Hypercomputation, Frege, Deleuze: Solving Thomson's Lamp

TL;DR

This paper offers a novel solution to Thomson's Lamp Paradox by integrating insights from philosophy, mathematics, and computer science, clarifying the paradox through transfinite ordinals and logic analysis.

Contribution

It provides the first known resolution to the Thomson Lamp Paradox and introduces a framework for classifying supertasks using transfinite and logical analysis.

Findings

Resolved the Thomson Lamp Paradox using transfinite ordinals

Identified the paradox between metrical and ordinal limits

Proposed a classification scheme for supertasks

Abstract

We present the first known solution to the original supertask, the Thomson Lamp Paradox. We also offer preliminary resources for classifying computational complexity of various supertasks. In so doing we consider a newly apparent paradox between the metrical limit and the ordinal limit. We use this distinction between the metrical and ordinal limits to explain the shortcomings both of Thomson's original formulation of the Lamp Paradox and Benacerraf's consequent critique. We resolve this paradox through a careful consideration of transfinite ordinals and locate its ambiguity as inherent to the identity relation under logic with a close reading of Frege's Begriffsschrift. With this close reading in hand we expose how the identity relation is counter-intuitively polyvalent and, with supertasks, how the logico-mathematical field operates on the basis of Deleuzian point-folds. Our results combine resources from philosophy, mathematics, and computer science to ground the field of hypercomputation for logically rigorous study.