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Because large language models (LLMs) are impressively successful in predicting text, it appears that they must have access to a 'world model' representing causal and definitional structure. However, the dominant formalisms of modern causal inference -- Judea Pearl's interventionist approach and the Neyman-Rubin potential outcomes framework -- struggle to illuminate how LLMs learn causal structure. I resolve this puzzle by arguing that LLMs employ a specific inductive approach based on a difference-making logic -- sometimes called variational induction. I demonstrate how central aspects of this logic are realized during training, where LLMs require enormous amounts of text data from a wide range of contexts to identify difference- and indifference-makers within word sequences. Furthermore, I analyze specific architectural features of LLMs -- such as token embeddings and self-attention -- to determine their roles in variational induction. The difference-making logic of LLMs fundamentally parallels the experimental method, where causal relations are derived by systematically varying individual circumstances to determine their influence on a phenomenon.