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By “epistemology,” we mean the critique of the principles of the logic of scienti ¤c research, be it the logic of science or formal logic. As we know, semiotics is another name for logic, according to Peirce, a comprehensive, inferential logic, which is both experimental and formal. This may seem original, but it is not. For the Greeks (see ch. 7), logic was already a theory of inference from signs, and it still is today, as well for Wittgenstein as for Frege. The difference between the latter two and Peirce is that for Peirce logic is not only a theory of inference from signs, but an inference from signs through signs. The theories of Frege and Wittgenstein are dyadic and dualistic ; that of Peirce is triadic and dialectic. I shall try to describe the basic axioms of Peircean epistemology, compare its concepts with those of Frege and Wittgenstein, and draw its methodological implications in the context of the philosophy of science today. FREGE, WITTGENSTEIN, PEIRCE Frege, Wittgenstein, and Peirce are logicians and semioticians. 1. From the historical point of view, Frege can undoubtedly claim priority to Peirce. The ¤rst version of Frege’s propositional calculus dates back to 1879. Peirce’s ¤rst systematic expositions of “the algebra of logic” were written in 1880 and 1885. Peirce’s work on the tables of truth (1902) is prior to Wittgenstein’s (1922). - 13 Semeiotic and Epistemology peirce, frege, and wittgenstein All testing, all con¤rmation and discon¤rmation of a hypothesis takes place already within a system. And this system is not a more or less arbitrary and doubtful point of departure for all our arguments: no, it belongs to the essence of what we call an argument. The system is not so much the point of departure, as the element in which arguments have their life. —Wittgenstein (1969: §105) On Peirce’s side, three independent inventions must be noted: that of the quanti¤ers, that of the Sheffer-function (1880), named after its re-inventor (1921), which stipulates that all the Boolian operations can be reduced to the negation of the alternative disjunction “neither—, nor—”; and that of trivalent logic (1909), ten years before Lukasievicz (Deledalle 1990: 59). 2. The pragmatistic tone of Wittgenstein’s work, from the Tractatus logicophilosophicus onward, is surprising. The question may be asked:did Wittgenstein know Peirce’s work? In fact he did, but this does not mean that he read all that Peirce wrote; far from it. He came across two of the main ideas of Peirce. One was through Frank P. Ramsey, co-translator with Charles K. Ogden, of the Tractatus , the same Ogden who, with I. A. Richards, was to give a certain publicity to Peirce’s semiotics in The Meaning of Meaning (1923). This theory is epistemological , properly speaking, and we shall come back to it later on.The other, which also seems to have reached Wittgenstein through Ramsey, is pragmatic: a critique of Cartesian doubt and a de¤nition of meaning by action. Peirce’s theory can be read in “The Fixation of Belief” (1877) and “How to Make Our Ideas Clear” (1878). The de¤nition of meaning by action can be read everywhere in Wittgenstein ’s writings after 1933–1934, from the Blue and Brown Books to the Investigations , and the question of doubt is studied in great detail in On Certainty, which was the last book Wittgenstein was to write (see ch. 8). THE AXIOMS OF PEIRCE’S EPISTEMOLOGY The basic theses of Peircean epistemology can be stated in the three following propositions: 1. A sign or representamen is a First which cannot furnish acquaintance with nor recognition of its object; 2. A law (a Third) without an occurrence (a Second) is empty;an occurrence without a law is blind; 3. A proposition is the individuation of a “general” (a Third) by an index (a Second). a. The ¤rst Peircean thesis is fundamental: it maintains that the sign or representamen is not the copy of its object. The sign represents its object as an ambassador represents his country in a foreign country. If we develop the metaphor , it is obvious that this ambassador has been appointed by someone having the power to do so. The object thus “determines” the sign, in a sense of the word, but without leaving its mark on it. The nature of the sign-representamen appears clearly in Peirce’s de¤nition of “percept.” Can the “percept” be identi¤ed with the “sign-representamen”? One...

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