Classification of Merge into Three Combination Schemata #

@cite{mueller-2013}

Explicit classification of Minimalist Merge operations into @cite{mueller-2013}'s three universal combination schemata: Head-Complement, Head-Specifier, Head-Filler.

The existing MergeUnification.lean proves that Internal and External Merge are the same operation. This file further classifies Merge by combination kind:

Merge type	Precondition	Schema
External (selection holds)	`selectsB a b`	Head-Complement
External (specifier)	neither selects, arg is maximal	Head-Specifier
Internal	`contains target mover`	Head-Filler

Connection to @cite{mueller-2013} #

§2.1: External Merge with selection ≈ Head-Complement
§2.2: External Merge without selection ≈ Head-Specifier
§2.3: Internal Merge ≈ Head-Filler

Classification of Merge #

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def Minimalism.classifyExternalMerge (a b : SyntacticObject) :

Core.CombinationKind

Classify an External Merge (known to have no containment).

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Minimalism.classifyExternalMerge a b = if (Minimalism.selectsB a b || Minimalism.selectsB b a) = true then Core.CombinationKind.headComplement else Core.CombinationKind.headSpecifier

Instances For

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def Minimalism.classifyInternalMerge :

Core.CombinationKind

Classify an Internal Merge (known to have containment).

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Minimalism.classifyInternalMerge = Core.CombinationKind.headFiller

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Which daughter is the head? #

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def Minimalism.mergeHead (a b result : SyntacticObject) :

Option SyntacticObject

Determine which daughter is the head of a Merge.

The head is the daughter whose label matches the result's label. In Minimalism, this is determined by which element projects.

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

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Key theorems #

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theorem Minimalism.selection_implies_headComplement (a b : SyntacticObject) (h : selectsB a b = true) :

classifyExternalMerge a b = Core.CombinationKind.headComplement

External Merge with selection is Head-Complement.

When one SO selects the other (first merge consuming a selectional feature), this is the Head-Complement schema: the selector is the head, the selectee is the complement.

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theorem Minimalism.no_selection_implies_headSpecifier (a b : SyntacticObject) (ha : selectsB a b = false) (hb : selectsB b a = false) :

classifyExternalMerge a b = Core.CombinationKind.headSpecifier

External Merge without selection is Head-Specifier.

When neither SO selects the other (e.g., subject merging with TP), this is the Head-Specifier schema.

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theorem Minimalism.internal_merge_is_headFiller :

classifyInternalMerge = Core.CombinationKind.headFiller

Internal Merge is always Head-Filler.

Movement (re-merge of a contained element) is always the Head-Filler schema, regardless of what the mover or target looks like.

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theorem Minimalism.classify_external_exhaustive (a b : SyntacticObject) :

classifyExternalMerge a b = Core.CombinationKind.headComplement ∨ classifyExternalMerge a b = Core.CombinationKind.headSpecifier

The classification is exhaustive: every External Merge is either Head-Complement or Head-Specifier.

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theorem Minimalism.label_from_head (a b : SyntacticObject) (h : selects a b) :

label (merge a b) = label a

Label = Head Feature Principle: when α selects β, the label of {α, β} = label α.

This is the Minimalist analogue of the Head Feature Principle: the selector projects, so the result's label equals the selector's label.

Monovalent Verb Serialization Problem (@cite{mueller-2013} §2.3) #

In Stabler's non-directional MG, a monovalent verb's only argument is classified as a complement (Head-Complement, since the verb selects it). Left-to-right linearization places the complement after the head, yielding "*Sleeps Max" instead of "Max sleeps".

Stabler's fix — positing an ad hoc empty object — is "entirely stipulative and entirely ad hoc, being motivated only by the wish to have uniform structures" (Müller, p. 937).

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def Minimalism.sleepsToken :

LIToken

"sleeps" — a monovalent verb (category V, selects D).

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