Both humans and large language models (LLMs) exhibit content effects: biases in which the plausibility of the semantic content of a reasoning problem influences judgments regarding its logical validity. While this phenomenon in humans is best explained by the dual-process theory of reasoning, the mechanisms behind content effects in LLMs remain unclear. In this work, we address this issue by investigating how LLMs encode the concepts of validity and plausibility within their internal representations. We show that both concepts are linearly represented and strongly aligned in representational geometry, leading models to conflate plausibility with validity. Using steering vectors, we demonstrate that plausibility vectors can causally bias validity judgements, and vice versa, and that the degree of alignment between these two concepts predicts the magnitude of behavioral content effects across models. Finally, we construct debiasing vectors that disentangle these concepts, reducing content effects and improving reasoning accuracy. Our findings advance understanding of how abstract logical concepts are represented in LLMs and highlight representational interventions as a path toward more logical systems.