This problem, originating in Seo's Kantian analysis of AI unexplainability (arXiv:2407.18950), asks three linked questions about the categorial structure — or categorial uninterpretability — of machine judgment. First, does there exist a principled, general method for mapping the numerical internals and outputs of artificial neural networks onto the formal structures of human judgment in Kant's sense (the four logical forms of quantity, quality, relation, and modality, and the corresponding pure concepts), or is such attribution irreducibly indeterminate (the paper's 'AI's uncertainty')? Second, could machine judgments legitimately instantiate forms of judgment that transcend Kant's table, and what apparatus would discover and characterize such forms? Third, can non-question-begging criteria be established for when a system genuinely functionally implements a pure, non-visually-grounded concept such as the self, and for validating that a natural-language explanation reflects genuine conceptual understanding rather than distributional competence? Adjacent work (machine-concept and representation-geometry research, consciousness-indicator analyses, understanding-vs-memorization benchmarks) is active on neighboring questions but leaves all three strands open.

Background

In the Critique of Pure Reason (1781/1787), Kant held that every human judgment has a fixed logical structure: it instantiates one form under each of four headings — quantity (universal, particular, singular), quality (affirmative, negative, infinite), relation (categorical, hypothetical, disjunctive), and modality (problematic, asserting possibility; assertoric, asserting actuality; apodictic, asserting necessity) — and that through these forms the understanding applies pure concepts or categories (e.g., cause and effect, necessity) that carry no empirical content. Seo (2024) used this framework to analyze artificial neural networks (ANNs, learned function approximators built from stacked differentiable matrix operations). A human judgment carries its form explicitly in natural language ('this image has a face', 'some images of this kind contain faces', 'if these features are present, there is a face'), but an ANN's output is a bare number or vector, and the same output (e.g., a 0/1 face-detector value) is consistent with several non-equivalent judgment forms. Seo calls the resulting entanglement of forms 'AI's uncertainty', and argues that the Softmax function — the output normalization softmax(z)i=ezi/∑jezjsoftmax(z)_i = e^{z_i}/\sum_j e^{z_j} used at the final layer of most classifiers and language models — acts as an 'epistemological filter' that forces every output to be read as a possibility judgment (a probability) regardless of the internal process that produced it. Explainable AI (XAI, the research program on making model decisions intelligible to humans) does not resolve this: saliency methods such as Grad-CAM (which highlight the input regions most influential for a decision) localize evidence, and generated natural-language rationales verbalize content, but neither exposes which form of judgment the system realized. A second strand concerns concepts. Drawing on Kant's claim that definitions are never complete, Seo argues there is no definitive criterion for when a concept has been functionally implemented (functionalism: mental states are individuated by their causal role in a system, not by physical constitution), and that fluent linguistic behavior can create the appearance of implementation while important functions are absent. His central example is the pure concept of the self: large language models (LLMs, text predictors trained on human-written corpora) use 'I' fluently, but a video-network experiment with Grad-CAM (following Seo and Lee 2021), in which a network had to distinguish self-generated camera motion from external object motion, suggests that self-related functions may extend beyond natural language, so linguistic fluency alone cannot establish possession of the concept. This connects to the long-standing debate on whether distributional competence — mastery of the statistical usage of words derived from text co-occurrence — constitutes, or even could constitute, understanding (Bender and Koller 2020), and to operational tests designed to detect generalization rather than memorized skill (Chollet 2019). Adjacent empirical work asks whether machine cognition could be foreign to human categories: representation-geometry research characterizes the linear concept structure of LLM embeddings (Park et al. 2023); the Platonic Representation Hypothesis argues that model representations converge toward a shared statistical model of reality (Huh et al. 2024); Hewitt, Geirhos, and Kim (2025) argue human vocabulary is inadequate for machine concepts and propose engineered neologisms; and Butlin et al. (2023) apply consciousness-science indicator properties (including self-models) to AI systems while remaining deliberately agnostic about machine consciousness. None of this supplies, or refutes, a Kantian-categorical account of machine judgment, and the question of whether machine judgments could have forms transcending the human table — explicitly posed in the introduction of Seo's paper — remains without any proposed methodology.

