Automatic analysis of the myriad discussion messages in large online courses can support effective educator-learner interaction at scale. Robust classifiers are an essential foundation for the use of automatic analysis of cognitive presence in practice. This study reports on the application of a revised machine learning approach, which was originally developed from traditional, small-scale, for-credit, online courses, to automatically identify the phases of cognitive presence in the discussions from a Philosophy Massive Open Online Course (MOOC). The classifier performed slightly better on the MOOC discussions than similar previous studies have found. A new set of indicators to identify cognitive presence was revealed in the MOOC discussions, unlike those in the traditional courses. This study also cross-validated the classifier using MOOC discussion data from three other disciplines: Medicine, Education, and Humanities. Our results suggest that the cognitive classifier trained using MOOC data in only one discipline cannot yet be applied to other disciplines with sufficient accuracy.