One of the most fundamental representations in linguistic semantics is that of the proposition (McGrath and Frank, 2005), standardly taken as the carrier of truth-conditions. Recent work shows that some form of truth can be decoded from language models (Azaria and Mitchell, 2023; Li et al., 2023), and strikingly, that for some models, truth is even represented linearly in intermediate layers (Marks and Tegmark, 2024, GoT). We take this line of work a step further and argue that neural language models can use propositional representations compositionally (Janssen 2010; Pickel and Szabó 2025 a.o.), drawing from evidence of the behaviour of logical connectives: the linear compositionality hypothesis. Specifically, we show (a) that the truth values of individual conjuncts can be decoded independently of the truth value of a complex conjunction, and (b) that we can causally intervene on individual conjuncts in a way that affects the truth value of the whole.