Frances to Cheerskep... The philosophic system that Peirce built is indeed a baroque structure full of neologisms, and few scholars have mastered it, but he did view his system as an evolutionary process that should grow and change. In his search for some clarity of all thought, Peirce did however reject the rigid claims of logical positivists. His realism tended to correct positivism by denying the existence of any perfect symbolic language. He proved with his theory of fallibilism that there can be no sign system without ambiguity and vagueness, in that all signs are prone to interpretation and all minds are subject to inference, so that there are limits to knowledge and science. His contention was that the use of exact mathematics and pure logics by humans must be moderated with phenomenal objects acting as signs, necessarily resulting in a degenerative or degraded version of objective mathematics and logics. Furthermore, linguistics was held by him to be a practical science, and not even needed for the theoretical sciences of semiotics or logics or mathematics; which of course is debatable, because it denies the need for any human involvement. The amazing thing he noted about the linguistic sign systems of verbal language is that human thinkers manage to communicate any meaningful information with each other at all.
Cheerskep partly wrote... Frances reports that Peirce wrote: "Philosophy has a peculiar need of a language distinct and detached from common speech, with a vocabulary so outlandish that loose thinkers shall not be tempted to borrow its words. ... The first rule of good taste in writing is to use words whose meanings will not be misunderstood; and if a reader does not know the meaning of the words, it is infinitely better that he should know he does not know it." This sounds good in principle, but it fails in practice. I know through personal experience, and Peirce himself is reported late in life to have lamented his style of writing because it made so much of his work "unreadable". The Peirce quote at the top continues: "This is particularly true in logic, which wholly consists, one might almost say, in exactitude of thought." So philosophers, "mathematical logicians", spent half a century or so devising several systems of symbolic logic. As Peirce anticipated, such systems had a virtue: Learning these strange new symbols was like learning a foreign language, a foreign alphabet. The student memorized the one and only notion the logicians wanted them to entertain when they saw a given symbol. This eliminated the problem of readers conjuring all sorts of varying notions because each individual had a head uniquely stocked with varying associations accumulated over lifetimes of varying experiences. But -- big, big fault: If the one-and-only notion was itself muddled, then ensuring that that notion was the one that arose each-and-every time the symbol was used was no virtue at all. And mathematical logic is riddled with ultimately indefensible notion.
