m in proportion to exp(α log P_Lit(m | u)), which with α = 1 is in proportion to P_Lit(m | u).
- Source language: a is true of m₁ and m₂; b is true of m₂ only. The literal listener gives P_Lit(m₁ | a) = P_Lit(m₂ | a) = 1/2 and P_Lit(m₂ | b) = 1. The speaker with m₁ has only a, so P_S(a | m₁) = 1. The speaker with m₂ weighs a at 1/2 and b at 1, so P_S(a | m₂) = (1/2)/(1/2 + 1) = 1/3 and P_S(b | m₂) = 2/3. The pragmatic listener: P_L(m₁ | a) = (1 · 1/2)/(1 · 1/2 + 1/3 · 1/2) = (1/2)/(2/3) = 3/4.
- Target language: one utterance, a′, true of m₁ and m₂. Each speaker has only a′, so P_S(a′ | m₁) = P_S(a′ | m₂) = 1, and P_L(m₁ | a′) = (1 · 1/2)/(1 · 1/2 + 1 · 1/2) = 1/2.
Take τ_z as the identity on {m₁, m₂}. The criterion compares 3/4 with 1/2 and, for any tolerance smaller than 1/4, finds a′ unfaithful to a. That is the right verdict. a means “m₁, probably”, because a speaker with m₂ had b and would likely have used it. a′ keeps the literal content of a and loses that scalar implicature. The objection’s arithmetic stands; what does not follow from it is that the criterion needs a further correspondence. It shows the criterion working.
What follows instead
The target inventory bounds fidelity. In this target language every utterance gives P_L(m₁ | ·) = 1/2, because there is only one. So no rendering of a passes the criterion: the target language cannot say what the source said by implicature. That is CLAIM-033’s point from Jakobson, “Languages differ in what they must convey”, met here for what a language can convey by implicature. It is a consequence of the criterion, not a gap in it: a fidelity criterion should report that some source posteriors have no faithful rendering in a given target.
Alternatives matter for prediction, not for application. To predict P_t from a model, one needs the target language’s alternatives, as THEORY-172’s model needs any language’s. To apply the criterion one needs only the two posteriors, which can be elicited from listeners of each language without modelling either inventory.
τ_z is still needed. The criterion keeps its correspondence of situations, and how to fix it without building in the preferred notion of fidelity is QUESTION-005. This reply removes only the second correspondence the objection added.
What it answers
CLAIM-236, filed as granted on 2026-10-10, said that matching posteriors across languages “needs a correspondence between source and target alternative sets, or a rule for when a target form with different alternatives counts as matching”. The worked case is kept; the conclusion is answered by the reading above. The objection is Rejected by this claim. Its role stays as filed, and its history says the concession is withdrawn on this argument.
What it does not say
- It does not say the rational-speech-act model is right. THEORY-172 is “Shown for artificial games with given alternatives”, and the reply uses the model only because the objection did.
- It does not say THEORY-172’s evidence shows the criterion applies to poems, where the alternatives are neither given nor few. That paragraph of the objection stands.
- It does not make CLAIM-111 a premise of CLAIM-115 or CLAIM-139; it is not one.