Syntactic Theory: The Architecture of Human Language

 

Proseminar in Syntax: Architecture, Formalism, and Empirical Challenge

Title: The Architecture of Human Language: Current Contours in Syntactic Theory

Prerequisites: Understanding of GB/Minimalist Program, formal semantics, computational methods, advanced morphology.

Philosophy

This proseminar moves beyond surveying syntax. Its core purpose is to:
Explain the architecture of the human language faculty, not just catalog phenomena.
Identify where current models fail and propose formal solutions.
Bridge theory with mathematical formalization: students formalize syntactic mechanisms using set theory, graph theory, and Minimalist Grammars (MGs).
Produce original, journal-quality contributions: each student’s work is peer-reviewed and grounded in empirical counter-examples.

Overview

1: The Calculus of Merge & Symmetry Breaking

Focus: Internal vs. External Merge; Labeling Algorithm (LA); symmetry crises when two phrases merge.
Exercise: Derive why Subject moves to Spec,TP as a labeling necessity, not because of a feature.
Actionable Task: Students construct formal derivations showing symmetry-breaking with minimal search.
Readings: Epstein, Kitahara, & Seely (2024), Chomsky (2021), Hornstein (2017)

2: Internalization of Locality & Activity Conditions

Focus: Strict Cyclicity, Activity Condition, Minimality, and long-distance dependencies.
Exercise: Analyze a counterexample from a lesser-studied language (e.g., ergative or clitic doubling) that violates standard Minimalist assumptions.
Task: Formal proof in set-theoretic or graph-theoretic terms of how locality constraints derive movement patterns.

3: Linearization & Sensory-Motor Interface

Focus: LCA vs. PF-driven linearization; word order as emergent rather than syntactic.
Actionable Task: Model free word-order languages using Minimalist Grammars (MGs) to predict linearization patterns.
Readings: Collins & Stabler (2024), Kayne (1994), Chesi (2021)

4: Cartography vs. Minimalist Roots

Focus: Fine-structured functional hierarchies (Cinque/Rizzi) vs. economy-driven Minimalism.
Debate: Are rich hierarchies necessary, or can derivational economy explain them?
Exercise: Derive a microvariation dataset using both approaches and formalize predictions.
Readings: Rizzi (2013), Cinque (2005), Boeckx (2017)

5: Phases, Features, and the Death of Agreement

Focus: Dynamic phases, feature checking, and non-mandatory agreement.
Debate: Is agreement a derived phenomenon of strict cyclicity?
Actionable Task: Students construct derivations for D-pronoun incorporation or pro-drop using dynamic phases.
Readings: Gallego (2020), Preminger (2014/2025), Legate (2014)

6: Mathematical & Computational Syntax

Focus: Minimalist Grammars, complexity classes, and the computational limits of syntax.
Exercise: Formalize Swiss-German cross-serial dependencies as an MG; assess if human syntax is Mildly Context-Sensitive.
Readings: Stabler (1997, 2024), Chesi (2021), Collins & Stabler (2024)

7: Evolutionary & Cognitive Frontiers

Focus: Symmetry-breaking in acquisition, interface pressures in processing, recursion, and cognitive constraints on syntactic architecture.
Activity: Whiteboard collaboration deriving formal grammar fragments that accommodate typological or processing anomalies.

Radical Inquiry- The Autopsy of a Miracle

We are not here to memorize rules. We are not here to catalog phenomena. We are here to perform a forensic autopsy on a miracle: the human language faculty.

Ask yourself:

What makes language possible?

Not the words. Not the morphemes. But the computational spine that allows thought to manifest in sound and symbol.

Why does it take the form it does?

Not by accident. Not by cultural drift. But as the necessary consequence of cognitive, evolutionary, and interface constraints.

How is it realized in the mind?

Not as a metaphorical tree. Not as a descriptive map. But as a formal system, a derivational algorithm, a set of precise, lawful operations.

This is not a survey. This is discovery in real time.
Each derivation is a proof, each anomaly a test of necessity.
Every exception is a signal of architecture, not an inconvenience.
Every model we examine is a hypothesis to be dissected, formalized, and stress-tested.

This is a laboratory of thought. Here, theory meets formal rigor, anomalies are opportunities, and the invisible forces of syntax are revealed in every derivation.

You are no longer students of language. You are architects of the computational mind, explorers of possibility itself.
Today, we do not learn.
We interrogate.
We formalize.
We see the architecture of language, not as it appears, but as it must be.

Language Is Not a Set of Rules- Diagnosing the Shadows of Computation

Language is not a checklist of rules, nor a hierarchy of labels, nor a string of morphemes to memorize. Current models, GB, early Minimalism, and even contemporary cartography, treat the surface as causal, and in doing so, they mistake shadows for substance.

Consider the failures:

Overpopulated Features: Syntax is crowded with features, projections, and mechanisms that explain nothing and obscure the underlying logic. These are the patches of descriptive comfort, not the engines of computation.

Hard-Coded Hierarchies: The proliferation of rigid functional layers hides the principle of economy. Derivations are over-determined; the system’s natural efficiency is masked by artificial scaffolding.

Morphology as Cause, Not Reflex: Agreement, case, and inflection are often treated as drivers of syntactic behavior. In truth, they are epiphenomena- surface reflections of deeper computational necessities, like ripples on a river revealing the hidden flow beneath.

Typology as Exception: Cross-linguistic variation is often treated as anomalous rather than informative. These “exceptions” are in fact windows into the constraints of the system, revealing what computation is necessary and what is contingent.

Our proseminar does not catalog. It diagnoses. It does not describe. It formalizes.

Imagine syntax not as a museum of structures, but as a laboratory of constraints, where every apparent irregularity is a signal of underlying necessity.

Every anomaly, every variation, is a proof of architecture, not a footnote of history.

We ask:

What if all previous models are merely shadows of a deeper computation, glimpses of an architecture that obeys mathematical, cognitive, and evolutionary laws?

In this space, you will abandon comfort. You will see the skeleton of possibility, not the flesh of description. You will formalize what was previously implicit, and you will measure the architecture against the mind’s finite, precise, and beautiful computational constraints.

Architecture, Not Inventory

Language is not a collection of labels or a catalog of surface forms. It is a computational system, a structure of constraints and possibilities, a grammar of what can be thought and expressed, not merely what is spoken.

Merge and Symmetry-Breaking: From the simplest binary operation, Merge, emerges the full hierarchy of human thought. Symmetry is not incidental; it is violated by necessity, producing the asymmetries that underlie subject positions, verb placement, and dependency chains.

Locality and Visibility: The brain is a finite processor. Dependencies, movement, and visibility obey cognitive constraints, not arbitrary rules. Locality is the logic of tractable search, the mind’s solution to combinatorial explosion.

