Two Fuzzy Logic Programming Paradoxes Imply Continuum Hypothesis="False" & Axiom of Choice="False" Imply ZFC is Inconsistent

TL;DR

The paper presents two paradoxes in fuzzy logic programming that lead to the conclusion that the Continuum Hypothesis and Axiom of Choice are false, implying ZFC set theory is inconsistent.

Contribution

It introduces two paradoxes in fuzzy logic programming that challenge foundational set theory assumptions and demonstrate inconsistency in ZFC.

Findings

CH is false

Axiom of Choice is false

ZFC is inconsistent

Abstract

Two different paradoxes of the fuzzy logic programming system of [29] are presented. The first paradox is due to two distinct (contradictory) truth values for every ground atom of FLP, one is syntactical, the other is semantical. The second paradox concerns the cardinality of the valid FLP formulas which is found to have contradictory values: both $\aleph_0$ the cardinality of the natural numbers, and $c$, the cardinality of the continuum. The result is that CH="False" and Axiom of Choice="False". Hence, ZFC is inconsistent.