Is Peirce's reduction thesis gerrymandered?

TL;DR

This paper critiques traditional views of Peirce's reduction thesis, proposing a more invariant formulation that clarifies the role of triads and Thirdness in relational structures, revealing new phenomena with negation and disjunction.

Contribution

It introduces a robust, invariant formulation of Peirce's reduction thesis using triads, addressing gerrymandering concerns and elucidating the role of Thirdness in complex relations.

Findings

Invariant formulation of the reduction thesis using triads

Identification of new phenomena with negation and disjunction

A proposed numerical measure of Thirdness

Abstract

We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce's justification of the categories, and invite the charge of gerrymandering to make it come out as true. We then develop a more robust invariant formulation of the thesis by explicating the use of triads in any relational operations, which is immune to that charge. The explication also allows us to track how Thirdness enters the structure of higher order relations, and even propose a numerical measure of it. Our analysis reveals new conceptual phenomena when negation or disjunction are used to compound relations.