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Syntax and Semantics of the Swarm Alternation
Hole, D. & Fraser, K. (2026). Linguistics
In the non-base alternant of the swarm alternation, the garden is swarming with bees, a pluractional swarming causes a state of the garden's inside being with bees, the garden being the landmark of the swarming and binding the variable of the inside (69). The pluractional head (66) asks for more atomic subevents than a contextual threshold, so the alternant is quasi-homogeneous, true of every part of its events with enough atomic subevents and of no atom, and atelic, as the in and for adverbials of (14) show. Locatum abundance is asserted and denied by a plain no, while the alternant's scalarity and mirativity (71) are not at issue. Granting that they project, their judgments in neutral contexts and in belief reports put them in the class of projective content with obligatory local effect and no strong contextual felicity constraint. Scalarity clashes with even under negation, which presupposes a low value, (38)–(40). The two contents need heads above tense, so a non-base gerund projects to mirativity where a base one stops at tense, and the adverbs only the former admits are those of the heads in between (§4). Levin's class pages attest the alternation for six of the seven verb classes of (11).
Implementation notes
- (66) counts the atomic proper parts of an event, here its atomic parts, the same above a threshold of one. Quasi-homogeneity takes the swarming to be quasi-homogeneous, the states of central coincidence (64) and the landmark relation to be divisive, and the parts of a causing event to cause parts of its state, as hypotheses; with is where the paper places homogeneity.
- Tonhauser, Beaver, Roberts and Simons classify projective contents, and the paper does not test projection, so the class is this file's inference. The contexts of (30)–(32), a normal count, are neutral about an unusually high one, and the sentences are read without nur so; (50a)'s "isn't a big deal" bears on remarkableness as much as on amount.
- Mirativity is just below Cinque's evaluative mood, the paper's "probably right below", and scalarity just above his past tense (§4.1); "continuative aspect I" is his continuative. Cinque pairs surprisingly with the evaluative mood, so (52)–(53) split his class. Future tense, irrealis mood and the alethic modals are below past tense, so then, perhaps, possibly and necessarily are predicted good in both gerunds.
Errata
- In (67)–(69) the abundance condition counts the parts of
e′, free oncee′is reduced away; it is read as counting the parts ofe. (67a) applies the one-placevto the PP and to the VP, which enters by event identification. - The locatum enters (69) only through the result state, so theme abundance does not follow from
event abundance as p. 24 says (
exists_nonBase_atom); the route through (64) on p. 23 is open. - (71) relativizes scalarity and mirativity to a parameter
Sread as the speaker, and leaveswfree. (25) and (50) need the attitude holder's evaluation, and no denotation shiftsS: with the holder's, (50b) is inconsistent (not_subset_compl_of_image_subset), with the speaker's it is not (exists_speaker_consistent). - §4.2 has habitual aspect "immediately dominated by T", where Cinque puts future tense, irrealis mood and the alethic modals between. P. 24 dates Dowty's dynamic texture 2000, §3.2 2001, and (55) refers to §3.2.2 for §3.3.2. The bibliography dates Henderson's dissertation 2014 for 2012, and "Dowty (2000: 2)" and "(2001: 6)" fall outside the page ranges it gives.
TODO
- The consider test (25) as the discretionariness that
Studies/Coppock2018.leanasks of consider, and the non-atomic locatum of (12) from central coincidence in a spatial model.
References
- Hole & Fraser 2026, Syntax and Semantics of the Swarm Alternation
- Cinque 1999, Adverbs and Functional Heads: A Cross-Linguistic Perspective formalized
- Tonhauser et al. 2013, Toward a Taxonomy of Projective Content formalized
- Krifka 1998, The Origins of Telicity formalized
- Levin 1993, English Verb Classes and Alternations: A Preliminary Investigation formalized
The non-base alternant, §5.2
The non-base alternant (69): a pluractional swarming that causes a state of the landmark's
inside and the locatum y being centrally coincident (64), the landmark g.
- nonBase θ swarm cause coincident landmark g y e = (pluract θ swarm e ∧ (∃ (s : S), coincident g y s ∧ cause s e) ∧ landmark g e)
Built from
Used by not_nonBase_of_atom, isQuasiHomogeneous_nonBase, not_isTelic_nonBase, exists_nonBase_atom
A predicate is quasi-homogeneous (§3.2.2) when it is true of every part of its events with
more than θ atomic parts.
