C. S. Peirce and the Square Root of Minus One: Quaternions and a Complex Approach to Classes of Signs and Categorical Degeneration

17 Pages Posted: 21 Feb 2017

See all articles by Rafael Venancio

Rafael Venancio

Universidade Federal de Uberlândia; University of São Paulo (USP) - Faculty of Comunications and Arts

Date Written: February 18, 2017

Abstract

The beginning for C. S. Peirce was the reduction of the traditional categories in a list composed of a fundamental triad: quality, respect and representation. Thus, these three would be named as Firstness, Secondness and Thirdness, as well given the ability to degeneration. Here we show how this degeneration categorical is related to mathematical revolution which Peirce family, especially his father Benjamin Peirce, took part: the advent of quaternions by William Rowan Hamilton, a number system that extends the complex numbers, i.e. those numbers which consists of an imaginary unit built by the square root of minus one. This is a debate that can, and should, have contributions that take into account the role that mathematical analysis and linear algebra had in C. S. Peirce’s past.

Keywords: Philosophy of Mathematics, Semiotics, Quaternions

Suggested Citation

Venancio, Rafael, C. S. Peirce and the Square Root of Minus One: Quaternions and a Complex Approach to Classes of Signs and Categorical Degeneration (February 18, 2017). Available at SSRN: https://ssrn.com/abstract=2919967 or http://dx.doi.org/10.2139/ssrn.2919967

Rafael Venancio (Contact Author)

Universidade Federal de Uberlândia ( email )

Av. João Naves de Avila, 2121
Uberlândia, Minas Gerais 38400-902
Brazil

HOME PAGE: http://www.researchgate.net/profile/Rafael_Duarte_Oliveira_Venancio

University of São Paulo (USP) - Faculty of Comunications and Arts ( email )

São Paulo, 05508-070
Brazil

Register to save articles to
your library

Register

Paper statistics

Downloads
46
Abstract Views
254
PlumX Metrics