The Coordination Problem: Why Language Exists

The Standard View and Its Limits

The dominant account of language treats it as a transmission medium: a speaker encodes a thought into a signal, the signal travels through a channel, a listener decodes the signal back into (approximately) the same thought. This model — Aristotle's De Interpretatione, Saussure's langue/parole, Shannon-Weaver's information theory, Chomsky's competence/performance distinction — treats meaning as pre-linguistic and language as its vehicle.^[1]

The transmission model faces three systematic failures:

1. The polysemy problem: Most words have multiple meanings that speakers navigate effortlessly. If meaning were encoded in signals, polysemy would be noise; instead, it is universal and structured.
2. The translation asymmetry problem: Translation is not symmetric. Some concepts translate readily across languages; others resist translation in systematic ways that correlate with cultural-cognitive structures, not signal complexity.
3. The pragmatic gap: What speakers mean routinely underdetermines and overdetermines what they say. Grice's implicature, Austin's illocutionary force, and Wittgenstein's language games all document this gap — but the transmission model has no principled account of it.

The Coordination Hypothesis

We propose that language is a coordination protocol, not a transmission medium. Its function is not to move content from one mind to another but to establish, maintain, and negotiate shared attentional and intentional states between agents.

Under this view, the fundamental unit of linguistic communication is not the proposition but the coordination operation: an act that modifies the joint attentional state of speaker and listener in a specific direction.

The four primary grammatical moods map onto four coordination operations:

Mood	Coordination Operation	Paraphrase
Declarative	STORE(description)	"Add this to your model of the world"
Interrogative	COMPUTE(query)	"Run this computation and return the result"
Imperative	EXTEND-AGENCY(act)	"Let me act through you"
Desiderative	EXPOSE-STATE(affect)	"Let me perceive your internal state"

This is not a taxonomy of sentence types — it is a functional decomposition of the coordination space that grammar must navigate.

Grammar Cases as Computational Operations

The Partition Function

Mental states are continuous. Grammar is discrete. The PSM proposes that grammatical categories constitute a partition of the latent mental-state space: different grammars partition the same underlying continuum differently, producing cross-linguistic variation that is not arbitrary but reflects the partition geometry.

Formally: let $\mathcal{M}$ be the space of possible mental states (a continuous manifold). A grammar $G$ induces a partition $\mathcal{P}_G$ of $\mathcal{M}$ into named regions (lexical and grammatical categories). The translation difficulty between grammars $G_1$ and $G_2$ is proportional to the measure of the set of mental states that lie on partition boundaries in one grammar but in the interior of a region in the other:

$$D(G_1, G_2) \propto \mu\left(\partial\mathcal{P}_{G_1} \triangle \partial\mathcal{P}_{G_2}\right)$$

This yields a testable prediction: translation difficulty between language pairs should correlate with typological distance in ways that track the geometry of partition mismatch, not the surface complexity of the target language.

Recursion as Sub-Reality Navigation

The Minimalist Programme (Chomsky, 1995) treats recursion as the defining cognitive primitive of human language — the operation MERGE that combines two syntactic objects into a new one, indefinitely.^[4] The PSM offers an alternative account.

Speakers routinely communicate about nested situations: what Alice thinks Bob said that Carol would do. Each embedding creates a new sub-reality — a context within which the embedded proposition is evaluated. Recursion is not a structural primitive but a navigational tool for managing sub-realities.

Prediction (Pirahã): Languages with reduced pressure to navigate nested sub-realities should show reduced recursion. This is consistent with Pirahã (Everett, 2005), which lacks grammatical recursion despite the cognitive capacity for it.^[5] The PSM predicts: Pirahã speakers have full recursive cognitive capacity, but their communicative norms do not require sub-reality navigation beyond depth 1, so recursion is not grammaticalised.

Polysemy as Multi-Vector Access

Under the transmission model, polysemy is a defect — ambiguity that should be resolved or avoided. Under the PSM, polysemy is a feature: multiple grammatical constructions provide multiple approach vectors to the same semantic region in $\mathcal{M}$.

Consider "run": run a race, run a program, run a company, run a fever, run for office. Each construction provides a different approach vector to a region in $\mathcal{M}$ characterised by directed, sustained activity with a goal. The vectors differ in their emphasis (agent vs process vs duration vs outcome) but converge on the same region.

This predicts that polysemous senses should be structurally related — not arbitrarily homophonous, but systematically connected via transformations of the approach vector. This is the empirical signature observed in construction grammar and cognitive semantics.

Theory of Mind and the Self-Other Boundary

The PSM Requires ToM

The coordination operations defined in Section 1 presuppose a particular cognitive architecture: the agent must model the other agent's mental state in order to select the appropriate coordination signal. Telling someone something (STORE) requires modelling what they currently believe and what gap the proposition fills. Asking a question (COMPUTE) requires modelling what they know and what computation they can perform.

