2019 Volume 25 Issue 2 Pages 55-64
In this research, we consider the subject in mathematics as a “sign”―in Peirce’s semiotics―that directs our attention to different things, and we clarify its ontological status. According to this perspective, since a sign consists of representamen, object, and interpretant, the existence of the subject could be determined by the relationship between the representamen and the object. In this study, we semiotically analyzed subjects through Euler’s activity in “Analysin Infinitorum.” The results highlighted the following points.
First, we should consider not only universals but also individuals as subjects in mathematics, because the subjects in mathematical activities evolve from individuals to universals. Second, the signs as subjects are initially the signs themselves (i.e., icon). Thereafter, these signs indirectly indicate a tacit class (i.e., index), and finally, they conventionally indicate mathematical objects (i.e., symbol). Peirce’s semiotics, therefore, gives a suggestion to be effective among frameworks for the subjects, because it covers various ontological positions and explains the evolution between them.
