Furthermore, a symbol is the sort of symbol it is linguistic, musical, pictorial, diagrammatic, etc.—in virtue of its belonging to a symbol system of a certain kind.
Hence, it is important here to emphasize, first, that reference has, in his view, different modes, and, second, that something is a symbol, and is a symbol of a given kind, only within a symbol system of that kind, a system governed by the syntactical and semantic rules distinctive of symbols of that kind.
"The underlying goal of these activities," she wrote, "is for us all to gain a better understanding of the relations between constructing things … and describing what we construct by using symbol systems of various kinds". More than 250 children from six to 14 would pass through the lab in four years.
They argued that some of the variations in students' number knowledge of number words and symbols appeared to be associated with "differential exposure to the language and symbol systems of mathematics (p. 64)".
The arguments are also addressed, at least in part, by Barsalou and his collaborators, who have proposed a theory of what they call "perceptual symbol systems" as an alternative to the language-like, "amodal" (mentalese) symbol systems of traditional cognitive science (Barsalou, 1993, 1999; Barsalou & Prinz, 1997; Barsalou et al., 2003; Kan et al., 2003).
As Carnap understood the analytic/synthetic distinction, it was a distinction drawn by a logician to enable greater theoretical systematicity in the reconstructive understanding of a given symbol system, typically a fragment of a historically developed one.
Goodman's theory of symbol systems, as composed of schemes of characters that are governed, depending on the sort of system, by different syntactical rules, and correlated to their extensions according to differing semantic rules, is at the basis of his claims on the identity conditions of works of art of different kinds.
One sort of theory of meaning a semantic theory is a specification of the meanings of the words and sentences of some symbol system.
Note, also, that there are different types of symbol system.
However, the analogy with language isn't perfect; obviously, the internal symbol system must lack many of the properties associated with a natural language.
Our own work with nucleic acid notations is based on the premise that one's choice of symbol system has immediate cognitive and functional implications for their use.
