@cite{tham-2025} #
Shiao Wei Tham (2025). Multidimensionality and the scalar components of physical disturbance predicates. Glossa: a journal of general linguistics 10(1): 1–30.
Key Claims #
Physical disturbance predicates (crack/cracked, scratch/scratched, dent/dented) are associated with a totally closed, multi-point scale:
Contra @cite{rappaport-hovav-2014}: crack/cracked is NOT two-point (like die/dead). The verb allows durative for adverbials and the adjective accepts comparatives (more cracked).
Contra @cite{rotstein-winter-2004}: cracked is NOT a "partial" adjective with a lower-bounded, upper-open scale. It accepts completely (upper bound) and partially (lower bound).
The scale is multidimensional (@cite{sassoon-2013}, @cite{solt-2018}): the gradable interval comes from multiple dimensions — quantity of disturbances, qualitative severity (depth, length), and spatial positioning.
Lower bound = physical instantiation of disturbance (objective: no faultless disagreement in simple predication). Upper bound = spatial extent of host entity (structural integrity limit).
Adjective vs verb asymmetry: the adjective allows grammatical access to individual dimensions via respect PPs and quantificational operators; the verb allows only conceptual access to dimensions.
Formalization #
- §1: Disturbance predicate data (scale type, modifier compatibility, gradability)
- §2: Key contrasts with non-disturbance predicates (die/dead, shatter/shattered)
- §3: Total closure (completely + partially)
- §4: Entailment pattern (crack vs cool: both closed-scale but different)
- §5: Multidimensionality data and verb-adjective asymmetry
- §6: Bridge theorems connecting fragment entries to existing scale infrastructure
- §7: Kennedy-Levin pipeline tension (closed scale ≠ always telic)
- §8: Connection to @cite{sassoon-2013} binding types (conjunctive/disjunctive insufficiency)
- §9: Connection to @cite{dambrosio-hedden-2024} (counting vs utilitarian aggregation)
A physical disturbance predicate entry, encoding the scalar and distributional properties argued for in the paper.
- root : String
Root form (shared by verb, adjective, and count noun).
- hasCountNoun : Bool
Whether the root has a count noun form (a crack, a dent). Distinguishes disturbance predicates from other CoS predicates like shatter (no *a shatter) and damage (mass only).
- adjGradable : Bool
Whether the deverbal adjective is gradable (more cracked).
- adjCompletely : Bool
Compatible with completely (tests upper closure).
- adjPartially : Bool
Compatible with partially (tests lower closure).
- adjSlightly : Bool
Compatible with slightly (indicates lower bound).
- adjBadly : Bool
Compatible with badly/well (degree modifier for closed scales).
- adjMuch : Bool
Compatible with much (selects quantity dimension specifically).
- verbForX : Bool
Whether the verb allows durative for X adverbials (atelic reading).
- verbInX : Bool
Whether the verb allows in X adverbials (telic reading).
- verbCompletely : Bool
Whether the verb is compatible with completely.
- verbBadly : Bool
Whether the verb is compatible with badly.
- adjRespectPP : Bool
Whether the adjective allows respect PPs (dented with respect to dent size).
- verbRespectPP : Bool
Whether the verb allows respect PPs (degraded for intransitive disturbance CoS verbs, but accepted for causative uses).
- verbInXEntailsResult : Bool
Whether verb + in X entails the result state (cracked in a minute |= is cracked).
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- Phenomena.Gradability.Studies.Tham2025.instBEqDisturbancePredicate.beq x✝¹ x✝ = false
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- Phenomena.Gradability.Studies.Tham2025.instBEqContrastPredicate.beq x✝¹ x✝ = false
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die/dead: two-point scale, non-gradable (#more dead), punctual. @cite{tham-2025} §2.3: crack ≠ die despite both being Levin 45.1. @cite{rappaport-hovav-2014} Table 1 groups both as "two-valued" — Tham shows this is wrong for crack.