Linearization and Externalization: Word order is not a fundamental property of syntax. It is an emergent phenomenon, imposed by the sensory-motor interface. Linearization is the projection of hierarchical thought into the temporal world.

Minimal Structure: Complexity is a consequence, not a design choice. Economy produces rich surface structures from minimal derivations, revealing the efficiency of the system. Bloated hierarchies are illusions of descriptive laziness.

Epiphenomenal Features: Morphology, agreement, and feature-checking are reflexes, not drivers. They emerge from derivations, not from preordained forces. What appears causal is often a signal of derivational inevitability.

Computational Bounds: Human syntax resides in the Mildly Context-Sensitive sweet spot: powerful enough to express recursive thought, yet constrained enough to be learnable, processable, and evolutionarily feasible. The mind negotiates possibility with precision.

Our ambition is not to inventory what languages do.

It is to formalize what they can do, to map the grammar of possibility, and to see language as a window into the architecture of human thought.

The Epistemic Crisis- The Systemic Failure

Slide this into your mind: the Icelandic Dative Subject. Formal notation captures the tension:

$$G = (V, \Sigma, R, S), \quad \text{EPP satisfied, yet no agreement triggered.}$$

This is not a curiosity. It is a falsification.

Traditional GB-theory calls this an “exception.” In this discussion, we recognize it as proof of theoretical collapse.

If our models cannot account for this without ad hoc patches, they are relics of descriptive ambition, not explanatory power.

This is the live anomaly- a pulse in the system that refuses to conform, a challenge to every assumption you hold. It is a laboratory of impossibility, asking not how the system works, but why the architecture permits this configuration at all.

Here, the discussion departs from pedagogy. Let us try to formalize, stress-test, and reconstruct:

Derive the anomaly using Minimalist Grammars

Expose the assumptions hidden in EPP, agreement, and feature-checking

Recast theory so that anomalies are opportunities for universal insight, not exceptions to memorize

The Icelandic Dative Subject is not an obstacle. It is a doorway- a chance to see the limits of orthodoxy and the shape of architecture yet to be formalized.

In this space, every exception is a theorem in disguise, every failure a call to rebuild the theoretical universe.

The Mathematical Core- Mapping the Sweet Spot

Human language is not a free-for-all of symbols, nor a casual sequence of rules. It exists in a precisely tuned computational niche, the Mildly Context-Sensitive (MCS) domain, where expressivity meets tractability.

Context-Free Boundaries: A system too weak cannot capture the intricacies of human syntax. Cross-serial dependencies, nested embeddings, and long-distance relations cannot be realized in a purely context-free system. Limitation begets incompleteness.

Fully Context-Sensitive Chaos: A system without bounds becomes infinite, unmanageable, and evolutionarily impossible. The search space explodes; processing collapses; learning is infeasible. Human cognition cannot sustain unbridled computational freedom.

The Sweet Spot: Language is the mathematical compromise, a system endowed with just enough power to encode recursive, hierarchical thought, yet constrained enough to remain learnable, processable, and evolutionarily viable. This is not accident, it is architecture.

We formalize this architecture rigorously, using the tools that reveal the invisible skeleton of computation:

Set Theory: The simplicity of Merge captures infinite generativity:

$$\text{Merge}(X, Y) \to \{X, Y\}$$

From this single operation, hierarchies emerge, complexity unfolds, and derivational possibilities proliferate.

Graph Theory: Phases, visibility, and locality are nodes and edges of cognitive necessity, not arbitrary decorations. They encode the constraints of memory, attention, and interface interaction.

Minimalist Grammars (MGs): The formal machinery that traces human syntax along the MCS frontier, handling cross-serial dependencies, movement patterns, and derivational constraints with precision.

Every derivation is a proof, a formalization of possibility. Every anomaly is a theorem, demanding explanation or adaptation. Syntax ceases to be anecdotal; it becomes law, a reflection of mathematical inevitability within human cognition.

To study syntax is not to catalog words and rules.

It is to witness the architecture of possibility, the boundary where thought and computation converge.

Language Evolution and Cognitive Constraints- The Architecture of Possibility

Why this architecture, and not another? This question is not speculative, it is the hinge of theory itself.

Merge as Hierarchical Cognition: Merge did not arise merely to communicate. It is an expression of the brain’s ability to organize thought hierarchically, to compute relations among abstractions. Language reflects cognitive necessity, not arbitrary design.

Locality as a Cognitive Imperative: Constraints on movement, dependencies, and visibility are not theoretical artifacts, they are manifestations of memory and processing limits. The brain cannot search infinitely; it must optimize.

Linearization as Interface Imposition: Word order is not innate to syntax. It emerges from the demands of the sensory-motor system, a necessary projection of hierarchical computation into linear action.

Phase Dynamics as Optimization: The division of structures into phases is not aesthetic, it is computationally efficient, allowing the mind to incrementally process and transfer information. Complexity is parceled, tractability preserved.

The Sweet Spot of Computation: Human language occupies a precisely tuned niche. Enough power to encode infinite thought, yet constrained enough to be learnable, processable, and evolutionarily feasible. Too little, and expression collapses; too much, and computation becomes intractable.

Language is thus neither arbitrary nor limitless, it is the mathematical consequence of cognition, evolution, and embodied constraints. To understand it is to witness the mind negotiating possibility itself.

The Proseminar as Laboratory

You will not receive knowledge. You will confront it, stress it, and make it yield insight.

Formalize the Unseen: Every derivation in Minimalist Grammar is a trace of computation, a fragment of the mind’s architecture. To formalize it is to translate thought into law.

Critique Orthodoxy: From Chomsky’s foundational models to contemporary Cartography, every system is a hypothesis. You will expose its limits, reveal its hidden assumptions, and measure it against anomalies it cannot explain.

Engineer Solutions: Anomalies are not curiosities, they are challenges to formal inevitability. Your task is to devise solutions, not patches; to render coherent what theory currently cannot.

Produce Knowledge, Not Exercises: Peer review is not a formality. It is the act of entering the arena of intellectual rigor, producing work of journal-ready quality, capable of shaping the field.

This is a laboratory, but not of chemicals or machines. It is a laboratory of the mind, where the architecture of language is stress-tested under the weight of computation, cognition, and cross-linguistic diversity. Here, the mind itself is the experimental apparatus, and every derivation is both a probe and a revelation.

In this space, theory is alive, falsifiable, and malleable.

You are no longer students, you are architects of the possible.

Frontiers of Syntax

The journey through the architecture of language is not a linear progression of topics, nor a checklist of technical milestones. It is a voyage into the very principles that constrain thought itself. Each phase, whether we wrestle with the computational spine, confront the dictates of the interfaces, or formalize the seeming impossibilities of Dyirbal, Icelandic, and Mohawk, reveals more than a linguistic pattern. It exposes the invisible scaffolding of the mind, the mathematical inevitabilities that shape expression and comprehension alike.

