# Shades of Zero: Distinguishing Impossibility from Inconceivability

arXiv: https://arxiv.org/abs/2502.20469 · HTML: https://mlsanity.com/paper/2502.20469/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 102 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Targeted Syntactic Evaluation of Language Models](https://mlsanity.com/paper/1808.09031/) (2018)
- [A Systematic Assessment of Syntactic Generalization in Neural Language Models](https://mlsanity.com/paper/2005.03692/) (2020)
- [Infini-gram: Scaling Unbounded n-gram Language Models to a Trillion Tokens](https://mlsanity.com/paper/2401.17377/) (2024)
- [Linearly Mapping from Image to Text Space](https://mlsanity.com/paper/2209.15162/) (2022)
- [Can Language Models Encode Perceptual Structure Without Grounding? A Case Study in Color](https://mlsanity.com/paper/2109.06129/) (2021)
- [When Do You Need Billions of Words of Pretraining Data?](https://mlsanity.com/paper/2011.04946/) (2020)
- [Evaluating Commonsense in Pre-trained Language Models](https://mlsanity.com/paper/1911.11931/) (2019)
- [Language Model Behavior: A Comprehensive Survey](https://mlsanity.com/paper/2303.11504/) (2023)
- [A Systematic Investigation of Commonsense Knowledge in Large Language Models](https://mlsanity.com/paper/2111.00607/) (2021)
- [From task structures to world models: What do LLMs know?](https://mlsanity.com/paper/2310.04276/) (2023)
- [Event knowledge in large language models: the gap between the impossible and the unlikely](https://mlsanity.com/paper/2212.01488/) (2022)
- [Language acquisition: do children and language models follow similar learning stages?](https://mlsanity.com/paper/2306.03586/) (2023)
- [Modeling Semantic Plausibility by Injecting World Knowledge](https://mlsanity.com/paper/1804.00619/) (2018)
- [Language Models Explain Word Reading Times Better Than Empirical Predictability](https://mlsanity.com/paper/2202.01128/) (2022)
- [Type theory in human-like learning and inference](https://mlsanity.com/paper/2210.01634/) (2022)

## Built on by (most cited first, 2 of 2)

- [Is This Just Fantasy? Language Model Representations Reflect Human Judgments of Event Plausibility](https://mlsanity.com/paper/2507.12553/) (2025)
- [Linear representations of grammaticality in neural language models](https://mlsanity.com/paper/2607.15175/) (2026)

## Abstract (arXiv)

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.