This means PSM operates at Theory of Mind Level 2+ — the capacity to attribute beliefs (not just goals) to other agents, and to distinguish those beliefs from one's own.^[7]

The Developmental Trajectory

The developmental milestones for PSM use align with ToM development:

Age	Milestone	PSM Implication
9 months	Joint attention, shared intentionality	Shared attentional state established
15 months	Implicit false belief (Onishi & Baillargeon)	STORE operates on other's model, not shared world
4 years	Explicit false belief (Sally-Anne task)	Full COMPUTE/STORE differentiation
6+ years	Recursive ToM	Sub-reality navigation; full recursion

The prediction: children should use declarative, interrogative, and imperative functions before they pass standard false-belief tests, because L1 coordination (goal-attribution) supports basic grammar use; L2 coordination (belief-attribution) is required for the full PSM repertoire.

Predictions for ToM Deficits

Condition	PSM Prediction
Autism spectrum disorder	Atypical Self-Other boundary partition → literal interpretation of coordination signals; pragmatic difficulties despite intact syntax
Williams syndrome	Hypersocial profile → over-partitioned Other space → heightened use of desiderative and interrogative modes
Psychopathy	Intact cognitive ToM, impaired affective ToM → coordination signals used instrumentally (EXTEND-AGENCY without EXPOSE-STATE reciprocation)

These predictions are distinct from those of standard ToM accounts because the PSM specifies which coordination operations are affected by which ToM components, not merely that ToM deficits produce communication difficulties.

Self-Modelling and Desiderative Speech

An undertheorised feature of language is the desiderative mood — expressions of wish, desire, and affect. The PSM reframes these as EXPOSE-STATE operations: the speaker invites the listener to model the speaker's internal state.

This creates a distinctive self-referential structure: the speaker uses grammar to model what the listener will model about the speaker. This recursive self-modelling is the linguistic analog of the non-orientable geometry proposed for the representational bulk in Paper 1. The connection between PSM and the holographic consciousness framework runs through this point.

Predictions and Falsification Criteria

Neural Predictions

The PSM predicts that grammatical mood processing should activate distinct brain regions corresponding to the cognitive operations involved in each coordination type:

Grammatical Mood	Predicted ROI	Contrast
Declarative	TPJ, mPFC (belief updating)	> Imperative baseline
Interrogative	DLPFC, angular gyrus (working memory + computation)	> Declarative baseline
Imperative	Premotor cortex, IPL (motor planning, agency)	> Interrogative baseline
Desiderative	Anterior insula, OFC (affect, interoception)	> Declarative baseline

Falsification (Claim C1): If fMRI during grammatical mood processing does not show ROI differentiation by mood type — if all four moods activate the same regions — the PSM account of grammar-as-coordination-operations is falsified.

Cross-Linguistic Predictions

Translation difficulty: The PSM predicts that translation difficulty between two languages $L_1$, $L_2$ correlates with the partition mismatch measure $D(G_1, G_2)$ defined in Section 2. Specifically:

• Languages that grammaticalise the Self-Other boundary differently (e.g., languages with elaborate evidentiality systems vs. languages without) should show higher translation difficulty for propositions involving knowledge attribution
• Languages with different aspectual partitions should show difficulty specifically for propositions involving temporal structure

Cross-linguistic universals: The PSM predicts that Greenberg-style universals (word order correlations, case-marking universals) are derivable from the geometry of the coordination space. Specifically: SOV languages should prefer postpositions (because the agency structure is encoded sentence-finally, and spatial relation operators align with that position). This is Greenberg's Universal 4 — here derived from coordination geometry rather than stipulated.^[10]

What Would Falsify the PSM

The PSM is falsified if any of the following are observed:

1. Neural: No ROI differentiation by grammatical mood in healthy adults (with adequate statistical power)
2. Developmental: Children use full grammatical mood distinctions before they attribute beliefs to others (before passing implicit false-belief tasks)
3. Cross-linguistic: Translation difficulty does not correlate with typological distance on dimensions predicted by PSM (controlled for surface complexity)
4. Formal: Greenberg's universals cannot be derived from the coordination geometry without additional stipulations that undermine the parsimony of the account

Relation to Existing Frameworks

Framework	PSM Position
Generative Grammar	Recursion is convergent tool, not cognitive primitive; UG is coordination constraint, not innate module
Construction Grammar	Compatible; constructions are cached coordination patterns
Relevance Theory	Compatible; relevance is coordination efficiency; ostensive-inferential communication is PSM coordination
Speech Act Theory	PSM provides architectural grounding for illocutionary acts
FEP/Active Inference	Compatible; PSM is the linguistic instantiation of active inference; STORE = Bayesian update; COMPUTE = query precision-weighting