Probes and Their Horizons @cite{keine-2020} #
Probes and Their Horizons. MIT Press, LI Monograph 81.
Summary #
@cite{keine-2020} is the monograph expansion of @cite{keine-2019}. It develops a comprehensive theory of selective opacity — where the same domain is opaque to some operations but transparent to others — based on probe-specific horizons and bilateral labeling.
Core Contributions Formalized #
Bilateral labeling (ch. 3): within an extended projection, both head and complement project labels. CP's label is
[C, T, v, V]. A probe's search terminates when the horizon category appears in the label. This derives Upward Entailment as an emergent property.Language-parameterized probes: Hindi, English, German, Itelmen, and Tsez have different probe–horizon pairings (
LanguageProbeConfig).NmlzP ≱ CP (ch. 2): Hindi has four clause sizes (vP, TP, NmlzP, CP) that are NOT linearly ordered — NmlzP is opaque to Ā but transparent to wh, while CP is the reverse.
ForceP (ch. 4): German V2 clauses are structurally larger than V-final CPs — they project ForceP.
vP is not a phase (ch. 5): φ-Agree crosses unboundedly many vPs but not CPs; selective opacity creates intractable problems for vP phases; previous arguments can be reanalyzed.
Default horizon (307): for probe [F] on X⁰, default horizon = X.
Horizons + phases coexist (ch. 4): horizons determine selective opacity (probe-specific); CP phases impose absolute opacity (all operations). These are orthogonal constraints.
Vacuous probes (§3.5, (274)–(278)): a probe whose sister's bilateral label contains the horizon category is vacuous — its search terminates at the sister, leaving no searchable domain.
Height-Locality Theorem ((279)): location→horizon and horizon→location constraints emerge from bilateral labeling + vacuity filtering.
Ban on Improper Movement (§3.4.1–3.4.2): Ā-movement cannot feed A-movement — derived from horizons, not stipulated.
A-movement–Agreement Generalization ((231)): A-extraction forces obligatory LDA — A-probes and φ-probes share horizons in Hindi.
Movement–agreement mismatches (§3.4.5): Itelmen and Tsez show that φ-agreement and A-movement can have different horizons in opposite directions, via @cite{bobaljik-wurmbrand-2005} and @cite{polinsky-potsdam-2001}.
Smuggling constraints (§3.4.3, (248)–(259)): A-movement out of Ā-moved constituents is blocked by horizons (CP encapsulates); Ā-movement out of A-moved constituents is not blocked.
Crosslinguistic A-movement typology (§3.6, (300)): three attested settings (Lubukusu ⊣ ∅, English ⊣ C, Hindi ⊣ T) form an entailment chain.
Phase–horizon orthogonality (ch. 4): phases provide absolute opacity (Spell-Out), horizons provide selective opacity (search termination). These are orthogonal constraints.
Architecture #
This file imports Probe.lean (for ProbeProfile, LanguageProbeConfig,
transparentToLabel) and ClauseSpine.lean (for clause spines with
bilateral labels). It verifies the book's predictions as theorems.
Hindi 4×4 Transparency Table #
| Operation | vP | TP | NmlzP | CP |
|---|---|---|---|---|
| φ-agreement | ✓ | * | * | * |
| A-movement | ✓ | * | * | * |
| wh-licensing | ✓ | ✓ | ✓ | * |
| Ā-movement | ✓ | ✓ | * | ✓ |
The key discovery: NmlzP and CP are NOT linearly ordered. NmlzP blocks Ā but not wh; CP blocks wh but not Ā.
NmlzP and CP are incomparable: each is opaque to one probe but transparent to the other. This cannot be captured by a linear fValue ordering — it requires bilateral labeling.
NmlzP and CP have the same number of projected heads — their difference is qualitative (which heads), not quantitative (how many).
The bilateral labels of NmlzP and CP differ precisely in their topmost head: Nmlz vs C.
German 4×4 Transparency Table #
| Operation | vP | TP | CP (V-final) | ForceP (V2) |
|---|---|---|---|---|
| scrambling | ✓ | * | * | * |
| relativization | ✓ | ✓ | * | * |
| wh-movement | ✓ | ✓ | ✓ | * |
| topicalization | ✓ | ✓ | ✓ | ✓ |
English hyperraising blocked: A-probe (T⁰, ⊣ C) cannot search into CP.
