Peirce's Logic

Charles Sanders Peirce (1839-1914) was an accomplished scientist, philosopher, and mathematician, who considered himself 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 upon, or draws its principles from, 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), namely 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 areas.