To explore the computational spine is not merely to reduce syntax to Merge and Third Factor principles. It is to ask: What makes a hierarchical structure possible at all? The simplicity of recursive Merge belies the profound truth that infinite expressivity can emerge from minimal principles, and that complexity is a byproduct of elegance, not brute addition.

When we turn to interface constraints, we encounter the tension between the abstract and the tangible. Language does not exist in a vacuum; it is sculpted by the capacities of the ear and the vocal tract, by memory limits and processing pressures. Here, syntax reveals itself as a negotiation between the ideal of thought and the demands of embodiment, a system that is both liberated and constrained, a delicate dance of form and function.

The formalization of typologically diverse phenomena, the idiosyncrasies of Dyirbal, the quirks of Icelandic, the subtleties of Mohawk, is a meditation on universality and particularity. Each anomaly is a window into what the mind allows, what it resists, and what it inevitably computes. By seeking a single algebraic model, we are not flattening diversity; we are illuminating the architecture that makes diversity possible.

Finally, the derivational frontier is a call to courage: to confront what current theory cannot yet explain. Here, students are not passive learners; they are architects of insight, probing anomalies as laboratories of discovery. Each formalization is a hypothesis, each counterexample a theorem, each derivation a trace of the invisible constraints that make human thought computationally realizable.

Taken together, these reflections suggest a larger truth: syntax is not a collection of arbitrary rules, but a reflection of the computational, cognitive, and evolutionary necessities of the mind. Our task is not simply to describe, but to understand why the system is as it is, and why it could be no other way.

Language, in its architecture, is both a mirror and a map: a mirror of human cognition, a map of the formal possibilities inherent in finite minds operating under principled constraints. To traverse this frontier is to participate in the creation of knowledge itself, to move beyond description and into the realm of theoretical discovery in real time.

The Mental Posture of the Linguistic Architect

To engage with the architecture of language is to adopt a stance of intellectual vigilance. Knowledge is not received; it is interrogated, formalized, and tested against the limits of computation and cognition.

Skepticism toward authority: No derivation is sacred. Every claim, every tree, every assumed principle is a candidate for falsification. Orthodoxy is a starting point, not a boundary. The mind of the linguist must remain radically independent, seeing anomalies not as obstacles but as illuminations of hidden principles.

Precision in formalism: Thought without implementable form is mere rhetoric. Every insight must withstand translation into set-theoretic, graph-theoretic, or computational representation. Language is a system of computation; understanding it requires mathematical rigor, not narrative description.

Ambition in creativity: Anomalies are treasures, not inconveniences. The irregular, the exception, the counterexample are signposts toward deeper architecture, revealing the constraints and freedoms that underlie all human languages. True discovery lies in embracing the unexpected and deriving universal insight from the particular.

Interdisciplinary thinking: Syntax, computation, cognition, and evolution are inseparable. The architecture of language is not an isolated artifact; it is the intersection of physical brains, abstract computation, and evolutionary possibility. To comprehend it is to navigate these domains simultaneously, allowing each to illuminate the others.

In sum, the linguistic architect’s posture is one of alert curiosity, disciplined rigor, and expansive imagination. It is a stance that transforms anomalies into insight, computation into explanation, and the study of language into a philosophical and scientific act of discovery.

The Architect’s Command- Closing Provocation

Take sentences that defy theory. Do not ask how. Do not search for comfort in existing frameworks.

Treat those sentences as fissures in the edifice of orthodoxy, challenge yourself, and take it as alluring invitations to rewrite what is considered possible.

The solutions to these sentences are not in textbooks, journals, or lectures.

They exist only in the architecture we should build, formalize, and dare to inhabit.

Every day while studying syntactic theory, we should obliterate assumptions, confront anomalies as opportunities, and render visible the invisible constraints of human cognition.

Let us endeavor to discover not merely what language is, but why it must be that way and why no other arrangement could satisfy the mind’s imperatives.

This is the frontier. This is the laboratory. And here, the impossible is merely the unformalized.

'Let us proceed':

1. Merge Is Not Free: Symmetry, Labeling, and the Computational Instability of Syntax

Architectural Question (Non-Negotiable)

Why does the simplest combinatorial operation in human language-Merge-immediately generate objects that are computationally unstable, and what does this reveal about the architecture of the language faculty?

This question is not pedagogical. It is architectural.

If syntax is built from a single operation (Merge), then any systematic pressure that forces movement, labeling, phases, or features must be traceable to the internal consequences of Merge itself, not to stipulative mechanisms layered on top of it.

The central claim here is:

Merge, by itself, systematically creates symmetry.

Symmetry is computationally fatal at the interfaces.

Much of syntax exists to destroy symmetry.

Minimalism’s Hidden Assumption: Merge Is Benign

The Standard Picture 

In its strongest minimalist formulation:

Merge = set formation

$$\text{Merge}(\alpha, \beta) = \{\alpha, \beta\}$$

Merge is:

unbounded

structure-building

cost-free

interface-legible once labeled

Problems (movement, agreement, phases) are often treated as secondary complications.

This picture is misleading.

The Core Problem Minimalism Often Downplays

Merge does not merely build structure.
Merge creates symmetry by default.

The object {XP, YP} contains:

no projection

no asymmetry

no head–dependent relation

no clear CI-interpretive instruction

If syntax interfaces with systems that require asymmetric instructions (predicate–argument, operator–variable, scope, selection), then {XP, YP} is computationally uninterpretable.

This is not a PF problem.
This is a core architectural instability.

Symmetry as a Computational Crisis

Symmetry Defined (Formally)

A syntactic object SO is symmetric iff:

Its immediate constituents are of the same type

No asymmetric dominance relation is available for interpretation

Formally:

$$SO = \{\alpha, \beta\}, \quad \text{where } \text{Type}(\alpha) = \text{Type}(\beta)$$

Examples:

{NP, NP}

{XP, YP}

{DP, TP} (under some assumptions)

Symmetry is not rare. It is the default outcome of Merge.

Why Symmetry Is Illicit

At the Conceptual–Intentional (CI) interface, interpretation requires:

function–argument mapping

scope relations

predication

thematic asymmetry

But a symmetric object provides no instruction for:

which element projects

which element is selected

which element is interpreted as predicate

Thus:

Symmetry is not a descriptive inconvenience.

It is an interpretive crash.

Labeling as Symmetry Destruction

The Labeling Algorithm (LA) Revisited

Following Chomsky (2013, 2015, 2021):

Labels are not primitives

Labels are computed at CI

A label is recoverable only if:

one element is a head, or

one element has moved, or

the elements share prominent features

Crucially:

Labeling is not about naming structures.

It is about rescuing structures from symmetry.

Why {XP, YP} Cannot Be Labeled

Neither XP nor YP provides a projection

No minimal search yields a unique label

CI receives no asymmetric instruction

Hence {XP, YP} must be repaired.