English wh-extraction OK: wh-probe (C⁰, ⊣ ∅) has no horizon.
Generalization (21): A-extraction renders clause transparent for LDA. A-movement and φ-agreement share the same probe settings in Hindi: both on T⁰ with horizon T.
Generalization (23): finite clauses (CP) are opaque to A-movement and φ-agreement but transparent to Ā-movement.
Hindi φ and A probes use the default horizon: probe on T⁰ with horizon T (= its own head).
German scrambling probe uses the default horizon: probe on T⁰ with horizon T.
Hindi exhibits four distinct locality types — one per operation. Using bilateral labeling, each probe produces a unique 4-tuple of transparency values across (vP, TP, NmlzP, CP).
Equations
- One or more equations did not get rendered due to their size.
Instances For
Under bilateral labeling, the specific horizon category matters. Hindi wh (horizon C) and Ā (horizon Nmlz) are both on C⁰ but have different transparency profiles — proving that the A/Ā distinction is not strictly derived from probe height.
ForceP projects all the heads that CP does, plus Force.
ForceP is strictly larger than CP in spine size.
Vacuous probes: bilateral-labeling-derived #
A probe is vacuous when its sister's bilateral label already contains the horizon category — the probe's search terminates at the sister, leaving no domain to search. Vacuous probes are undetectable: they cannot trigger movement or agreement.
Example: a probe on C⁰ with horizon T is vacuous, because the sister
of C⁰ is TP, whose label [V, Appl, v, Voice, T] contains T.
Standard vacuous examples: C⁰ ⊣ T, C⁰ ⊣ v, C⁰ ⊣ V are all vacuous.
Hindi Ā (C⁰ ⊣ Nmlz) is NOT vacuous: Nmlz is not in TP's label.
All Hindi probes are nonvacuous — each produces observable effects.
All German probes are nonvacuous.
HLT: Location→Horizon and Horizon→Location constraints #
The HLT emerges from bilateral labeling + vacuity. Only nonvacuous probe–horizon pairings produce observable dependencies:
(279a) A probe on C⁰ cannot have T, v, or V as horizon (vacuous). It CAN have C, Nmlz, or Force.
(279b) A probe with horizon T cannot be on C⁰ or Force⁰ (vacuous). It can be on T⁰ (default horizon).
HLT (279a) for Hindi: the attested probes on C⁰ (wh ⊣ C, Ā ⊣ Nmlz) are exactly the nonvacuous options.
HLT (279b) for Hindi: φ and A probes use T⁰ ⊣ T (nonvacuous), but ⊣ T on C⁰ or Force⁰ would be vacuous.
BIM: Ā cannot feed A #
Ā-movement places DP in [Spec,CP], creating a CP. A-probes have horizons that make CP opaque. Therefore the A-probe cannot reach an Ā-moved element — improper movement is blocked.
Conversely, A-movement feeds Ā-movement freely: Ā-probes can search into CP (Hindi Ā: C⁰ ⊣ Nmlz, CP lacks Nmlz).
BIM premise: CPs are opaque to A-probes in all three languages.
Proper movement (A feeds Ā) is permitted: Ā-probes can enter CP.
(231): A-extraction forces obligatory LDA #
If A-movement of any element out of an embedded clause has taken place, that clause is obligatorily transparent for LDA. This is derived from horizons: A-movement and φ-agreement share the same probe settings in Hindi (both T⁰ ⊣ T), so anything transparent to one is transparent to the other. Ā-movement has a DIFFERENT horizon (C⁰ ⊣ Nmlz), so Ā-extraction does not force agreement.
A-probes and φ-probes are identical in Hindi — same head, same horizon.
CP transparent to Ā (C⁰ ⊣ Nmlz) but opaque to φ (T⁰ ⊣ T): Ā-extraction does not force agreement.
English has three probes, including extraposition #
English extraposition ([extr] on T⁰ ⊣ T) is more local than A-movement (T⁰ ⊣ C): it cannot cross even TP boundaries.
