Chapter 18: Internal Sets and Boundedness

What does it mean to exist inside τ? This chapter introduces the distinction between internal and external constructions, formulates NF-addressability as the criterion for ontic standing, and deploys the ZFC-as-VM thesis from Book III: orthodox set theory functions as a virtual machine running on τ-hardware. The resulting ontic/virtual distinction dissolves most metaphysical puzzles about mathematical existence. Unbounded constructions—actual infinities, proper classes, uncomputable objects—are virtual: useful for reasoning but not part of τ’s internal ontology.