Peirce's Philosophy of Notations and the Trade-offs in Comparing Numeral Symbol Systems

In this paper, we connect two research directions concerning numeral symbol systems and their epistemological significance. The first direction concerns the cognitive processes involved in acquiring and applying different numeral symbols, e.g. the Indo-Arabic or Roman numeral systems. The second direction is a semiotic one, with focus on Charles Peirce’s Philosophy of Notation. Peirce’s work on logical formalism is well known, but he also wrote extensively on numeral systems. Here we take Peirce’s considerations on central notions like iconicity and simplicity and examine their relevance for comparing different numeral symbol systems. We argue that simplicity and iconicity, for example, cannot be understood as single notions. Instead, they should be connected to different aims of numeral symbols that different systems fulfill to different degrees. Consequently, we focus on the kind of trade-offs that different symbol systems imply in acquiring and applying numeral symbol systems.