Galen insists that genuine epistêmê, in the Aristotelian sense of securely-founded scientific understanding, is available to the serious medical investigator. The foundations consist in propositions that are evidently true, and hence require no further support. These come in two types: those evident to the senses and those evident to reason, and these are ex heautôn pista, self-crediting, intrinsically trustworthy. On the basis of such propositions the diligent inquirer can erect a firmly-founded structure of practical knowledge, a technê, but one which is, none the less, in a genuine sense demonstration. In this chapter I re-examine what Galen says about a number of inter-related key issues: What is the ‘orderly method’ of discovery which Galen regularly commends, and berates his opponents for failing to adhere to? What supplies the ‘context of justification’ for such a firmly-founded science, and how does this relate to Galen’s oft-repeated affirmation of the necessity for empirical testing, peira? And finally, and relatedly, what specific role in all of this is played by what he calls ‘differentiated experience’, peira diorismenê?