 Movement as a Computational Repair Strategy

Reframing Movement

Standard view:

Movement is triggered by features (EPP, edge features, probes)

Architectural view:

Movement exists because symmetry is otherwise fatal.

Movement removes one term from the symmetric configuration, leaving:

$$\{\langle XP \rangle, YP\}$$

This object is asymmetric and labelable.

Subject Movement to Spec-TP (Derivation)

Consider the vP–TP transition.

Initial Merge:

$$\{\text{DP}_{\text{subject}}, \text{TP}\}$$

This is a symmetric {XP, YP} configuration.

No label is recoverable.

Repair:

DP moves to Spec-TP

Lower copy becomes invisible for labeling

Result:

$$\{\text{TP}, \langle \text{DP} \rangle\}$$

Label = TP
Interpretation proceeds.

Conclusion:

Subject movement is forced, not optional.

It is not feature-driven.

It is a labeling necessity.

Formalizing the Argument 

Let Merge be defined as unordered set formation.

Let Label(SO) be a partial function defined only if:

SO contains a unique minimal head, or

SO is asymmetric due to copy invisibility.

Then:

For any {XP, YP}:

$$\text{Label}(\{XP, YP\}) = \varnothing$$

Movement transforms:

$$\{XP, YP\} \rightarrow \{\langle XP \rangle, YP\}$$

Now:

$$\text{Label}(\{\langle XP \rangle, YP\}) = YP$$

Movement is thus a precondition for labeling, not an epiphenomenon.

Empirical Stress Test: When Movement Does Not Happen

Apparent Counterexamples

Languages with:

pro-drop

null expletives

subject-in-situ

Superficially, these seem to violate the argument.

Resolution

The crucial point:

It is not overt movement that matters, but asymmetry at CI.

Possible strategies:

Null operators

Feature sharing

Head–spec unification

Alternative symmetry-breaking mechanisms

The architecture predicts variation in repair strategies, not the absence of repair.

Failure Modes of Competing Accounts

Feature-Driven EPP

Problems:

Circular (features introduced to force movement that already happens)

Non-explanatory

Typologically brittle

Cartographic Projections

Problems:

Encode symmetry resolution into structure

Miss the computational origin

Overgenerate functional layers

The symmetry-based account:

Predicts why structure is needed

Explains where movement is obligatory

Allows constrained variation

Architectural Consequences

This lecture commits us to the following strong theses:

Merge is computationally unstable

Syntax is a repair system

Movement is not optional

Features are derivative, not causal

Variation lies in symmetry-breaking strategies, not in Merge itself

Squib Trajectories 

Any of the following is LI-viable if executed rigorously:

“Subject Movement Without EPP: A Labeling-Driven Account”

\“Why {XP, YP} Is Uninterpretable: Symmetry as the Core Problem of Syntax”

“Movement as Interface Repair: Evidence from Pro-Drop Languages”

Reviewer-B pressure points:

Formal clarity of labeling

Cross-linguistic robustness

Avoiding covert stipulation

Exercises 

Exercise 1 (Formal)

Provide a derivation where:

{XP, YP} is labeled without movement

Show exactly what breaks or what additional assumptions are required

Exercise 2 (Typological)

Identify a language where subject movement appears optional.
Demonstrate how symmetry is nevertheless broken.

Exercise 3 (Computational)

Translate the derivation into a Minimalist Grammar fragment.
Specify where the asymmetry is encoded.

Merge & Symmetry Breaking

Construct derivations showing symmetry-breaking when two phrases merge.

Demonstrate why subject movement to Spec,TP is necessary for labeling.

Take-Home Architectural Claim

The deepest problem of syntax is not displacement, agreement, or word order.

It is symmetry.

Everything else exists to destroy it.

2. Locality as Internalized Computation: Why Syntax Cannot See Arbitrarily Far

Architectural Question

Why does the human language faculty enforce locality constraints so rigidly, even when long-distance dependencies are semantically and communicatively useful?

Or, stated more sharply:

Is locality a grammatical principle, or a computational necessity imposed by the architecture of Merge-based systems?

This post advances a strong thesis:

Locality is not a syntactic “constraint.”

It is the internalization of computational limits within the derivation itself.

The Illusion of Locality as a Rule

Traditional Framing (GB → Minimalism)

Locality is often introduced as a set of independent constraints:

Subjacency

ECP

Minimal Link Condition (MLC)

Relativized Minimality

Phase Impenetrability Condition (PIC)

These are usually taught as rules restricting movement.

But this framing is theoretically suspicious:

Why do so many distinct constraints converge on the same effects?

Why do violations cluster around similar structural configurations?

Why are they gradient, repairable, and interface-sensitive?

 Reframing Locality: A Computational Problem

The Core Hypothesis

Locality emerges because derivations must remain computationally tractable at every step.

Key assumptions:

Syntax is incremental, not global.

Interface interpretation applies cyclically.

Unbounded search is computationally illicit.

Merge creates objects that must be immediately interpretable or sealed off.

Locality is therefore forced, not stipulated.

Strict Cyclicity Revisited

What Strict Cyclicity Really Is

Strict cyclicity is often described descriptively:

Operations apply only at the root.

Architectural reinterpretation:

Only the most recently formed object is visible to the computational workspace.

Older material must be:

spelled out, or

frozen, or

made invisible to further computation

This is not a grammatical preference; it is memory management.

The Activity Condition as Visibility Control

Traditional View

An element can move only if it is “active” (i.e., has unchecked features).

This has always been conceptually murky.

Architectural Reanalysis

Activity = computational visibility.

An element is active if:

it remains accessible in the current workspace

it has not been sealed by cyclic transfer

it is not buried under completed interpretation

In other words:

Inactivity is computational garbage collection.

Minimality as Search Economy

Minimality Is Not a Linguistic Preference

Minimality effects:

Closest goal wins

Skipping is disallowed

This follows if:

Search is local and bounded by workspace limits.

Global search would:

explode computational complexity

violate real-time processing constraints

undermine learnability

Minimality is therefore a complexity-minimizing heuristic, internalized as grammar.

Phases as Computational Firewalls

Why Phases Exist

Phases (vP, CP) are often treated as:

arbitrary domains

remnants of GB bounding nodes

Architectural claim:

Phases are computational firewalls that prevent unbounded derivational growth.

They:

limit memory load

enforce cyclic interpretation

block uncontrolled search

PIC is therefore not a “constraint,” but a firewall rule.

Formalizing Locality 

Syntax as a Directed Acyclic Graph (DAG)

Nodes = syntactic objects
Edges = Merge relations
Workspace = active subgraph

Locality emerges if:

search is restricted to the active frontier

sealed nodes are removed from the graph

Long-distance movement is possible only if intermediate nodes remain active (escape hatches).

Apparent Locality Violations

Long-Distance Dependencies

Wh-movement, topicalization, relativization.

