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Linglib.Phenomena.Conditionals.Studies.VonFintelIatridou2005

@cite{vonfintel-iatridou-2005} — Anankastic conditionals and related matters #

The "Harlem Sentence" — If you want to go to Harlem, you have to take the A train — and the puzzle: no straightforward Kratzerian analysis delivers its truth conditions. vF&I rule out three candidate analyses (if-clause restricts the modal base, modifies the ordering source à la @cite{saebo-2001}, or is restricted by a covert higher modal), then propose a Designated Goals account paired with @cite{sloman-1970}'s have-to-vs-ought-to distinction.

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Example data lives in Linglib/Data/Examples/vonFintelIatridou2005.json and is generated into the Examples section below by scripts/gen_examples.py vonFintelIatridou2005.

Analytical predicates #

Each candidate analysis is a predicate parameterized by the relevant propositions on a world type. Concrete vF&I scenarios (Hoboken, Conflicting Goals) instantiate these arguments with their own predicates and decide discharges the refutation. Bundling the propositions into a Scenario structure would hide the per-predicate decidability the refutations need behind a field projection; the explicit-argument form keeps each refutation mechanically verifiable. The circumstantial modal base is taken as universal (the worked vF&I scenarios do not exploit modal-base restriction).

Obvious analysis and the Hoboken Problem #

vF&I eq. (9): [have to](w)(f)(g)(q) = 1 iff ∀w' ∈ max_{g(w)}(∩f(w)) : q(w') = 1. vF&I eq. (10): [if φ](f) = λw. f(w) ∪ {⟦φ⟧}.

Combined, the "obvious analysis" of the Harlem Sentence asserts: in the best (per actual goals) worlds where you want to go to Harlem, you take the A train. In the Hoboken scenario the actual ordering source ranks worlds by satisfaction of want-Hoboken. Best want-Harlem worlds are then those that simultaneously achieve Hoboken — i.e., take the PATH train — so the obvious analysis predicts the sentence false (vF&I p. 5 intuition: true).

def Phenomena.Conditionals.Studies.VonFintelIatridou2005.obviousAnalysis {W : Type u_1} (wantHyp achieveAct candidate : WProp) :

The obvious analysis: the candidate is true at every want-Harlem world that maximizes actual-goal-achievement.

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    The Hoboken scenario. Four worlds: w0: A train, achieves Harlem; w1: PATH, achieves Hoboken; w2: PATH, achieves both Hoboken AND want-Harlem holds — the counterexample world; w3: A train, achieves Harlem.

    Sæbø 2001's analysis and the Conflicting Goals refutation #

    @cite{saebo-2001} adds the if-clause's proposition to the ordering source rather than the modal base: g⁺(w) := g(w) ∪ {⟦want-Harlem⟧}. The modal quantifies over best worlds in the modal base under g⁺. This survives the basic Hoboken setup but is non-compositional (want has to be zapped) and fails on Conflicting Goals scenarios (vF&I (13), (22)) where actual and hypothetical goals are jointly satisfiable yet conflicting in the concrete instance.

    def Phenomena.Conditionals.Studies.VonFintelIatridou2005.saeboAnalysis {W : Type u_1} (achieveAct achieveHyp candidate : WProp) :

    Sæbø's analysis: quantifies over worlds maximizing actual goal ∧ hypothetical goal jointly.

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      The Conflicting Goals scenario (vF&I (13)/(22)). Five worlds: w0: A, Harlem-only; w1: PATH, Hoboken-only; w2: A, both; w3: PATH, both — the counterexample world; w4: neither, neither.

      The Conflicting Goals scenario falsifies Sæbø's analysis: at w3 both goals are jointly achieved but the candidate (A train) is false.

      Nested Modality #

      vF&I §5 propose that the if-clause restricts an additional covert necessity modal scoping over the teleological modal: [ NEC if you want to go to Harlem ] [ have-to (you take the A train) ]. This survives the Hoboken Problem but fails on the Conflicting Goals scenario and on Huitink's van Nistelrooy (correlated-irrelevant). The shared failure motivates the Designated Goals move below. Not formalised here.

      The Designated Goals proposal #

      @cite{vonfintel-iatridou-2005} §6 parameter for a teleological modal: a designated goal supplied by the to/if-clause, ancillary considerations ranking goal-achieving worlds, and a circumstantial modal base.

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        vF&I (24a): to p, ought-to q — q at every ancillary-best goal-achieving world.

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          vF&I (24b): to p, have-to q — q at every goal-achieving world in the modal base. The exhaustification (no ranking) is the formal counterpart of @cite{sloman-1970}'s "only candidate".

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            theorem Phenomena.Conditionals.Studies.VonFintelIatridou2005.haveTo_implies_oughtTo_of_best_subset_accessible {W : Type u_1} (dg : DesignatedGoal W) (q : WProp) (w : W) (hHave : haveTo dg q w) (hBestSubset : w'Semantics.Modality.Kratzer.bestWorlds dg.modalBase (fun (v : W) => dg.ancillary v ++ [dg.goal]) w, w' Semantics.Modality.Kratzer.accessibleWorlds dg.modalBase w dg.goal w') :
            oughtTo dg q w

            @cite{sloman-1970} / vF&I §6: have-to entails ought-to, under the structural assumption that every ancillary-best world is accessible and goal-achieving.

            Cross-reference to @cite{chung-mascarenhas-2024} #

            C&M's mustCM operator (Phenomena/Modality/Studies/ChungMascarenhas2024.lean) realises @cite{sloman-1970}'s "only candidate" condition as an exhaustification clause on expected values: mustCM φ iff E[μ_R ∣ φ] > θ ∧ ∀ψ ∈ Alt(φ). E[μ_R ∣ ψ] ≤ θ. The first conjunct is strong permissibility (φ achieves the goal well enough); the second is the only-candidate condition. Under deontic/teleological R = R_D, this directly maps to vF&I's have-to: φ has to be the unique good-enough way of achieving the designated goal.

            Handled cleanly by C&M:

            Not dissolved by C&M:

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