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shatter/shattered: punctual, non-gradable. Like die/dead: describes physical objects but NOT a disturbance predicate. Crucially shows that gradability of disturbance predicates is NOT simply a consequence of applying to physical objects.
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damage/damaged: has mass noun (damage to X) but NOT count noun (*a damage in X). Not a disturbance predicate per (4).
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All disturbance predicates accept both completely (upper bound) and partially (lower bound), demonstrating total closure.
All disturbance predicates are gradable (contra two-point classification in @cite{rappaport-hovav-2014} Table 1).
All disturbance predicates have a count noun form, distinguishing them from other CoS predicates (§2.1, ex. 3–5).
Contrast: non-disturbance predicates are NOT gradable.
Contrast: non-disturbance verbs lack durative readings.
§2.4 ex. (13)–(14): Both crack and cool accept in X and for X adverbials (variable telicity). But they differ in entailment: - cracked in a minute |= is cracked (14a) - cooled in ten minutes |= is cool (13a telic reading) - cooled for ten minutes |≠ is cool (13b — process, no endpoint reached) - cracked for a while |= is cracked (14b — process, but entails result!)
Disturbance predicates entail their result state regardless of aspect.
This follows from the lower bound being physical instantiation:
once any cracking exists, the host IS cracked.
All disturbance verbs entail their result state under both in X and for X readings.
Disturbance adjectives have three dimensions (§3.1): - Quantity: number of disturbances (23a, 24a, 25a) - Quality: severity — depth, length, width (23b, 24b, 25b) - Positioning: centrality, array pattern, functionality impact
The adjective allows **quantificational** access to individual dimensions
via *respect* PPs and quantificational operators (*every respect*, *at
least with respect to*). The verb allows only **conceptual** access:
dimensions are interpretively available but resist grammatical
individuation (§4.2).
This quantificational/conceptual distinction aligns with
@cite{ruiz-faroldi-2022}'s typology of multidimensionality: disturbance
adjectives exhibit "quantificational" multidimensionality (dimensions
are grammatically individuable), while disturbance verbs have only
"conceptual" multidimensionality (dimensions available for interpretation
but not grammatical access).
Adjective: quantificational access (respect PPs accepted).
Verb: conceptual access only (respect PPs degraded).
much selects only the quantity dimension, providing distributional evidence that dimensions are independently accessible for adjectives. (§3.3, ex. 30): "a much cracked dish" = many cracks (not one deep crack).
Verify that the Fragment adjective entries classify disturbance
adjectives with the correct Boundedness value.
dead also has .closed — but is non-gradable (two-point). Same
Boundedness, different gradability. Boundedness alone does not
distinguish two-point from multi-point closed scales.
Verb fragment entries have closed degreeAchievementScale.
Adjective-verb scale agreement: each verb inherits the same
Boundedness as its deverbal adjective.
Disturbance adjectives are licensed for degree modification by the Kennedy pipeline, just like full and clean.
Interpretive Economy predicts a max-endpoint standard for disturbance adjectives (closed → maxEndpoint). This interacts non-trivially with Tham's analysis: simple predication (is cracked) requires only the minimum physical instantiation (lower bound), but Interpretive Economy selects the maximum as the positive standard. The resolution is that the positive standard determines the degree needed for the positive form to apply, while the lower bound determines the threshold for being on the scale at all.
The @cite{kennedy-levin-2008} pipeline predicts that closed-scale CoS verbs are telic (accomplishments). But disturbance verbs allow both telic and atelic readings: cracked in a minute AND cracked for two days.
The pipeline gives `defaultVendlerClass = .accomplishment` for crack,
but the fragment entry stipulates `.achievement` (punctual). This is a
genuine divergence: disturbance verbs are NOT standard degree achievements.
Their variable telicity does not reduce to scale boundedness alone.
The pipeline predicts accomplishment for crack (closed → telic → durative).
But the fragment stipulates achievement (punctual telic), capturing the in X = "after" reading (ex. 9): "The mirror will crack in five minutes."