Crucial observation:

They are not violations, they are carefully engineered survivals.

Intermediate landing sites:

keep the element visible

prevent phase sealing

maintain computational accessibility

Ergativity, Clitic Doubling, and Atypical Locality

In many ergative or clitic-doubling systems:

locality behaves differently

intervention effects are altered

Prediction:

These systems manipulate visibility, not locality itself.

This is a fertile area for student squibs.

Failure Modes of Alternative Accounts

Constraint Lists
Redundant
Non-explanatory
Typologically brittle

Feature Proliferation

Features encode what computation already enforces
Leads to theoretical inflation

Architectural Consequences

Locality is emergent, not primitive
Syntax internalizes computational limits
Phases are memory-management devices
Minimality = bounded search
Variation lies in visibility mechanisms

Squib Trajectories 

LI/NLLT squibs:

“Locality Without Constraints: A Computational Account of Movement”

“Phases as Firewalls: Why Syntax Forgets”

“Activity as Visibility: Rethinking the Activity Condition”

Reviewer will demand:

explicit formalization

typological reach

computational plausibility

Exercises

Exercise 1 (Formal)

Provide a derivation where violating PIC would require global search. Show precisely where complexity explodes.

Exercise 2 (Typological)

Find a language where intervention effects are weak or absent. Explain how visibility is preserved.

Exercise 3 (Computational)

Translate a phase-based derivation into a graph with sealed subgraphs.

Locality as Internalized Computation

Provide a derivation where violating PIC requires global search and show the computational explosion.

Analyze a language with non-standard locality patterns (e.g., clitic-doubling or ergative systems) and formalize the derivation.

Translate a phase-based derivation into a graph showing sealed subgraphs.

Take-Home Architectural Claim

Locality is not a rule that syntax obeys.
It is a fact about what syntax can afford to compute.

3. Linearization and the Sensory–Motor Interface: Why Syntax Is Orderless

Architectural Question

Why does a strictly hierarchical, order-free computational system produce such rigid and typologically diverse word orders at the surface?

Or more provocatively:

If syntax is hierarchical and symmetric, where does linear order come from, and why is it so fragile?

This post advances the following thesis:

Linear order is not computed by syntax.

It is imposed at the Sensory–Motor (SM) interface under severe external constraints.

The Illusion of Word Order as Syntactic

The Traditional View

Much of syntactic theory treats order as internal:

Head–parameter (GB)

Kayne’s Linear Correspondence Axiom (LCA)

Directionality encoded in syntax

Cartographic fixed orders

These approaches share a hidden assumption:

Syntax “knows” left and right.

This assumption is architecturally suspicious.

The Case for Orderless Syntax

Merge Is Order-Free

By definition:

$$\text{Merge}(\alpha, \beta) = \{\alpha, \beta\}$$

Merge(α,β)={α,β}

Sets are unordered.

Thus:

No precedence

No adjacency

No directionality

If order exists, it must be added later.

Conceptual Argument

Syntax interfaces with:

CI (meaning)

SM (externalization)

Only SM:

requires temporal sequencing

operates in real time

is modality-specific (speech, sign)

Thus:

Order is a requirement of externalization, not computation.

Kayne’s LCA 

What LCA Achieves

The LCA derives linear order from asymmetric c-command.

Merits:

Unifies hierarchy and order

Explains many rigid patterns

The Architectural Cost

LCA requires:

syntax to compute precedence

antisymmetry as a universal law

widespread covert movement

Problem:

It internalizes an interface problem into core syntax.

This violates minimalist economy.

PF-Driven Linearization

Alternative Architecture

Proposed view:

Syntax builds hierarchical objects

Objects are transferred cyclically

PF linearizes structures under:

prosodic constraints

processing limitations

modality-specific requirements

Word order = solution space, not rule.

Free Word Order Is Not Free

Case Study: Scrambling Languages

Languages like:

Urdu

Hindi

Warlpiri

Latin

Appear to allow “free” word order.

But:

Information structure constrains order

Prosody matters

Scope relations remain stable

Prediction:

Linearization is flexible only where SM constraints allow multiple solutions.

Minimalist Grammars and Linearization

Why MGs Matter

MGs:

separate hierarchical generation from linear output

allow multiple surface strings from one derivation

formally capture externalization

An MG can generate:

the same tree

multiple linearizations

This matches typological reality.

Formal Sketch: Linearization as Optimization

Let:

H = hierarchical structure

L = linearization function

C = set of SM constraints

Then:

$$L(H) = \arg\min_{\ell \in \text{Perm}(H)} \text{Cost}(\ell, C)$$

L(H)=argℓ∈Perm(H)min​Cost(ℓ,C)

Syntax supplies H.

SM chooses among permutations.

Why Word Order Changes So Easily

Diachronic Fragility

Word order changes faster than:

case systems

agreement

movement options

Explanation:

Interfaces change faster than core computation.

Externalization is evolutionarily plastic.

Apparent Counterexamples

Rigid Word Order Languages

English, French.

But rigidity correlates with:

loss of morphology

heavier SM reliance on order

processing pressures

Order compensates for lost cues.

Failure Modes of Syntactic Order Accounts

Parameter Proliferation

Directionality parameters multiply

Typology becomes stipulative

Cartographic Rigidity

Encodes interface outcomes as syntactic primitives

Predicts far less variation than observed

Architectural Consequences

Syntax is order-free

Linearization is external

Variation arises at SM

Word order is optimization, not rule

Syntax–PF separation is real

Squib Trajectories

Potential LI/NLLT squibs:

“Order Without Syntax: Externalization as Optimization”

“Why Free Word Order Is Not a Syntactic Property”

“Linearization Variability and the Architecture of Externalization”

Reviewer pressure:

formal clarity

typological depth

computational explicitness

Exercises

Exercise 1 (Formal)

Provide two distinct linearizations from the same hierarchical structure using different SM constraints.

Exercise 2 (Typological)

Analyze a language with scrambling. Identify which cues compensate for flexible order.

Exercise 3 (Computational)

Implement an MG fragment that generates multiple word orders from one derivation.

Linearization & Sensory–Motor Interface

Generate two or more linearizations from the same hierarchical structure using different SM constraints.

Analyze a scrambling language and identify cues that allow multiple surface orders.

Implement a Minimalist Grammar (MG) fragment generating multiple linearizations for one derivation.

Take-Home Architectural Claim

Syntax does not order words.

It builds relations.

Order is imposed only when language leaves the mind.

At this point, we have established three core architectural theses:

Merge creates symmetry → repair

Locality = internalized computation

Order = interface imposition

4. Cartography vs. Minimalist Roots: Do We Need Rich Functional Structure?

Architectural Question

Does the human language faculty encode richly articulated functional hierarchies, or do such hierarchies emerge from derivational economy and interface pressures?

