Peirce on the nature of logic

Charles Sanders Peirce (1839-1914) was an accomplished scientist, philosopher, and mathematician, who considered himself to be primarily a logician. His contributions to the development of modern logic at the turn of the 20th century were colossal, original and influential. Formal, or deductive, logic was just one of the branches in which he exercized his logical and analytical talent. His work developed upon Boole’s algebra of logic and De Morgan’s logic of relations. He worked on the algebra of relatives (1870-1885), the theory of quantification (1883-1885), graphical or diagrammatic logic (1896-1911), trivalent logic (1909), higher-order and modal logics. He also contributed significantly to the theory and methodology of induction, and discovered a third kind of reasoning, different from both deduction and induction, which he called abduction or retroduction, and which he identified with the logic of scientific discovery. Philosophically, logic became for Peirce a broad discipline with internal divisions and external architectonic relations to other parts of scientific inquiry. Logic depends on mathematics, phaneroscopy (= phenomenology), and ethics, while metaphysics and psychology depend upon logic. One of the most important characters of Peirce’s late logical thought is that logic becomes coextensive with semeiotic (his preferred spelling), the theory of signs. Peirce divides logic, when conceived as semeiotic, into (i) speculative grammar, the preliminary analysis, definition and classification of those signs that can be used by a scientific intelligence; (ii) critical logic, the study of the validity and justification of each kind of reasoning; and (iii) methodeutic or speculative rhetoric, the theory of methods. Peirce’s logical investigations cover all these three departments.

Newsletter of the Society for the Advancement of American Philosophy, 1998

Press, 1997. xii plus 653 pp. $49.95. On September 10, 1989 philosophers, semioticians, logicians, and others celebrated Peirce's birthday with a Charles S. Peirce Sesquicentennial International Congress, with 26 countries represented by over 450 scholars. One o f the foci of the Congress was a "principal logic symposium," which provided technical papers on Peirce's contributions to logic and his impact on contemporary logic. This long-awaited edition o f that symposium has been expanded beyond the symposium papers, to include the philosophy o f logic. In the editors' words: "We think the result is the most comprehensive account and exposition o f Peirce's contributions to technical logic."

Cognitio: Revista de Filosofia, 2021

In her book Deviant Logic (1974), Susan Haack argued for a “pragmatist” conception of logic. This conception holds that, (i) logic is a theory on a par with other scientific theories, differing only from such theories by its degree of generality and (ii) the choice of a particular logic is to be made based on pragmatist principles, namely, economy, coherence, and simplicity. This view was contrasted, in this book, with an “absolutist” view of logic, according to which logical laws are necessary and immune to revision. Two decades later, however, Haack acknowledged, in the Introduction to an enlarged version of the same book, that she would not approach the question of the revisability of logic in the same way she did earlier. What was missing in her first book was a distinction between the question of the necessity of the laws of logic and the question of our fallibility in recognizing which are the true laws of logic and what structures are essential to representation. She also ack...

2016

describes Euclid’s procedure in proving theorems. Euclid first presents his theorem in general terms and then translates it into singular terms. Peirce pays attention to the fact that the generality of the statement is not lost by that move. The next step is construction, which is followed by demonstration. Finally the ergo-sentence repeats the original general proposition. Peirce lays much emphasis on the distinction between corollarial and theorematic reasoning in geometry. He takes an argument to be corollarial if no auxiliary construction is needed. For Peirce, construction is “the principal theoric step ” of the demonstration. Peirce also stresses that it is the observation of diagrams that is essential to all reasoning and that even if no auxiliary constructions are made, there is always the step from a general to a singular statement in deductive reasoning; that means introducing a kind of diagram to reasoning. This paper seeks to argue for two theses. One is that the way of ...

Modern Logic, 1990

Notre Dame Journal of Formal Logic, 1979

1996

This paper * has two separate aims, with obvious links between them. First, to present Charles S. Peirce and the pragmatist movement in a historical framework which stresses the close connections of pragmatism with the mainstream of philosophy; second, to deal with a particular controversial issue, that of the supposed logicistic orientation of Peirce's work.

This paper is a contribution to the long-standing debate over the coherence of Charles Sanders Peirce’s overall system of philosophy. It approaches that issue through the lens of a contemporary debate over the notion of metaphysical grounding, or more broadly, the nature of metaphysical explanation, employing the laws of logic as a case study. The central question concerns how we can take seriously what we shall call Peirce’s Rule—that nothing can be admitted to be absolutely inexplicable—without being vulnerable to a vicious regress or equally vicious circularity. I first argue that in Peirce’s early work he offers a quietist conception of grounding that provides a persuasive and ground-breaking answer to this central question. I then raise a familiar concern, that in Peirce’s later work we find hints of a more metaphysical conception of grounding that seems unable to answer that question and is thus inconsistent with his earlier work. The paper ends with a speculative interpretation of Peirce’s approach to metaphysics and its possible role in grounding logical principles.

Historia Mathematica, 1986

Signs of logic , 2006

ÖÐ × Ë ÒØ Ó Ë Ò Ö× È Ö (b. 1839), son of the mathematician Benjamin P., brought up in a circle of physicists and naturalists, and specially educated as a chemist, derived his first introduction to philosophy from the K.d.R.V. [Immanuel Kant's Critique of Pure Reason, published in 1781] and other celebrated German works, and only later made acquaintance with English, Greek, and Scholastic philosophy. Accepting unreservedly Kant's opinion that the metaphysical conceptions are merely the logical conceptions differently Kant's table of functions of judgment as culpably superficial.