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Galen's discussions of philosophical issues show a complete mastery of the school debates of his time. Galen, however, is not a school philosopher: his philosophical allegiance is controversial and he refers to philosophical theories and debates for specific purposes that pertain to his views about the status of medical knowledge. The extant fragments of his lost treatise On Demonstration offer an interesting example of this attitude. The present paper focuses on some passages from Galen's lost On Demonstration book 4, which deal with the generation of cosmos and its incorruptibility. They are preserved in John Philoponus' On the Eternity of the World and in al- Rāzī's Doubts on Galen. Galen's argument relies heavily on philosophical sources such as Plato, Aristotle and the Platonic philosopher Atticus. Galen's treatment of the topic, however, is highly original and can plausibly be seen as a discussion pro et contra the eternity of the cosmos, which aims to show the limits and fallacies of speculative knowledge. [ABSTRACT FROM AUTHOR]