Extraposition is blocked by TP; A-movement is not.
Extraposition uses the default horizon for T⁰.
Itelmen and Tsez: φ-agreement ≠ A-movement #
@cite{keine-2020} §3.4.5 discusses languages where φ-agreement and A-movement have different locality — the A-movement–Agreement Generalization ((231)) is Hindi-specific, not universal.
The two languages show opposite mismatch directions:
Itelmen (@cite{bobaljik-wurmbrand-2005}, (269)): A-movement out of a nonfinite clause forces obligatory high scope, but there are locality constraints on agreement that do not apply to movement. A-movement is more permissive than φ-agreement.
Tsez (@cite{polinsky-potsdam-2001}, (271)): LDA into an embedded clause is possible, but crossclausal movement is blocked. φ-agreement is more permissive than A-movement.
This demonstrates that there is no inherent directionality to movement–agreement mismatches.
Itelmen (269): A-movement can probe into TP, φ-agreement cannot. Movement is more permissive than agreement.
Tsez (271): φ can probe into TP, A-movement cannot. Agreement is more permissive than movement — the inverse of Itelmen.
In Hindi, by contrast, φ and A-movement are IDENTICAL — no mismatch.
Itelmen and Tsez have opposite mismatch directions: in Itelmen movement is more permissive, in Tsez agreement is more permissive. Their configs are genuinely different.
Smuggling: selective opacity in nonidentity movement #
@cite{keine-2020} §3.4.3 shows that smuggling derivations (where XP is Ā-moved to [Spec,CP], then YP is A-subextracted from XP) exhibit selective-opacity effects. The horizon account derives these without any special constraint on movement sequences:
A-movement out of Ā-moved constituent: BLOCKED. Ā-movement creates a CP structure around the moved constituent. The A-probe has C (or T) as its horizon, so CP is opaque. Example:
*Oscar is known [CP how likely [to win]] it was tᴬ tᴬ̄Ā-movement out of A-moved constituent: OK. A-movement does not create an opaque boundary for the Ā-probe. Example:
Which movie do you think [the first part of tᴬ̄] is likely tᴬ to create a scandal?
The key insight is that these constraints are domain-based (the CP created by Ā-movement is opaque to the A-probe), not item-based (no reference to the movement history of the DP).
Smuggling: Ā-movement creates CP, which blocks the A-probe. In all three languages, A-probes cannot search into CP — this is exactly the BIM premise, which also derives smuggling restrictions.
Smuggling: A-movement does NOT create an opaque boundary for Ā-probes. The Ā-probe can still search into the domain because TP (the landing site of A-movement) does not contain the Ā-probe's horizon.
Three attested A-movement horizons #
@cite{keine-2020} §3.6, (300) identifies three crosslinguistically attested A-movement probe settings:
| Language | Horizon | Hyperraising? |
|---|---|---|
| Lubukusu | ⊣ ∅ | Yes (finite) |
| English | ⊣ C | No (CP blocks) |
| Hindi/Russian | ⊣ T | No (TP blocks) |
These form an entailment chain: anything transparent to Hindi's A-probe is transparent to English's, and anything transparent to English's is transparent to Lubukusu's.
The three A-movement settings verified against clause types.
Horizons and CP phases coexist #
@cite{keine-2020} ch. 4 argues that horizons and CP phases are orthogonal constraints on syntactic locality:
Horizons determine selective opacity: which operations can cross a given boundary. Probe-specific — different probes see different boundaries.
CP phases determine absolute opacity: all material inside the phase complement is removed from the workspace (Spell-Out). This affects ALL operations uniformly, but leaves the phase edge (specifier) accessible.
The division of labor:
- Ā-extraction is possible but must proceed successive-cyclically (enforced by phases, not horizons)
- A-extraction is categorically blocked (enforced by horizons, not phases — [Spec,CP] is at the phase edge but still beyond the A-probe's horizon)
Phase-horizon division of labor for English:
- Phases allow Ā-extraction via successive cyclicity ([Spec,CP] is accessible to Ā-probe)
- Horizons block A-extraction even from [Spec,CP] (CP contains C, which is [A]'s horizon)
Hindi shows the same division: Ā can enter CP, A cannot.