Problem Statement

The problem asks, for artificial neural networks in general (classifiers, language models, and their internal representations):

(1) Does there exist a principled, general method for attributing to a network's internal states and outputs the forms of human judgment in Kant's table — a determinate assignment of quantity, quality, relation, and modality, and of the corresponding pure concepts — across architectures and tasks? Or can such attribution be shown to be irreducibly indeterminate, i.e., a rigorous formulation and proof of the 'AI's uncertainty' claim that distinct judgment forms are entangled in any numerical output?

(2) Could machine judgments legitimately instantiate kinds or forms of judgment that transcend Kant's table (forms not captured by any combination of the twelve moments or twelve categories), and, if so, what epistemic or methodological apparatus would be required to discover and characterize such machine-specific forms?

(3) Can non-question-begging criteria be established for (a) when a system genuinely functionally implements a pure, non-visually-grounded concept such as the self — going beyond functional correlation, saliency localization, and natural-language fluency — and (b) when a natural-language explanation (whether generated by the model or about it) reflects genuine conceptual understanding rather than distributional competence over training text?

The research objective is either a principled framework (with explicit fidelity to, or explicitly flagged departures from, Kant's text, and demonstrated determinacy or quantified residual ambiguity on concrete models) or a rigorous negative/indeterminacy argument, together with an answer to (2) (an argument for or against machine-specific forms of judgment transcending Kant's table and, if affirmative, the epistemic or methodological apparatus required to discover and characterize them) and defensible validation criteria for the questions in (3). These three strands jointly pursue one objective — a categorial interpretability framework for machine judgment or a principled proof of its impossibility.

References

  1. Seo, Jongwoo (2024, revised through v5, 2026). Unexplainability of Artificial Intelligence Judgments and Functional Implementation in Kant's Perspective. arXiv:2407.18950, DOI 10.48550/arxiv.2407.18950. https://arxiv.org/abs/2407.18950
  2. Kant, Immanuel (1781/1787). Critique of Pure Reason (J. M. D. Meiklejohn, trans.). Project Gutenberg eBook no. 4280. https://www.gutenberg.org/ebooks/4280
  3. Seo, Jongwoo; Lee, Sang Wan (2021). Neural Network-Based Intuitive Physics for Non-Inertial Reference Frames. IEEE Access, DOI 10.1109/ACCESS.2021.3103876. https://doi.org/10.1109/ACCESS.2021.3103876
  4. Bender, Emily M.; Koller, Alexander (2020). Climbing towards NLU: On Meaning, Form, and Understanding in the Age of Data. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, DOI 10.18653/v1/2020.acl-main.463. https://doi.org/10.18653/v1/2020.acl-main.463
  5. Chollet, François (2019). On the Measure of Intelligence. arXiv:1911.01547. https://arxiv.org/abs/1911.01547
  6. Park, Kiho; Choe, Yo Joong; Veitch, Victor (2023). The Linear Representation Hypothesis and the Geometry of Large Language Models. arXiv:2311.03658; also in Proceedings of the 41st International Conference on Machine Learning (ICML), 2024. https://arxiv.org/abs/2311.03658
  7. Huh, Minyoung; Cheung, Brian; Wang, Tongzhou; Isola, Phillip (2024). The Platonic Representation Hypothesis. arXiv:2405.07987. https://arxiv.org/abs/2405.07987
  8. Hewitt, John; Geirhos, Robert; Kim, Been (2025). We Can't Understand AI Using our Existing Vocabulary. arXiv:2502.07586. https://arxiv.org/abs/2502.07586
  9. Butlin, Patrick; Long, Robert; Elmoznino, Eric; Bengio, Yoshua; Birch, Jonathan; Constant, Axel; Deane, George; Fleming, Stephen M.; Frith, Chris; Ji, Xu; Kanai, Ryota; Klein, Colin; Lindsay, Grace; Michel, Matthias; Mudrik, Liad; Peters, Megan A. K.; Schwitzgebel, Eric; Simon, Jonathan; VanRullen, Rufin (2023). Consciousness in Artificial Intelligence: Insights from the Science of Consciousness. arXiv:2308.08708. https://arxiv.org/abs/2308.08708
  10. Geng, Hejia; Xu, Boxun; Li, Peng (2023). UPAR: A Kantian-Inspired Prompting Framework for Enhancing Large Language Model Capabilities. arXiv:2310.01441. https://arxiv.org/abs/2310.01441