The pragmatic theory of sign relations is called for in settings where everything that can be named has any number of other names, that is to say, the usual case.  Of course we’d like to replace the multiplicity of signs with an organized system of canonical signs, one for each object that needs to be named, but reducing the redundancy too far, beyond what is necessary to eliminate the factor of “noise” in the language and thus clear up its effectively useless distractions, can destroy the utility of natural languages and bespoke formal systems, which are evolved to provide a ready means for expressing present situations, clear or not, and to describe ongoing conditions of experience in just the way they present themselves.  Within a fully fleshed out framework of language, moreover, the process of transforming the manifestations of a sign from its ordinary appearance to its canonical aspect is the whole problem of computation in a nutshell.

It’s a well‑known fact but an often forgotten truth that no one computes with numbers, but solely with numerals in respect of numbers, and numerals themselves are symbols.  Among other things, that renders all discussion of numeric versus symbolic computation a bit beside the point, since it’s only a question of what types of symbols are required for one’s immediate application or for one’s selection of ongoing objectives.  The numerals everyone knows best are just the canonical symbols, the standard signs or the normal forms for numbers, and the process of computation is a matter of getting from the obscure signs a situation impresses on us in the form of data to the indications of the situation’s character which can be rendered clear enough to motivate action.

Resources

• Cactus Language • Pragmatics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science