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 Duarte Oliveira Venancio

Rafael Duarte Oliveira Venancio

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 Duarte Oliveira, 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 Duarte Oliveira Venancio (Contact Author)

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

Av. Prof. Lucio Martins Rodrigues 443
São Paulo, São Paulo 05508-020
Brazil

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