Extending Cantor Paradox

TL;DR

This paper explores foundational issues in set theory by extending Cantor's paradox, questioning the consistency of actual infinity, and analyzing self-reference through syntactic and semantic critique, impacting Godel's theorem interpretations.

Contribution

It introduces an extension of Cantor's paradox suggesting inconsistency of actual infinity and offers a new critique approach based on w-order and self-reference analysis.

Findings

Proposes an extension of Cantor's paradox challenging actual infinity.

Introduces a critique method using w-order to analyze set-theoretic paradoxes.

Examines the impact of self-reference on Godel's incompleteness theorem interpretations.

Abstract

The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to be an exhaustible source of paradoxes and contradictions. It seems therefore legitimate to pose some questions concerning their formal consistency. This is just the objective of this paper. Starting from an extension of Cantor's paradox that suggests the inconsistency of the actual infinity, the paper makes a short review of its controversial history and proposes a new way of criticism based on w-order. Self-reference is also examined from a critique perspective which includes syntactic and semantic considerations. The critique affects the formal sentence involved in Godel's first incompleteness theorem and its ordinary language interpretation.