What did the Greeks call the “trial and error” reasoning process?

Question

What did the Greeks call the "trial and error" reasoning process?

Bruce Aune's review of Wilson's Peirce's Empiricism: Its Roots and Its Originality claims "The name 'empirici' is in fact traceable to a Greek verb meaning 'to make trial of.'"

Answer 1

"Trial and error" applied not to a "reasoning process" but to medical practice, and the name of the practice was derived from Greek ἐμπειρία, experience. The inspiration for the approach apparently came from Greek Pyrrhonism, which recommended permanently suspending judgment on how things are in their own nature, what Pyrrho of Elis (c. 360 – 270 BC) called ακατάληψία in contrast to Stoic κατάληψις, perceptual grasping of knowledge. As Aune writes in the review:

"He begins with the ancient empirici who were physicians. Unlike their competitors, the dogmatici, the empirici paid little attention to the supposed underlying causes of disease; their concern was principally directed to methods of treatment founded on trial and error... Later empiricists were less concerned specifically with trial and error practice; they instead focused on endorsing only factual claims with an evidential basis in sense experience".

Wikipedia even has an article about the empirici. Perhaps the best known figure of the school is Sextus Empiricus (c. 160-210 AD), whose multi-volume Adversus Mathematicos is one of our major sources on the ancient science and philosophy. Literally, the title translates as Against the Mathematicians, but Greek tà mathémata meant what can be learned and taught, so the commonly used free translation Against the Professors is closer to the original meaning.

But Sextus belongs to the later, more philosophical, generation of empirici. The founders of the school in 3rd century BC, Serapion of Alexandria and Philinus of Cos, were physicians who opposed the "dogmatic" Hippocratic tradition. Their works have not survived, but some fragments are quoted by Galen, Pliny and others.