The article presents Galen's system of scientific medicine and some problems of its top-level principles. He endeavored to build an axiomatic and deductive system of medicine. Methods of reasoning had to respect the laws of logic; they were to follow from certain premises and to discover new truths. The lower-level premises are often secured by good empirical methods. They were not questioned, but they had not enjoyed the status of axioms. The top-level principles that have to do the work of indemonstrable primary premises are self-evident axioms and definitions. The definitions generally fulfilled the required conditions though Galen himself showed that they owed their status of being self-evident and valid to empirical research. The axioms have to be non-definitional and self-evident but as some of them are either vacuous or highly problematic, Galen's top-level medical indemonstrables are inadequate for that task.