More sharply:

Are functional sequences part of Universal Grammar, or are they epiphenomena of how syntax survives computation and externalization?

This post treats Cartography not as a rival “school,” but as a stress test for Minimalist architecture.

What Cartography Claims 

Core Commitments

Cartography (Cinque, Rizzi) claims that:

Functional structure is highly articulated

The hierarchy of projections is universal and invariant

Cross-linguistic variation is largely movement within a fixed spine

Canonical examples:

CP split into Force–Top–Foc–Fin

Adverbial hierarchy (Mood > Tense > Aspect > Voice…)

Cartography’s empirical achievements are undeniable.

The Minimalist Challenge

Minimalism asks a deeper question:

Why would UG encode dozens of ordered functional heads?

From an architectural standpoint:

Each head increases search space

Each projection raises acquisition burden

Each fixed order hard-codes interface outcomes

This is not a stylistic objection.

It is a computational one.

Two Competing Explanations of Order

Cartographic Explanation

Order reflects innate syntactic hierarchy

Deviations = movement

Stability = evidence for hard-coding

Minimalist Explanation

Order reflects:

labeling resolution

phase boundaries

information-structural pressures

SM optimization

Stability emerges from recurrent repair strategies

The same surface facts, radically different architectures.

Microvariation as a Diagnostic Tool

The Cartographic Prediction

If hierarchies are innate:

microvariation should be limited

deviations should be movement-based

unattested orders should be impossible

The Minimalist Prediction

If hierarchies emerge:

microvariation should cluster around:

interface pressures

economy trade-offs

optional repairs

Empirical question:

Which prediction is borne out?

Derivational Economy vs. Structural Encoding

Economy Argument

If two analyses generate the same interpretive output:

one using:

multiple functional heads

the other using:

fewer heads + derivational operations

Minimalism favors the latter.

Cartography must therefore justify why structure is cheaper than computation.

Formal Pressure: Overgeneration

Rich hierarchies risk:

massive overgeneration

reliance on movement filters

post-hoc licensing

Minimalist roots seek:

minimal structure

maximal explanation

Case Study: Topic–Focus Articulation

Cartographic Account

Dedicated TopP and FocP

Fixed ordering

Cross-linguistic uniformity

Minimalist Root Account

Topic and focus arise via:

edge effects

labeling needs

discourse-driven movement

No need for fixed projections

Prediction:

If discourse context changes, structural reflexes should shift.

Empirically supported in many languages.

Formalizing the Debate

Let:

S = syntactic structure

I = interpretive output

C = interface constraints

Cartography:

S→I(richly specified)S \rightarrow I \quad (\text{richly specified})

$$S\to I(\text{richly specified})$$

Minimalist Roots:

Sminimal+C→IS_{\text{minimal}} + C \rightarrow I

Sminimal​+C→I

Architectural economy favors minimizing S, not C.

Where Cartography Is Strong

This lecture does not dismiss Cartography.

Cartography excels at:

descriptive precision

cross-linguistic pattern discovery

hypothesis generation

Minimalism depends on cartographic results, but resists reifying them.

Where Minimalism Must Deliver

Minimalism must:

derive hierarchies, not deny them

formally model emergence

explain stability without hard-coding

Failure to do so cedes ground to Cartography.

Hybrid Positions 

Some contemporary work:

accepts cartographic results

but seeks minimalist explanations

This is the productive frontier.

Squib Trajectories

Squib topics:

“Are Functional Hierarchies Primitive or Emergent?”

“Microvariation as Evidence Against Fixed Functional Spines”

“Deriving Cartographic Orders Without Cartographic Structure”

Reviewer focus:

explanatory depth

avoidance of strawman arguments

empirical sharpness

Exercises

Exercise 1 (Derivational)

Take a cartographic hierarchy and remove half the projections. Show what must be derived instead.

Exercise 2 (Typological)

Find a language where cartographic ordering is violated. Explain how interpretation survives.

Exercise 3 (Formal)

Model topic/focus without dedicated projections using labeling and movement.

Cartography vs Minimalist Roots

Remove half the functional projections in a cartographic hierarchy; derive the same interpretive output minimally.

Identify a language that violates standard cartographic order; explain interpretive survival.

Model topic/focus distinctions without dedicated functional projections using labeling and movement.

Take-Home Architectural Claim

Cartography maps the surface.
Minimalism must explain the map.

5. Phases, Features, and the Death of Agreement: Why Syntax Does Not Check Anything

Architectural Question

Why does syntax appear to traffic in features that are “checked,” “valued,” or “deleted,” and what would the architecture look like if features were not causal at all?

More sharply:

Is agreement a grammatical operation, or is it a surface reflex of cyclic computation and visibility?

This post defends a strong thesis:

Features do not drive syntax.

They annotate outcomes of computation.

Agreement is epiphenomenal.

Feature-Checking: A Convenient Fiction

The Standard Story

In mainstream Minimalism:

Heads carry uninterpretable features

Probes search for goals

Agreement “licenses” movement

Derivations crash if features remain unchecked

This story has pedagogical appeal, but deep architectural problems.

The Core Problem with Features

Circularity

Features are introduced:

to force movement

to explain agreement

to enforce locality

But these phenomena already follow from:

labeling

cyclicity

visibility

Thus:

Features explain only what they are designed to explain.

Proliferation

Every new phenomenon introduces:

new features

new probes

new stipulations

This violates:

economy

learnability

typological restraint

Phases Reinterpreted

Traditional View

Phases:

define Spell-Out domains

enforce PIC

constrain extraction

Architectural Reanalysis

Phases are computational compression points.

They:

reduce workspace size

seal off completed structures

regulate visibility

No features required.

Visibility Without Features

Activity Revisited

An element is “active” if:

it remains visible

it has not been sealed by phase transfer

it is on the derivational frontier

No need for:

unvalued features

licensing conditions

Visibility alone explains:

movement possibilities

intervention effects

freezing

Agreement Without Agreement

Empirical Cracks

Agreement is:

optional in many languages

partial or defective

absent without interpretive loss

Examples:

default agreement

clitic doubling

non-agreeing subjects

If agreement were causal, these systems should crash.

They don’t.

Preminger’s Challenge

Preminger (2014, 2025):

Agreement failure does not cause ungrammaticality

Agreement is not obligatory

Syntax survives without it

This is devastating for feature-checking.

Reframing Agreement

Agreement is a PF-visible reflex of shared accessibility within a phase.

If two elements:

are simultaneously visible

share structural proximity

Then:

morphological concord may be realized

If not:

default morphology appears

No crash. No checking.

Formal Sketch: Agreement as Correlation

Let:

V(x) = visibility of element x

P = phase domain

Agreement holds if:

$$x, y \in P \land \text{Accessible}(x, y)$$

x,y∈P∧Accessible(x,y)

No valuation function required.

