A note on a couple of recurring themes may be useful at this point.
- Peirce’s “metaphorical argument” for transforming discussion of interpretive agents, whether individuals or communities, to discussion of interpretant signs is as follows.
I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term — or one which has become identified with it, — in short, has an interpretant.
Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. … A thing cannot stand for something without standing to something for that something. Now, what is this that a word stands to? Is it a person?
We usually say that the word homme stands to a Frenchman for man. It would be a little more precise to say that it stands to the Frenchman’s mind — to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what image, what remembrance? Plainly, the one which is the mental equivalent of the word homme — in short, its interpretant. Whatever a word addresses then or stands to, is its interpretant or identified symbol. …
The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand to something, every symbol — every word and every conception — must have an interpretant — or what is the same thing, must have information or implication. (Peirce, CE 1, 466–467).
There’s additional discussion of this passage at the following locations.
- When we employ mathematical models to describe any domain of phenomena, we are always proceeding hypothetically and tentatively, and the modality of all mathematics, in its own right, is the possible. That is because mathematical existence is existence in the modest sense of “whatever’s not inconsistent”. In the idiom, “It’s would-be’s all the way down.” In effect the ordinary scales of modality are flattened down to one mode, to wit, Be ♭. It is not until we take the risk of acting on our abduced model that we encounter genuine brute force Secondness.
- Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.
- Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–. Cited as (CE volume, page).