Mathematics, Semiotics, And Pragmatism

This dissertation chooses to reconstruct Peirce's system of philosophy from his distinctive conception of logic and clarify its much relevance to contemporary philosophical inquiry, rather than limiting Peirce's complicated and ingenious philosophical thoughts to the fashionable pragmatism. In Peirce's view, Logic conceived as Semiotics belongs to philosophy and not mathematics. Comparing with contemporary "mathematical logic", Peirce developed the first-order logic independent of Frege and Russell, and had a much deeper concern and broader vision of modern logic than them. The aim of Peirce's much work in revising Boolean algebra and improving his algebra of relation was the analysis of reasoning and thought, which was the business of logic and not of mathematics. In Peirce's natural classification of sciences, logic was a branch of Cenoscopy, a kind of positive science in non-Comtean sense. Logic studies the matter of ought-to, but it has to rest upon some common experience and general facts, not like mathematics irrelevant of any experiential reality. Basing on his comprehensive studies in history of logic, Peirce argued that logic in modern time should play the same role of the Method of methods as in ancient and medieval worlds, so that his grand logic science equaling in scope to his semiotics. Thought is in sign, and one reasons only by the vehicle of sign. So, semiotics, the inquiry into all forms of signs and their functions, is the analysis of the nature of reasoning. Peirce's semiotics, as a division of philosophy, lies after phenomenology and before metaphysics. As one of the normative sciences, it in itself has three departments,1st, Speculative Grammar, including the epistemology getting rid of psychologism; 2nd, Critic, including the logic called as usual; 3rd, Methodeutic, including lots of rhetoric strategies of advancing the inquiry of truth. Peircean pragmatism is the scientific method to make our ideas more clear, and it is a logical maxim in the semiotics. Peirce thought of pragmatism as the logic of abduction, and set forth a logic of scientific inquiry including not only deductive reasoning but also abductive reasoning and inductive reasoning, which could be used to solve many practical problems in real human life.Just as there is a philosophical psychology and a philosophical anthropology, there is a philosophical logic. As seen by Peirce, logic is not "mathematical logic" taught in today's textbooks, nor is any special arts. Different from other contemporary logicians, Peirce's concerns with reasoning were much more general and inclusive. Just as analytic philosophy is not merely another sect in philosophy circle but stands as a new approach of philosophical inquiry, Peirce's philosophical logic did not annul any successful logical studies but tried to renew a systematic vision which had been neglected since modern times. In the context of the expanded logic, the great difference between Peirce and other pragmatists consists in that Peircean pragmatism is essentially synechism relating to his logic of continuity, in which scholastic realism, contrite fallibilism, objective idealism, and mild naturalism were interlocked closely. In the whole, the logic prospect designed by Peirce one hundred years ago was more consistent with the philosophical attitudes in the late 20th century and the 21st century than those in the 19th century and the early 20th century. It is evolutionary but not revolutionary, continuous but not dichotomous; it commits to diversity but not relativism, objectivity but not foundationalism.