- IsQuasiHomogeneous θ P = ∀ ⦃e e' : E⦄, P e → e' ≤ e → θ < (Mereology.atomsBelow e').encard → P e'
Used by isQuasiHomogeneous_nonBase, IsQuasiHomogeneous.not_isTelic, not_isTelic_nonBase
Built from
Built from ,
Built from
The non-base alternant is atelic, by its quasi-homogeneity (§3.2.2).
Built from ,
Built from
At-issue and projective content, §3.1 and §3.3
The two alternants.
Derives DecidableEq, Repr.
Used by alternantOf, BeneathSatisfiable, beneathSatisfiable_iff, required, size
The alternant of a row.
- alternantOf d = d.parse? "alternant" [("base", Alternant.base), ("nonBase", Alternant.nonBase)]
Built from
Used by nonBase_class_eq_C, even_rows, gerund_rows
The contents of the non-base alternant that the diagnostics target.
Derives DecidableEq, Repr.
Used by Content.IsAtIssue, contentOf
A content is at issue when (69) asserts it, as it does locatum abundance through the threshold of (66); scalarity and mirativity are the definedness conditions of (71).
- c.IsAtIssue = (c = Content.abundance)
Built from
A reply to the alternant, a plain denial or Hey, wait a minute.
Derives DecidableEq, Repr.
Used by responseOf
The content a row targets.
The definition is too large to print here; read it in the source.
Built from
Used by denial_rows
The reply of a row.
- responseOf d = d.parse? "response" [("denial", Response.denial), ("wait a minute", Response.waitAMinute)]
Built from
Used by denial_rows
A plain no denies locatum abundance but not scalarity or mirativity.
Built from , ,
The diagnostic a row answers: an unembedded sentence in a context neutral about the content, or a belief report whose holder's state denies it.
The definition is too large to print here; read it in the source.
Used by nonBase_class_eq_C
Of the classes of projective content, the judgments of the non-base rows fit exactly the one with obligatory local effect and no strong contextual felicity constraint.
Built from ,
Not even, §3.3.4
The presuppositions of even under negation, a value below the low threshold lo (36), and
of the non-base alternant's scalarity, a value above the upper threshold of normalcy hi (71a),
can be met together.
- BeneathSatisfiable lo hi a = ∃ v < lo, a = Alternant.nonBase → hi < v
Built from
Used by beneathSatisfiable_iff, even_rows
Built from ,
not even is good exactly with the base alternant, (38)–(40).
Built from ,
The size of a gerund, §4
The heads of the paper's hierarchy: Cinque's, a mirative head and a scalarity head.
- cinque (h : Cartography.Head) : Head
- mirative : Head
- scalarity : Head
Derives DecidableEq, Fintype.
Used by Head.rank, Head.instLinearOrder, Head.ofCinque, required, size, projectionOf, mem_Ioc_size_iff
The place of a head, three to each of Cinque's: mirativity just below his evaluative mood, scalarity just above his past tense.
- (Head.cinque a).rank = 3 * a.ctorIdx + 1
- Head.mirative.rank = 3 * Cartography.Head.moodEvaluative.ctorIdx
- Head.scalarity.rank = 3 * Cartography.Head.tPast.ctorIdx + 2
Built from
Used by Head.instLinearOrder
- Head.instLinearOrder = LinearOrder.lift' Head.rank Head.instLinearOrder._proof_1
Built from ,
Cinque's hierarchy embeds in the paper's.
- Head.ofCinque = OrderEmbedding.ofStrictMono Head.cinque Head.ofCinque._proof_1
Built from
The heads a gerund of an alternant requires: tense, and the scalarity and mirativity of the non-base alternant (§4.1).
- required Alternant.base = {Head.cinque Cartography.Head.tPast}
- required Alternant.nonBase = {Head.cinque Cartography.Head.tPast, Head.scalarity, Head.mirative}
Built from ,
Used by size
A gerund projects as high as its highest required head (§4.1).
Built from , ,
Used by size_base, size_nonBase, gerund_rows, mem_Ioc_size_iff
Built from
Built from
The head of the adverb class a row tests, by the projection the paper names.
The definition is too large to print here; read it in the source.
Built from
Used by gerund_rows
An adverb is good in a gerund exactly when its head is no higher than the gerund projects, (51)–(60).
Built from , ,
Built from ,
The participating verb classes, §2
The verb classes of (11).
The definition is too large to print here; read it in the source.
Used by participates_swarm_iff