# Toward the Axiomatization of Intelligence: Structure, Time, and Existence

arXiv: https://arxiv.org/abs/2504.14596 · HTML: https://mlsanity.com/paper/2504.14596/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 20 Apr 2025.

## Builds on (most cited first, 3 of 3)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Inverse Scaling: When Bigger Isn't Better](https://mlsanity.com/paper/2306.09479/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation](https://mlsanity.com/paper/2508.00853/) (2025)

## Abstract (arXiv)

This study aims to construct an axiomatic definition of intelligence within a meta-framework that defines the method of definition, addressing intelligence as an inherently naive and polysemous concept. Initially, we formalize a set-theoretic representation of the universe as the domain wherein intelligence exists and characterize intelligence as a structure that involves temporal evolution and interaction with other sets. Starting from a naive definition of intelligence as "an entity possessing structures for externally inputting, internally processing, and externally outputting information or matter," we axiomatically reformulate it within this set-theoretical depiction of the universe. Applying this axiomatic definition, we compare and interpret three examples -- Hebbian non-optimized neural networks (NNs), backpropagation-optimized NNs, and biological reflexive systems -- in terms of their intelligence, structural properties, and biological plausibility. Furthermore, by extending our definition into a categorical framework, we introduce two categories, "Time Category" and "Intelligence Category," along with the functorial relationships between them, demonstrating the potential to represent changes and mimicry relationships among intelligent systems abstractly. Additionally, since intelligence, as defined herein, functions effectively only when accompanied by temporal interactions, we introduce the concept of "activity" and explore how activity-based conditions influence classifications and interpretations of intelligence. Finally, we suggest that our definitional methodology is not limited to intelligence alone, but can be similarly applied to other concepts, such as consciousness and emotion, advocating for their formal reinterpretation through the same procedural steps: defining a universal representation, selecting naive definitions, and axiomatic formalization.