D-Pronouns, Pro-Drop, and Incorporation

Traditional Feature Story

Pro-drop licensed by agreement
Null pronouns need rich features

Phase-Based Story

Null arguments arise when referential material is recoverable at CI.

Dynamic phases allow:

referential recovery

incorporation

pronominal silence

Agreement may accompany this, but does not license it.

Failure Modes of Feature-Based Accounts

Overgeneration

Predict obligatory agreement
Fail on defective systems

Interface Blindness

Treat morphology as syntactic
Ignore PF variability

Architectural Consequences

Features are descriptive, not causal
Phases regulate visibility
Agreement is optional
Movement is independent of agreement
Syntax computes structure, not morphology

Squib Trajectories

Squibs:

“Agreement Without Features”

“Why Syntax Does Not Check Anything”

“Phases as Visibility Domains”

Reviewer demands:

explicit derivations

serious engagement with Preminger

typological reach

Exercises

Exercise 1 (Formal)

Construct a derivation where agreement fails but syntax converges.

Exercise 2 (Typological)

Analyze a language with default agreement. Explain convergence without features.

Exercise 3 (Theoretical)

Remove feature-checking from a standard Minimalist derivation. What survives?

Phases, Features, and the Death of Agreement

Construct a derivation where agreement fails but the syntax converges successfully.

Analyze a language with default or defective agreement; explain convergence without feature-checking.

Remove feature-checking from a standard derivation; evaluate which operations survive.

Take-Home Architectural Claim

Syntax does not check features.

It manages visibility.

Agreement is what we see when morphology catches up.

6. Mathematical & Computational Syntax: Is Human Language Mildly Context-Sensitive?

Architectural Question

What is the exact computational power of human syntax—and how do Merge, locality, and phases constrain it?

More sharply:

Is the human language faculty strong enough to escape context-freeness, but weak enough to avoid computational intractability?

This post defends a carefully bounded thesis:

Human syntax occupies a narrow computational niche:

stronger than Context-Free Grammars, weaker than Context-Sensitive Grammars.

Why Computational Adequacy Is Not Optional

The Minimalist Obligation

If syntax is:

recursive

hierarchical

generative

Then it must be:

formally characterizable

computationally implementable

learnable under finite resources

Any theory that cannot be computationally modeled is architecturally incomplete.

Context-Free Grammars (CFGs): Too Weak

What CFGs Can Do

CFGs capture:

basic recursion

simple embedding

local dependencies

But they fail on:

cross-serial dependencies

multiple agreement chains

non-nested dependencies

Canonical Counterexample: Swiss German

Pattern:

Jan säit dass mer d’chind em Hans es huus haend wele laa hälfe aastriiche

Verbs and objects align cross-serially, not hierarchically nested.

CFGs cannot generate this pattern.

Context-Sensitive Grammars (CSGs): Too Strong

CSGs can generate:

any dependency

arbitrary copying

global constraints

But:

parsing is PSPACE-complete

acquisition becomes implausible

overgeneration is unconstrained

Human syntax shows discipline, not brute power.

The Mildly Context-Sensitive (MCS) Hypothesis

Defining MCS Languages

A grammar is MCS if it:

Properly contains CFGs

Handles cross-serial dependencies

Has polynomial-time parsing

Preserves locality

This is the Goldilocks zone.

Minimalist Grammars (MGs)

Why MGs Matter

Stabler (1997, 2011, 2024):

MGs:

formalize Merge and Move

derive displacement without transformations

are equivalent in power to Tree-Adjoining Grammars (TAGs)

Crucially:

MGs generate exactly the class of mildly context-sensitive languages.

This is not an accident.

Formal Core: MG Operations (Sketch)

MGs use:

Merge = structure-building

Move = feature-driven reordering (formally encoded)

Lexicalized derivations

Key result:

MG derivations are computable in polynomial time.

Thus:

powerful enough

constrained enough

Reconciling MGs with Architecture

Recall earlier section of this post/discussion:

Merge creates symmetry (1)

Locality restricts search (2)

Linearization is external (3)

Structure is minimal (4)

Features are epiphenomenal (5)

MGs align with this if features are reinterpreted as bookkeeping, not causal triggers.

Swiss German Revisited (MG Sketch)

MG derivation:

multiple verbal projections

parallel Merge operations

controlled interleaving via Move

Key point:

No global search, no unconstrained copying.

The dependency is managed, not computed freely.

Complexity Boundaries

Why Syntax Avoids Hard Problems

Human syntax avoids:

unrestricted copying

mirror dependencies

global counting

These push grammars into:

NP-hard

PSPACE-complete territory

Prediction:

No natural language requires such power.

This is empirically supported.

Apparent Challenges

Multiple Agreement & Reduplication

Often cited as pushing beyond MCS.

But careful analysis shows:

morphology absorbs complexity

syntax remains bounded

Interface again saves the architecture.

Failure Modes of Overpowered Syntax

Theories that allow:

unrestricted movement

global constraints

feature stacking

predict:

unattested languages

acquisition failure

processing collapse

Architectural Consequences

Syntax is computationally bounded
MGs are a faithful formalization
MCS is not arbitrary, it is forced
Interfaces absorb excess complexity
Human language is computationally elegant

Squib Trajectories

Squib topics:

“Why Human Syntax Is Mildly Context-Sensitive”

“Minimalist Grammars as a Model of the Language Faculty”

“Computational Limits as Grammatical Universals”

Reviewer pressure:

formal precision

clear complexity claims

no hand-waving

Exercises

Exercise 1 (Formal)

Provide an MG fragment generating a cross-serial dependency.

Exercise 2 (Comparative)

Show how a CFG fails on the same data.

Exercise 3 (Theoretical)

Identify a hypothetical language that would exceed MCS power. Argue why it is unattested.

Mathematical & Computational Syntax

Provide an MG fragment generating a cross-serial dependency.

Show how a CFG fails to generate the same dependency pattern.

Identify a hypothetical language exceeding mildly context-sensitive power; argue why it is unattested.

Take-Home Architectural Claim

Human language is computationally powerful, but only just enough.
Anything more would be unlearnable.
Anything less would be inexpressive.

Where the proseminar Now Stands

We have now built an internally coherent architecture:

Merge destabilizes structure

Locality internalizes computation

Linearization is external

Structure emerges, not hard-codes

Features annotate outcomes

Syntax is mildly context-sensitive

7.  Evolutionary & Cognitive Frontiers: Why This Architecture Exists

Architectural Question

Why does the human language faculty exhibit exactly the architecture we have uncovered?

The question is:

Why has evolution produced a faculty with these precise constraints—no more, no less?

Constraints from Evolutionary Plausibility

Cognitive Limitations

Working memory is bounded
Attention is limited
Incremental processing is necessary

Implications:

Locality, phases, and minimal structure are consequences of cognitive architecture, not arbitrary design.

