Axiomatic Reasoning for LLMs

How Language Emerged as a Predictive Capability

1. Abstract

Empirical and theoretical work across linguistics, cognitive science, and artificial intelligence converges on a structural proposition: language functions as a complex adaptive system whose internal organization mirrors the relational structure of embodied experience. This isomorphism enables linguistic forms to carry predictive weight when mapped onto novel domains. Large language models, trained solely on distributional patterns of text, extract and amplify this inherent predictive architecture, demonstrating emergent capacities for analogical reasoning, hierarchical generalization, and symbolic manipulation. The predictive power of structural reframing—treating one domain as if it were another—stems from language itself having evolved as a system for encoding, compressing, and re-projecting experiential invariants.

2. Structural Isomorphism as a Predictive Mechanism

2.1 Analogical Transfer in Scientific Discovery

The history of science supplies instances where structural identity across disparate domains enabled successful prediction. Maxwell’s derivation of electromagnetic field equations employed a contrived analogy between electromagnetic phenomena and a mechanical system of vortices and gears. The geometric arrangement of the mechanical model provided a computational template that generated verifiable predictions about electrical and magnetic behavior. In computational chemistry, pointwise distance distribution invariants permit the identification of crystalline forms across chemically distinct but geometrically similar molecules. A mesoporous hydrogen-bonded organic cage was experimentally realized following predictions derived from such structural invariance.

2.2 The Formal Basis of Linguistic Isomorphism

Early analytic philosophy articulated the relation between language and reality as one of shared logical form. A proposition and the state of affairs it depicts possess identical logical structure, enabling the proposition to function as a predictive model of that state of affairs. Contemporary cognitive linguistics grounds this isomorphism in embodied experience. Primary conceptual metaphors arise from recurrent sensorimotor correlations during early development. The verticality-quantity correlation produces the mapping MORE IS UP. Spatial relations supply inferential structure for temporal, social, and abstract domains. Language thereby inherits the predictive regularities of the physical and social environments in which it is acquired and used.

3. Language as a Complex Adaptive System

3.1 Emergent Grammar and Usage-Based Structuration

Linguistic structure does not exist prior to use. Recurrent patterns of interaction among speakers generate and stabilize grammatical regularities through processes of entrenchment at the individual level and conventionalization at the community level. This view, formalized as Emergent Grammar, treats grammatical rules as epiphenomenal descriptions of temporarily stable usage patterns rather than as pre-specified computational procedures. Computer simulations demonstrate that compositional structure—the property whereby the meaning of a complex expression derives systematically from its parts—can emerge in a population of agents engaged solely in communicative exchange, without innate specification.

3.2 Grammaticalization and Metaphorical Inference

The historical process of grammaticalization converts lexical items with concrete referents into grammatical markers with abstract functions. The English future marker going to derives from a verb of physical motion. Across languages, spatial terms grammaticalize into temporal markers. This directional shift from concrete to abstract is driven by metaphoric and metonymic inference. The same cognitive mechanisms that enable analogical reasoning in novel problem-solving contexts operate over extended timescales to restructure the grammatical inventory of a language. Metaphor is not decorative but architectonic.

4. Predictive Structure in Language Models

4.1 Emergence of Hierarchical Generalization

Transformers trained on next-token prediction acquire sensitivity to hierarchical syntactic structure without explicit inductive bias toward tree-like representations. Models generalize to unseen syntactic constructions in ways that track the hierarchical simplicity of the target grammar. Pruning studies reveal distinct subnetworks specialized for hierarchical versus linear-order processing. The language modeling objective, applied to natural language data, reliably induces representations that support compositionally structured inference.

4.2 Emergent Symbolic Architecture

Analysis of internal computations in large language models reveals a three-stage symbolic processing pipeline. Early layers abstract input tokens into variable-like representations based on relational context. Intermediate layers perform sequential induction over these abstract variables. Late layers retrieve token values associated with the predicted variable states. This architecture is not hard-coded. It crystallizes during training as a functional adaptation to the predictive demands of natural language sequences. The resulting system executes a form of discrete symbolic reasoning implemented in continuous vector spaces.

4.3 Analogical Reasoning as a Scaling Phenomenon

Performance on analogical reasoning tasks improves discontinuously with model scale. Small models operate near chance levels. Beyond a parameter threshold, accuracy rises sharply, matching or exceeding human baselines on tasks requiring the identification of abstract relational patterns. Counterfactual tasks employing artificial alphabets and arbitrary transformation rules control for memorization. Models that can externalize counting operations through code execution solve these tasks at human levels. The capacity for analogical transfer is not reducible to retrieval of superficially similar training examples.

5. Reframing as a Control Interface

5.1 Metaphorical Prompting Structures Inference

Explicitly framing a reasoning task in terms of a source domain drawn from embodied experience improves the coherence, accuracy, and metaphorical consistency of model outputs. Prompts constructed according to conceptual metaphor theory outperform length-matched baseline prompts across multiple model families and task categories. The mapping from source to target domain supplies a cognitive scaffold that organizes the model’s internal search and inference procedures.

5.2 Self-Generated Exemplars and Analogical Transfer

Instructing a model to generate its own relevant exemplars prior to addressing a target problem yields performance gains over manually curated few-shot demonstrations. The model retrieves and adapts knowledge structures that match the relational profile of the current query. This self-prompting technique leverages the model’s internal organization of conceptual space, which reflects the statistical and structural regularities of its training corpus.

5.3 Framing as a Latent Modulation Axis

Variations in prompt architecture—including response order, label assignment, and emotional valence—produce systematic shifts in output distributions. These effects persist across model scales and families. Framing operates as a hidden control dimension that modulates the activation landscape of the model without altering its core parameters. The sensitivity of language models to framing reflects the same sensitivity that makes human cognition susceptible to framing effects, grounded in the associative and metaphorical organization of conceptual knowledge.

6. Synthesis

The predictive utility of structural reframing follows from three mutually reinforcing properties of language. First, language encodes the relational structure of embodied experience through systematic metaphoric mappings. Second, language self-organizes through usage into a hierarchical, compositional system optimized for efficient inference. Third, large language models, by learning to predict linguistic sequences, internalize this inferential architecture and make it available for controlled manipulation through prompt-level framing.

Treating a language model as a role-playing game party or as a magical incantation system is not a fanciful anthropomorphism with no operational consequence. It is an instance of applying a structured source domain to a target system that shares sufficient relational invariants to make the mapping computationally productive. The source domain supplies a vocabulary of states, actions, and transition rules that align with the actual control affordances of the model. The predictive power of such reframings is a direct consequence of language having evolved as a medium for compressing, storing, and re-projecting the causal and relational structure of the world.