We have considered the role of logical demonstration. We should consider further the role of mathematics and geometry: Galen looks to these as providing a model of the possibility of certain knowledge, and a refutation of Skepticism. He recommends a training in these disciplines, where “the fact itself bears witness of its truth, once discovered”—i.e., where one cannot doubt the rightness of the solution one has reached—for anyone interested in truth-giving enquiry (Aff. Pecc. Dig. II.3, 290–2; II.4–5, 299–305). A paradigmatic case is that of the construction of a sundial: if one has done it correctly, the facts themselves confirm that. That is, one can simply observe that the sun hits the first line at daybreak and the last at sunset; moreover, the correctness of the positioning of the remaining lines can be checked against a simply constructed water clock.