# Falsehood and Impossibility Are Different Directions in an AI's Representation of Language

arXiv: https://arxiv.org/abs/2608.12852 · HTML: https://mlsanity.com/paper/2608.12852/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [On the Conversational Persuasiveness of Large Language Models: A Randomized Controlled Trial](https://mlsanity.com/paper/2403.14380/) (2024)
- [AI model GPT-3 (dis)informs us better than humans](https://mlsanity.com/paper/2301.11924/) (2023)
- [Do Sparse Autoencoders Identify Reasoning Features in Language Models?](https://mlsanity.com/paper/2601.05679/) (2026)
- [Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States](https://mlsanity.com/paper/2606.02907/) (2026)

## Abstract (arXiv)

Language can describe states of affairs that are false and states of affairs that could not be the case at all. Whether an AI model internally distinguishes these failures remains unclear. I report an exploratory activation study of the multimodal open-weight model Gemma 3 4B IT using 85 prompts from 17 philosophical families and a topic-matched modality set of 15 topics, each expressed as a truth, contingent falsehood, improbable claim, semantic anomaly, and necessary falsehood. In its answers, the model conflates contingent falsehood with contradiction, labeling 12 of 15 false statements "contradiction." Its activations show a different pattern. A linear truth probe separates impossible from true statements (AUC 0.93) but not impossible from false statements (AUC 0.20). An impossibility probe evaluated on held-out topic families separates necessary from contingent falsehood at AUC 1.00, peaking at layer 15 with balanced accuracy 0.97 (Bonferroni-adjusted P=0.018). The truth and impossibility directions are close to orthogonal, whereas the impossibility direction partially overlaps a semantic anomaly direction while remaining distinguishable from it. Sparse autoencoder features at the same layer repeat this geometry. Features selective for impossibility also fire on anomalous sentences but rarely on contingent falsehoods. In this model's activation space, necessary falsehoods are not extreme cases of contingent falsehood but lie closer to the experimentally defined category of semantic anomaly. This representational proximity does not imply that impossible statements are intrinsically meaningless. These correlational observations from one small model offer an empirical footnote to an old philosophical distinction.