Questions Concerning Certain Faculties Claimed For Signs
One thing I always say at these junctures is that people really ought to take Peirce’s advice and study his logic of relative terms and its relation to what most mathematics and computer science folks these days would call the mathematical theory of relations. Personally I find his 1870 Logic of Relatives very instructive, partly because he gives such concrete and simple examples of every abstract abstrusity and partly because he maintains a healthy balance between the extensional and intensional views of things, drawing on both our empiricist and rationalist ways of thinking.
Thereby hangs another hang up, a problem people often have with understanding Peirce’s logic and semiotics. We have what might be called diverse “cognitive styles” or “intellectual inclinations” that range or swing between the above two poles. I doubt if there’s anything like pure types in the human arena, but thinkers do tend to lean in one direction or the other, at least, at any given moment. As a rule, though, we are almost always operating at two different levels of abstraction, whether we are aware of it or not, and our task is to get better at doing that, through increased awareness of how thought works. There is the level of intension, or rational concepts, and there is the level of extension, or empirical cases.
To be continued …