We all love natural languages, our native tongues, but each one has a mind of its own and a habit of saying both more and less and something other than the meanings we intend at the moment of utterance. So maybe it’s a love-hate relationship, or at least a Liebeskampf.
Whether we are endowed with an inborn faculty for language, even a genetic blueprint for selected species of languages on a par with our naturally evolved motor and sense organs, or whether we acquire our initial languages from scratch, every natural language worth its salt preserves a rich heritage of biological and cultural meanings its users will assimilate, consciously or otherwise. I would not say “resistance is futile” but habits of thought built into our first and second natures demand persistent habits of critical reflection to break.
We do use natural language paraphrases to “express the meaning of [a logical formula] using different words, especially to achieve greater clarity” and up to a point they serve that end. But there’s a catch. If a natural language paraphrase could express the precise meaning of a logical formula with greater clarity, what would be the use of the formula?
Well, that’s the beginning of a post I started on the spectrum of formality from form to formal object to formula to paraphrase. But I decided to let it simmer for another day. Now that we have a workbench stocked with concrete examples of triadic relations and sign relations we might as well use them to illustrate the abstractions while keeping our feet on more solid ground.
I’ll turn to that task next.
- Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, pp. 269–284. Abstract. Online.
- 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.