  In this essay we examine some aspects of the classical theory of definition
as codified in Aristotle's \emph{Topics} and Porphyry's \emph{Eisagog\^e} in
the light of the way definition is carried out in modern mathematical practice.
Our goal is to contribute to the understanding of the alleged gap existing
between ancient and modern logic and science as well as the reasons behind
allegations of inadequacy and lack of sophistication in the ancient theory of
definition. Also to investigate the possibility of a co-interpretation between
modern mathematical definitional practice and ancient definitional practice in
particular in the light of topos theory. We find the ancient definitional
practice asks relevant and overlooked questions about modern mathematical
practice which apparently have escaped current philosophical and mathematical
logical literature. We also present some general considerations about the
structure and development of theories as these relate to the theory of
definition.
