On Chwistek's criticism of Principia

TL;DR

This paper critically analyzes Chwistek's claim about Richard's paradox in Principia, demonstrating that the original proof is flawed due to incorrect logical steps and substitution rules.

Contribution

It clarifies the logical validity of Chwistek's criticism and corrects misconceptions about the system of Principia's handling of classes and definitions.

Findings

Chwistek's proof relies on incorrect elimination of a defined term.

Faulty substitution rule is used in the criticized proof.

The demonstration does not hold within Principia's logical framework.

Abstract

This paper examines Chwistek's claim that with Principia's definition of a class "Richard's paradox can be formulated". It is shown that the demonstration fails since it requires an incorrect elimination of a defined term and use of a faulty substitution rule, neither of which form part of the system of Principia.