Infinity is Not a Size

TL;DR

This paper introduces a dynamic model theory that replaces completed infinities with potential infinities and uses a finitistic interpretation to avoid classical paradoxes associated with actual infinities.

Contribution

It proposes a novel approach to infinity by avoiding completed infinities, providing a paradox-free framework that does not rely on translating formulae.

Findings

Avoids classical paradoxes of infinity

Replaces actual infinite sets with potential ones

Uses finitistic interpretation of quantifiers

Abstract

We present a dynamic model theory that avoids the paradoxes stemming from completed infinities, but does not require any translation of formulae. The main adoption is the replacement of an actual infinite carrier set by a potential infinite one, and by a finitistic interpretation of the universal quantifier.