Tham (2025): Multidimensionality and the Scalar Components of Physical Disturbance Predicates #
This file formalizes [Tha25]'s account of physical disturbance predicates, change-of-state verbs such as crack, dent and scratch and their deverbal adjectives, whose root has a count noun form naming an irregularity in an affected host ([Kar77a]). The paper argues that the predicates are associated with a gradable scale closed at both ends, against the two-point scale of [RH14] and the partial, upper-open scale of [RW04b]: the verb has durative uses and the adjective comparative ones, (10)–(11), both take completely and partially, (15), (20)–(21), and both telic and atelic uses of the verb entail the adjectival state, (14), (17). The adjective is multidimensional in the sense of [Sas13] and [Sol18a]: badly evokes the quantity, quality or positioning of the disturbances, (22)–(25), and respect phrases individuate the dimensions, (28). The three scalar components have three sources (section 3.4): the lower bound is the existence of a disturbance, so unmodified predication is objective, (26); the gradable interval comes from the dimensions, so degree-modified predication admits faultless disagreement, (27); and the upper bound is the spatial extent of the host, (33).
The adjective's measure function (47b) is the weighted extent of the disturbances relative to
the host's spatial extent, degree, with the weights the context's dimensions; the positive
form (46) compares it with a degree, Pos. A weighting positive on every dimension makes the
degree positive exactly when some disturbance has positive extent, degree_pos_iff, so
whether the host is cracked does not depend on the weighting, degree_pos_iff_degree_pos,
while the weightings that select single dimensions, the respect phrases respect, can rank two
hosts oppositely, more_respect_and_more_respect. A disturbance within the host's extent has a
degree at most one, degree_le_one, and the same disturbance on a smaller host has a higher
degree, degree_lt_degree_of_lt. The verb (48) describes an event whose final degree meets the
root's standard and exceeds the initial degree by a difference degree, Event, Verb: every
use of the verb entails the adjective at the standard, Verb.pos_final, and the verb modified
by a high difference degree entails the adjective modified by the same degree, Verb.pos, but
not conversely, since a pre-existing crack that grows a little leaves the windshield badly
cracked without its having cracked badly, Event.pos_not_verb.
Implementation notes #
The measure sums over an index type of dimensions, each with a nonnegative extent measure on
hosts, in the profile vocabulary of SocialChoice; the paper's comparative at a
weighting is the utilitarian rule on the extent profile when the hosts have the same spatial
extent, more_iff_utilitarian. A respect phrase is the weighting Pi.single i 1, so respect
phrases and quantification over respects are the paper's grammatical access to dimensions for
the adjective; the paper's claim that the verb allows only conceptual access, and its speculation
that the difference degree is the reason, are not formalized. The examples are the rows of
Data.Examples.Tham2025; the consultant counts of section 4.2 and the online survey of section
3.2.2 are recorded in their comments.
References #
The adjective (section 5.2, (46)–(47)) #
The degree of disturbance of a host (47b) is the extent of its disturbances along each dimension, weighted by the context, relative to its spatial extent.
Equations
- Tham2025.degree k v spatial x = k ⬝ᵥ v x / spatial x
Instances For
A respect phrase weights the single dimension it names.
Equations
- Tham2025.respect i = Pi.single i 1
Instances For
Completely (20), (33) says that the disturbance exhausts the host's extent.
Under a respect phrase the degree is the extent along the named dimension.
The positive form (46) holds when the host is disturbed to degree d or beyond.
Equations
- Tham2025.Pos k v spatial d x = (d ≤ Tham2025.degree k v spatial x)
Instances For
The comparative holds when x is more disturbed than y.
Equations
- Tham2025.More k v spatial x y = (Tham2025.degree k v spatial y < Tham2025.degree k v spatial x)
Instances For
The lower bound is the existence of a disturbance (section 3.4). Under a weighting positive on every dimension, the host has a positive degree exactly when some disturbance has positive extent.
Unmodified predication is objective (section 3.2.1), since whether the host is disturbed at all does not depend on the weighting of the dimensions.
The upper bound is the spatial extent of the host (section 3.4), so a disturbance within the host's extent has degree at most one.
The same disturbance on a smaller host is a higher degree of disturbance.
At equal spatial extents the comparative is the utilitarian rule of the weighting on the extent profile.
Respect phrases (sections 3.2.2 and 4.2) #
In more dented with respect to dent size (28a), (42a), the comparative under a respect phrase compares the named dimension alone.
Degree-modified predication allows faultless disagreement (27), (28a), since two hosts can each be more disturbed than the other with respect to some dimension.
The verb (section 5.2, (48)) #
A physical disturbance event (48) is a change between states whose final degree of disturbance meets the root's standard and exceeds the initial degree. The initial degree may already meet the standard, when the host bears an earlier disturbance.
- init : σ
The state at the start of the event.
- final : σ
The state at the end of the event.
- std_le : std ≤ μ self.final
Instances For
The verb at a difference degree, its degree argument in (48).
Equations
- Tham2025.Verb d e = (d ≤ e.diff)
Instances For
Cracked completely/slightly entails is cracked (17a), since every event entails the adjectival state at the root's standard, whatever its difference degree.
Badly cracked holds without cracked badly (section 5.2). A windshield with a pre-existing crack that grows a little is badly cracked at the end, yet did not crack badly, since the difference degree is small.