Theoremizing Yablo's Paradox
Logic
2024-04-17 v1 Information Theory
Logic in Computer Science
math.IT
Abstract
To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic.
Cite
@article{arxiv.1406.0134,
title = {Theoremizing Yablo's Paradox},
author = {Ahmad Karimi and Saeed Salehi},
journal= {arXiv preprint arXiv:1406.0134},
year = {2024}
}
Comments
Preprint; all comments/suggestions are most welcome!