In his *Harmonics*, Ptolemy (2nd century CE) outlines a strategy for
obtaining and refining scientific knowledge through alternating appeals to
sense perception and to reason, and he puts this strategy into practice in
both the *Harmonics* (concerning the pitch systems of Greco-Roman music)
and the *Almagest* (concerning the apparent movements and appearances of
the heavenly bodies). The fundamental role of empirical evidence in
Ptolemy’s scientific epistemology, however, is qualified by three
limitations: first, that all sense perceptions are inexact; second, that
identical phenomena can sometimes be explained through more than one
scientific hypothesis; and third, that mathematical structures may subsist
in some components of the cosmos without giving rise to clear phenomena.
This talk will explore ways in which Ptolemy addresses these limitations.