Psych Verb Syntax-Semantics Interface

@cite{pesetsky-1995} @cite{kim-2024} @cite{kratzer-1996} @cite{schaefer-2008}## Directions of determination

The psych verb interface involves three layers with distinct directions of determination:

    SYNTAX determines SEMANTICS determines
    ───────────────── ────────────────────
    Voice_CAUSE head → ∃ causer argument
         ↑ ↓
    (that's all) DP denotation (percept vs representation)
                                    ↓
                              CausalSource (external vs internal)
                                    ↓
                          ┌─────────┴──────────┐
                    StimulusType opacity, temporality,
                    (T vs SM) event sort, transition
                          ↓
                    PP frame (*of* vs *about*)
                    Cause cooccurrence

Syntax determines one thing: whether there is a causer argument at all. This is the contribution of Voice_CAUSE (= Pesetsky's CAUS head). Agentive/causer Voice projects a specifier; non-thematic/expletive Voice does not. The syntax is "done" after this — it cannot see what kind of entity fills the specifier.

Semantics determines everything else. The DP's referential type (percept vs representation) is a property of its denotation, invisible to the syntax. From this single semantic property, all other properties follow: CausalSource, StimulusType, opacity, temporal structure, event sort, PP frame selection, and Cause cooccurrence.

The zero syntax thesis: the syntactic structure is invariant across the two DP types. No head, feature, or morpheme distinguishes percept from representation DPs. The syntax is blind to the T/SM distinction. All variation is semantic.

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.pesetskyCAUS : Minimalism.VoiceFlavor

@cite{pesetsky-1995}'s CAUS head is identified with Schäfer's Voice_CAUSE (@cite{schaefer-2008}). Both introduce a causer external argument.

This identification follows Occam: the two analyses posit the same structural position (Spec,vP/VoiceP) introducing the same kind of argument (causer).

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.pesetskyCAUS = Minimalism.VoiceFlavor.causer

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.syntax_determines_causer_exists : Minimalism.voiceCauser.assignsTheta = true

Syntax determines: Voice_CAUSE introduces a causer argument. This is what the syntax contributes — the existence of a causer in the structure.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.syntax_determines_phase : Minimalism.voiceCauser.phaseHead = true

Syntax determines: Voice_CAUSE is a phase head, creating a domain boundary.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.syntax_blind_to_causer_kind : Minimalism.voiceCauser.hasD = Minimalism.voiceAgent.hasD

Syntax does NOT determine: the kind of causer. All θ-assigning Voice heads project the same structural position (Spec,VoiceP with [D] feature). The syntax treats agentive and causer Voice identically in this respect.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.syntax_determines_no_causer : Minimalism.voiceAnticausative.assignsTheta = false ∧ Minimalism.voiceMiddle.assignsTheta = false

Contrast: non-thematic Voice does NOT introduce any argument. This is where syntax makes its one cut: causer argument vs no causer argument.

inductive Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.CauserDenotation : Type

The referential type of the DP in Spec,Voice_CAUSE.

This is a semantic type, not a syntactic one. The syntax sees only "DP in Spec,VoiceP" — it cannot distinguish percepts from representations. The distinction is a property of the DP's denotation, visible only to the semantic component.

• .percept: mind-external entity/event — "the noise" in "the noise frightened John"
• .representation: mind-internal representation — "the problem" in "the problem concerns John" (John's mental representation of the problem, not the problem itself)

• percept : CauserDenotation
• representation : CauserDenotation

instance Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instDecidableEqCauserDenotation : DecidableEq CauserDenotation

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instDecidableEqCauserDenotation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instBEqCauserDenotation.beq : CauserDenotation → CauserDenotation → Bool

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instBEqCauserDenotation.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instBEqCauserDenotation : BEq CauserDenotation

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instBEqCauserDenotation = { beq := Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instBEqCauserDenotation.beq }

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instReprCauserDenotation.repr : CauserDenotation → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instReprCauserDenotation : Repr CauserDenotation

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instReprCauserDenotation = { reprPrec := Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.instReprCauserDenotation.repr }

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToSource : CauserDenotation → Semantics.Causation.PsychCausation.CausalSource

Semantics determines: causal source from DP denotation.

The referential type of the DP determines the causal source. This is a semantics-internal derivation: from what the DP denotes, we know what kind of causation is involved.

Equations

• One or more equations did not get rendered due to their size.

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToOpacity (d : CauserDenotation) : Bool

Semantics determines: subject opacity from DP denotation.

Composed via CausalSource: denotation → source → opacity.

Equations

• One or more equations did not get rendered due to their size.

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToLink (Time : Type u_1) [LinearOrder Time] (d : CauserDenotation) : Semantics.Causation.PsychCausalLink.PsychCausalLink Time

Semantics determines: causal link profile from DP denotation.

Composed via CausalSource: denotation → source → temporal structure, event sorts, transition.

Equations

• One or more equations did not get rendered due to their size.

def Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToStimulusType (d : CauserDenotation) : Semantics.Causation.PsychCausation.StimulusType

Semantics determines: stimulus subtype from DP denotation.

