Selections from C.S. Peirce, “New Elements (Καινὰ Στοιχεῖα)”
Editors’ Headnote from The Essential Peirce, Volume 2
MS 517. [First published in NEM 4:235–63. This document was most probably written in early 1904, as a preface to an intended book on the foundations of mathematics.] Peirce begins with a discussion of “the Euclidean style” he planned to follow in his book. Euclid’s Elements presuppose an understanding of the logical structure of mathematics (geometry) that Peirce, in his “New Elements,” wants to explicate. Having recently concluded that the scope of logic should be extended to include all of semiotics, Peirce now wants to work out the semiotic principles that he hopes will shed light on the most abstract science. Building on the work in his 1903 “Syllabus,” Peirce deepens his semiotic theory by linking it with the mathematical conceptions of “degrees of degeneracy.” Symbols are taken to be non-degenerate, genuine, signs, while indices are signs degenerate in the first degree and icons are degenerate in the second degree. Symbols must always involve both indices and icons, and indices must always involve icons. Peirce limits his attention to this trichotomy but carries his discussion deeply into epistemology and metaphysics, making such arresting claims as that “representations have power to cause real facts” and that “there can be no reality which has not the life of a symbol.” Max Fisch described this paper as Peirce’s “best statement so far of his general theory of signs.” (EP 2, 300).
Peirce Edition Project (eds., 1998), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington and Indianapolis, IN. Cited as EP 2.