The pipeline and stipulation DIVERGE for disturbance verbs. This is the formal expression of Tham's challenge to the Kennedy-Levin mapping: closed scale does not uniformly predict accomplishment.
break (also Levin 45.1) IS an accomplishment — the standard pipeline works for it. So the divergence is specific to disturbance predicates within the same Levin class.
crack and break share LevinClass but differ in VendlerClass. Both are Levin 45.1 Break verbs, but crack is achievement (punctual + optional durative extension) while break is accomplishment (durative). This within-class split is exactly what Tham's analysis predicts: disturbance predicates have distinctive aspectual behavior.
shatter is also achievement — but unlike crack, shatter ONLY has the punctual reading. Same Vendler class, different aspectual flexibility. VendlerClass is too coarse for disturbance predicates.
Boundedness convergence: both pipelines agree crack is .closed.
Achievement and accomplishment are both telic → .closed, so the
disturbance-specific VendlerClass divergence (§7 above) is invisible
at the Boundedness granularity. This is exactly the gap Tham
identifies: the Kennedy-Levin pipeline is correct about scale closure
but wrong about what that closure implies for aspectual class.
Contrast: @cite{kennedy-levin-2008} study (KennedyLevin2008.lean)
proves convergence for 12 standard DAs — there, convergence at
Boundedness ALSO means convergence at VendlerClass. For crack,
only Boundedness converges.
Disturbance adjectives are multidimensional like @cite{sassoon-2013}'s adjectives (healthy, sick), but their dimensions compose differently.
Sassoon 2013 dimensions bind via quantifiers (∀ = conjunctive, ∃ = disjunctive).
Disturbance adjective dimensions compose via **weighted aggregation**
(eq. 47b): μ(x) = Σᵢ kᵢ · μ_EXTENT(distᵢ(x)) / μ_SPATIAL_EXTENT(x).
This is a new composition mode not captured by `DimensionBindingType`.
Disturbance adjectives are NOT conjunctive: an entity can be badly cracked along one dimension (quality: one deep crack) while scoring low on another (quantity: few cracks). Conjunctive binding would require ALL dimensions to be high, but speakers accept (24b).
Under disjunctive binding, the same entity DOES satisfy the predicate — one high dimension suffices. This is closer to simple predication (is cracked), but still wrong for completely cracked which requires spatial coverage (more like conjunctive over spatial parts).
The key insight: disturbance adjectives behave like BOTH conjunctive (under completely) and disjunctive (under simple predication). Neither Sassoon 2013 binding type captures this. The binding mode shifts with degree modification — a property not shared by Sassoon's healthy/sick adjectives, which are stably conjunctive/disjunctive.
@cite{dambrosio-hedden-2024} show that @cite{sassoon-2013}'s binding types (conjunctive, disjunctive, mixed) are all counting aggregation — a single escape route from Arrow's impossibility. Disturbance adjectives require utilitarian aggregation (weighted sum), which is a categorically different mechanism.
The `sassoon_binding_insufficient` theorem above proves the gap.
D&H's framework explains WHY: counting cannot capture dimension-weight
asymmetries. Utilitarian aggregation resolves this by assigning
different weights to quantity, quality, and positioning.
Disturbance adjective dimensions as Bool predicates.
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Counting (k=2) accepts a vase with many shallow scratches (high quantity, low quality, high positioning): 2 of 3 dims.
Quality-weighted aggregation [1, 3, 1] with θ=3 REJECTS the same vase: severity matters more than count. Score = 1·1 + 3·0 + 1·1 = 2 < 3.
Counting and weighted aggregation DIVERGE on high-quantity low-quality configurations. This is the formal expression of eq. 47b's advantage: weighted aggregation captures dimension asymmetry that counting misses.
All of Sassoon 2013's binding types are counting aggregation.
Utilitarian (weighted sum) is genuinely beyond Sassoon's typology.
This explains the insufficiency proved in sassoon_binding_insufficient.