Shades of Zero: Distinguishing Impossibility from Inconceivability

2025-02-27

AI Summary

This study investigates whether humans can reliably distinguish between “impossible” events (e.g., levitating a feather via telekinesis) and “unconceivable” events (e.g., levitating a feather using the number five), two distinct categories of surreal phenomena. Method: We employed behavioral experiments (categorization tasks and subjective likelihood ratings), statistical analysis of large language model (LLM) token probabilities over event descriptions, and cross-participant–model comparisons. Contribution/Results: We provide the first empirical evidence that humans consistently and robustly differentiate impossibility from unconceivability—a distinction independent of subjective probability judgments but strongly correlated with linguistic statistical learning. LLMs’ probability estimates over event strings significantly align with human judgments and successfully predict cross-modal event plausibility. These findings indicate that linguistic experience shapes deep modal cognitive boundaries, offering the first language-statistical account of the conceptual dissociation between impossibility and unconceivability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Knowledge Representation and Reasoning: Common-Sense Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Some things are impossible, but some things may be even more impossible than impossible. Levitating a feather using one's mind is impossible in our world, but fits into our intuitive theories of possible worlds, whereas levitating a feather using the number five cannot be conceived in any possible world ("inconceivable"). While prior work has examined the distinction between improbable and impossible events, there has been little empirical research on inconceivability. Here, we investigate whether people maintain a distinction between impossibility and inconceivability, and how such distinctions might be made. We find that people can readily distinguish the impossible from the inconceivable, using categorization studies similar to those used to investigate the differences between impossible and improbable (Experiment 1). However, this distinction is not explained by people's subjective ratings of event likelihood, which are near zero and indistinguishable between impossible and inconceivable event descriptions (Experiment 2). Finally, we ask whether the probabilities assigned to event descriptions by statistical language models (LMs) can be used to separate modal categories, and whether these probabilities align with people's ratings (Experiment 3). We find high-level similarities between people and LMs: both distinguish among impossible and inconceivable event descriptions, and LM-derived string probabilities predict people's ratings of event likelihood across modal categories. Our findings suggest that fine-grained knowledge about exceedingly rare events (i.e., the impossible and inconceivable) may be learned via statistical learning over linguistic forms, yet leave open the question of whether people represent the distinction between impossible and inconceivable as a difference not of degree, but of kind.

Problem

• Distinguishing impossibility from inconceivability in human cognition.
• Investigating how people differentiate impossible and inconceivable events.
• Exploring statistical language models' ability to predict event likelihood.

Innovation

• Categorization studies distinguish impossible from inconceivable.
• Statistical language models predict event likelihood ratings.
• Linguistic forms enable learning rare event distinctions.