Abstract
Semiotics has been applied to innumerable domains of human intellectual, symbolic, and expressive activities. It has also been developed broadly in terms of its epistemology and theoretical ramifications by many semioticians over the years. However, rarely has it been considered to be a metalanguage for mathematics and the physical sciences, even though these use semiotic resources unconsciously, including annotation in mathematics, equation formulation of phenomena in physics, and so on. The purpose of this paper is to consider semiotics in terms of its value as a metalanguage for the sciences since it allows the scientist and mathematician to reflect consciously on the nature of the symbolic resources used in carrying out representation within their disciplines. For example, set theory logic in mathematics, as Peirce clearly understood, was an attempt by mathematicians to develop a metalanguage of their own for the study of mathematics. As it turns out, and as Peirce persuasively showed, set theory is itself a manifestation of semiotic principles that define its metalinguistic structure. The modern concept of metalanguage can be traced to Russell and Whitehead’s (1913) construction of a set of principles that were free of logical circularity and inconsistency for mathematics, logic, and thus the sciences. As it turned out, that set contained a “flaw” - a proposition that could not be shown to be true or false - leading to the notion of indeterminacy in logic (Godel 1931). A semiotic metalanguage, on the other hand, would show the structural and signifying characteristics of such constructions, not present them as monolithic frameworks.