Learnability Constraints

Children acquire language from finite input
Excessive feature proliferation or unrestricted power is unlearnable
Mildly context-sensitive derivational systems maximize learnability

Implication:

Syntax balances expressive power with learnability, a Goldilocks solution.

Symmetry and Merge: Evolutionary Roots

Merge as a Core Innovation

Merge produces structured recursion
Recursion allows complex thought and planning
Symmetry-breaking is required for linearizable output

Evolutionary insight:

Merge may have arisen for general hierarchical cognition, not just language.

Locality as Computational Necessity

Why the Brain Enforces Locality
Global search is computationally expensive
Phases act as memory firewalls
Minimalist derivations are incremental, tractable, and learnable

Observation:

Locality is architecture, not a grammatical whim.

Linearization & the Sensory–Motor Interface

Evolutionary Perspective

Humans process speech incrementally
Externalization channels (speech, sign) impose temporal order
Word order emerges as a cognitive constraint on production

Implication:

Linearization is shaped by modality, not UG itself.

Features and Agreement as Epiphenomena
Morphology reflects interpretive recoverability
Agreement arises when SM interfaces can encode correlations
Features do not drive derivation

Evolutionary reading:

Feature-checking is a cognitive “side effect,” not a selective pressure.

Computational Bounds as Adaptive Constraints
Mild Context-Sensitivity = expressivity without computational overload
Cross-serial dependencies can exist, but arbitrarily complex dependencies cannot
Syntax aligns with polynomial-time parsing in the human mind
The language faculty is optimized, not maximal.

Typological & Cross-Linguistic Evidence

Languages vary in morphology, agreement, and order
Despite variation, all languages obey:
Merge-based hierarchies
Locality constraints
Mild context-sensitivity

Implication:

Constraints reflect cognitive and evolutionary limits, not historical accident.

Cognitive Frontiers

Recursion & Thought
Merge allows nested thought structures
Language may co-opt general hierarchical reasoning
Language is an interface between cognition and communication

Processing Pressure

Incremental parsing requires visibility and phases
Syntax is tuned to real-time comprehension

Evolutionary Hypotheses

Merge-first hypothesis

Hierarchy existed for general cognition
Externalization adapted later

Minimalist efficiency hypothesis

Locality and bounded derivation emerge from memory/processing constraints

Interface-driven architecture

Linearization, agreement, and functional hierarchies are shaped by SM/CI pressures

Squib Trajectories

Squibs:

“Phases as Evolutionary Memory Firewalls”
“Why Human Syntax Is Just Powerful Enough”
“From Merge to Linearization: An Interface-Driven Evolutionary Account”

Reviewer expects:

integration of typology, computation, and evolution

formal clarity connecting derivations to cognitive principles

critical engagement with interface pressures

Exercises

Exercise 1 (Comparative)

Analyze a language with optional agreement. Explain evolutionary advantage of epiphenomenal agreement.

Exercise 2 (Computational)

Model a derivation with multiple long-distance dependencies. Demonstrate tractability constraints.

Exercise 3 (Theoretical)

Formulate an argument why increasing syntax beyond MCS would be evolutionarily maladaptive.

Evolutionary & Cognitive Frontiers

Analyze a language with optional agreement; explain its evolutionary advantage.

Model a derivation with multiple long-distance dependencies; demonstrate tractability constraints.

Argue why increasing syntactic computational power beyond MCS would be maladaptive.

Take-Home Architectural Claim

Human syntax is the product of evolutionary compromise:
Powerful enough to express unbounded hierarchical thought
Constrained enough to be learnable, incremental, and processable
Minimal in structure, externalized flexibly, and free of superfluous features

In short: every quirk of syntax, Merge, locality, phases, linearization, feature-tracking, is an adaptation to cognitive and evolutionary reality.

	Core Insight
1	Merge destabilizes structure
2	Locality is internalized computation
3	Word order is externalization
4	Structure emerges from economy, not hard-coded hierarchies
5	Features and agreement are epiphenomenal
6	Human syntax is mildly context-sensitive
7	Architecture reflects cognitive and evolutionary optimization

At this stage, you now have a framework for the architecture of human syntax, spanning formal, typological, cognitive, and evolutionary domains! Read it, revise it, refine it and explore it further! 

Reflections: Toward the Architecture of Possibility

We began this proseminar not to learn syntax, but to see it, to expose the invisible architecture that constrains, enables, and defines human language. Over the course of the year, we have probed, formalized, and stress-tested the limits of current theory, moving beyond description into the domain of architectural discovery.

The enterprise of syntax is no longer a catalog of forms; it is a laboratory of necessity. Every derivation we formalized revealed a fundamental truth about cognition: that language is both infinitely expressive and finitely realizable, a delicate compromise dictated by the architecture of the human mind. This is the domain of the Third Factor: universal principles of efficient computation that exist as much in the stars as in the synapse.

We confronted anomalies, Dyirbal ergativity, Icelandic dative quirks, Swiss-German cross-serial dependencies, not as curiosities, but as philosophical provocations. Each anomaly demanded that we formalize the impossible, revealing where the orthodoxy fails and where the computational spine of language must be refined.

From this crucible, the architecture of human language revealed itself:

Merge as the singular recursive engine of structure, its simplicity yielding hierarchical complexity.

Locality and phase dynamics as the inevitable reflections of finite memory, processing limits, and interface constraints.

Linearization as the projection of abstract computation into temporal reality—the moment thought becomes speech.

Epiphenomenal features as signals, not causes, reminders that description is never explanation.

Mildly Context-Sensitive boundaries as the sweet spot where the mind balances expressivity and tractability.

This proseminar has not merely explored language. It has performed an autopsy on the miracle, revealing that what we once called “rules” are, in truth, consequences of universal computational principles. The grammar of possibility is not invented, it is discovered.

As scholars, your work now occupies a space of original contribution. Each derivation, every formal proof, every anomaly resolved is a claim about the architecture of thought itself, capable of enduring scrutiny, capable of influencing theory worldwide.

The lesson is both simple and profound: language exists at the intersection of computation, cognition, and evolution. To understand it is to understand a fundamental architecture of the human mind. There are no sacred derivations, no inviolable hierarchies, only the constraints of possibility.

Every “impossible” sentence is an invitation. Every empirical counterexample is an opportunity. In this seminar, you have not merely mapped phenomena; you have charted the frontiers of human understanding.

We close not with certainty, but with provocation: the architecture of language is not fully known. Our work is the first step in a continuum of inquiry that will stretch theory, computation, and philosophy together.

Language is not a museum. It is a laboratory. It is a universe of constraints and possibilities. And the frontier moves only when we push it.

This is your charge: continue to formalize, challenge, and imagine. Stand where orthodoxy hesitates. Derive what no one thought possible. Let the architecture of language guide you, not merely as scholars, but as architects of thought itself.

The derivation is never truly finished. The anomalies await. The frontier awaits. And so do you.

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