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This study investigates how the multimodal model Gemma 3 4B IT distinguishes between falsehoods and impossibilities through an exploratory activation analysis using 85 prompts across various philosophical categories. The findings reveal that the model conflates contingent falsehoods with contradictions, while a linear truth probe effectively separates true from impossible statements but struggles with falsehoods. Notably, the model demonstrates a clear distinction in its activation patterns, with an impossibility probe achieving perfect separation between necessary and contingent falsehoods, suggesting a nuanced representation of these concepts within the model's architecture.
The model Gemma 3 4B IT reveals a striking distinction in its representation of falsehoods and impossibilities, challenging our understanding of how AI interprets language.
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.