Composed via CausalSource: denotation → source → T/SM.

Equations

• Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToStimulusType d = (Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.denotationToSource d).toStimulusType

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.percept_source : denotationToSource CauserDenotation.percept = Semantics.Causation.PsychCausation.CausalSource.external

Percept DP → external source.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.representation_source : denotationToSource CauserDenotation.representation = Semantics.Causation.PsychCausation.CausalSource.internal

Representation DP → internal source.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.percept_transparent : denotationToOpacity CauserDenotation.percept = false

Percept DP → transparent subject.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.representation_opaque : denotationToOpacity CauserDenotation.representation = true

Representation DP → opaque subject.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.percept_target : denotationToStimulusType CauserDenotation.percept = Semantics.Causation.PsychCausation.StimulusType.target ∧ (denotationToStimulusType CauserDenotation.percept).ppFrame = "of"

Percept DP → Target stimulus, of-PP.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.representation_sm : denotationToStimulusType CauserDenotation.representation = Semantics.Causation.PsychCausation.StimulusType.subjectMatter ∧ (denotationToStimulusType CauserDenotation.representation).ppFrame = "about"

Representation DP → Subject Matter stimulus, about-PP.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.percept_temporal {Time : Type u_1} [LinearOrder Time] : (denotationToLink Time CauserDenotation.percept).temporalConstraint = Core.Time.Interval.precedes ∧ (denotationToLink Time CauserDenotation.percept).involvesTransition = true

Percept DP → temporal precedence, BECOME transition.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.representation_temporal {Time : Type u_1} [LinearOrder Time] : (denotationToLink Time CauserDenotation.representation).temporalConstraint = Core.Time.Interval.overlaps ∧ (denotationToLink Time CauserDenotation.representation).involvesTransition = false

Representation DP → temporal overlap, no BECOME.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.semantics_determines_all {Time : Type u_1} [LinearOrder Time] : denotationToSource CauserDenotation.percept = Semantics.Causation.PsychCausation.CausalSource.external ∧ denotationToSource CauserDenotation.representation = Semantics.Causation.PsychCausation.CausalSource.internal ∧ denotationToStimulusType CauserDenotation.percept = Semantics.Causation.PsychCausation.StimulusType.target ∧ denotationToStimulusType CauserDenotation.representation = Semantics.Causation.PsychCausation.StimulusType.subjectMatter ∧ (denotationToStimulusType CauserDenotation.percept).ppFrame = "of" ∧ (denotationToStimulusType CauserDenotation.representation).ppFrame = "about" ∧ (denotationToStimulusType CauserDenotation.percept).conflictsWithCause = false ∧ (denotationToStimulusType CauserDenotation.representation).conflictsWithCause = true ∧ denotationToOpacity CauserDenotation.percept = false ∧ denotationToOpacity CauserDenotation.representation = true ∧ (denotationToLink Time CauserDenotation.percept).involvesTransition = true ∧ (denotationToLink Time CauserDenotation.representation).involvesTransition = false

Semantics determines all: one semantic property of the DP (its referential type) determines seven downstream properties. None of these are syntactically encoded.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.zero_syntax_invariant_head : pesetskyCAUS = pesetskyCAUS

Zero syntax thesis: the syntactic head projected is the same regardless of DP denotation.

The syntax contributes exactly Voice_CAUSE in both cases. There is no syntactic feature, morpheme, or head that distinguishes the percept configuration from the representation configuration. All seven semantic differences (§ 3) arise from the DP's denotation, not from any syntactic distinction.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.syntax_constant_semantics_varies : pesetskyCAUS = pesetskyCAUS ∧ denotationToSource CauserDenotation.percept ≠ denotationToSource CauserDenotation.representation ∧ denotationToOpacity CauserDenotation.percept ≠ denotationToOpacity CauserDenotation.representation ∧ denotationToStimulusType CauserDenotation.percept ≠ denotationToStimulusType CauserDenotation.representation

The zero syntax thesis stated as a gap: syntax is constant while semantics varies. The two conjuncts make the directions explicit — same syntax, different semantics.

theorem Theories.Interfaces.SyntaxSemantics.CausalSourceBridge.interface_division_of_labor : Minimalism.voiceCauser.assignsTheta = true ∧ pesetskyCAUS = pesetskyCAUS ∧ denotationToSource CauserDenotation.percept ≠ denotationToSource CauserDenotation.representation ∧ denotationToOpacity CauserDenotation.percept ≠ denotationToOpacity CauserDenotation.representation ∧ denotationToStimulusType CauserDenotation.percept ≠ denotationToStimulusType CauserDenotation.representation

Interface summary: the syntax-semantics division of labor.

Syntax contributes: causer argument exists (θ-role assigned). Syntax does NOT contribute: what kind of causer, opacity, temporality, T/SM, PP frame — none of these are syntactically encoded.

Semantics contributes: all variation between percept and representation configurations.