Enthymemes are arguments that leave a premise or conclusion unstated, and they are a common persuasion device on social media. Because readers must fill in the missing part themselves, they often disagree on whether a text contains one. This paper asks how to detect and evaluate enthymemes when such disagreement is part of the task. On tweets about vaccination and immigration, each labeled by five annotators, F1 stalls around 0.67 for every fine-tuned model we train, regardless of data size, added features or label type. We therefore ask how these models should be evaluated instead, and propose metrics that compare predictions with the full distribution of annotator votes, together with a model that predicts this distribution directly and captures disagreement better at no cost in F1. We then ask what role discourse structure plays. Models learn to rely on explicit argumentative structure: they reliably recognize tweets without an enthymeme but rarely commit on tweets that contain one. Both the models and a discourse parser miss arguments whose links are left implicit and must be inferred by the reader. Finally, we discuss what these blind spots mean for content moderation systems trained on majority labels.

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