Infinitesimal Gunk

TL;DR

This paper introduces the concept of Infinitesimal Gunk, a novel view of space structure using nonstandard analysis, addressing previous philosophical objections and offering a richer measure theory.

Contribution

It proposes a new model of space with infinitesimal regions, providing solutions to prior inconsistency issues and improving upon existing gunky space theories.

Findings

Resolves inconsistency arguments against gunk using nonstandard analysis.

Avoids regions with no interior unlike some previous models.

Offers a more comprehensive measure theory than Russell's approach.

Abstract

In this paper, I advance an original view of the structure of space called \textit{Infinitesimal Gunk}. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson's (1966) nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius (2008) and Russell (2008), which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors suggested. Unlike Arntzenius's proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell's proposal and does not retreat to mere finite additivity.