@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.
This file contains:
obviousAnalysis(if-clause adds to modal base) refuted on the Hoboken Problem (vF&I (11));saeboAnalysis(if-clause adds to ordering source) refuted on the Conflicting Goals scenario (vF&I (13));- the Designated Goals structure with
oughtTo/haveTooperators and the Sloman entailmenthaveTo_implies_oughtTo_of_best_subset_accessible; - cross-reference (in the closing docstring) to @cite{chung-mascarenhas-2024}: the C&M exhaustification clause is the formal expected-value realisation of Sloman's "only candidate". C&M handles the Harlem base case, Burdick's contextual designation, and Breathe-style trivialities (via §5 plausibility). Open: Nissenbaum Pedro Martinez (no causal-essentialness filter); Huitink van Nistelrooy (correlated-irrelevant).
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).
The obvious analysis: the candidate is true at every want-Harlem world that maximizes actual-goal-achievement.
Equations
- Phenomena.Conditionals.Studies.VonFintelIatridou2005.obviousAnalysis wantHyp achieveAct candidate = ∀ (w : W), wantHyp w → (∀ (w' : W), wantHyp w' → achieveAct w' → achieveAct w) → candidate w
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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.
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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.HobokenScenario.wantHypothetical w = (↑w = 0 ∨ ↑w = 2 ∨ ↑w = 3)
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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.HobokenScenario.achieveActual w = (↑w = 1 ∨ ↑w = 2)
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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.HobokenScenario.takeCandidate w = (↑w = 0 ∨ ↑w = 3)
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The Hoboken scenario falsifies the obvious analysis: at w2 the
candidate (A train) is false.
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.
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.
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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.ConflictingGoalsScenario.achieveHypothetical w = (↑w = 0 ∨ ↑w = 2 ∨ ↑w = 3)
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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.ConflictingGoalsScenario.achieveActual w = (↑w = 1 ∨ ↑w = 2 ∨ ↑w = 3)
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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.
- goal : W → Prop
The designated goal: a proposition the addressee is taken to pursue.
- ancillary : Core.Logic.Intensional.OrderingSource W
Ancillary considerations: a Kratzer ordering source over worlds.
- modalBase : Core.Logic.Intensional.ModalBase W
Circumstantial modal base.
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vF&I (24a): to p, ought-to q — q at every ancillary-best goal-achieving world.
Equations
- Phenomena.Conditionals.Studies.VonFintelIatridou2005.oughtTo dg q w = ∀ w' ∈ Semantics.Modality.Kratzer.bestWorlds dg.modalBase (fun (v : W) => dg.ancillary v ++ [dg.goal]) w, q w'
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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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- Phenomena.Conditionals.Studies.VonFintelIatridou2005.haveTo dg q w = ∀ w' ∈ Semantics.Modality.Kratzer.accessibleWorlds dg.modalBase w, dg.goal w' → q w'
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@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:
- Harlem base case (
vFI2005_1_harlem,vFI2005_4_harlemPurpose). - Burdick's hot chocolate (
vFI2005_28_burdicks) via contextually suppliedR. - Trivially-true Breathe (
vFI2005_34c_harlemBreathe) via §5 plausibility requirement onR. - Sloman's have-to-vs-ought-to (
vFI2005_23_slomanOughtNot,vFI2005_p13_londonByNoon) by dropping the exhaustification clause for ought-to.
Not dissolved by C&M:
- Pedro Martinez (
vFI2005_36_pedroMartinez): C&M'sRis a flat set of propositions, no causal-essentialness filter. Nissenbaum's insight (the to-clause requires the consequent to be an essential part of a way of achieving the goal) is not in C&M. - Van Nistelrooy (
vFI2005_p12_vanNistelrooy): correlated-irrelevant preferences enterRand skew the expected value.
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