Set Theory Fictionalizes the Object Before It Explodes

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Authors: Dedong Zhan
Cited by: 2

Abstract

This paper argues that the deepest failure of set theory does not begin with paradox, power set growth, or hierarchy, but earlier, at the moment an object is fictionally posited and then treated as if it were already a completed bearer of predicates. Once that license is granted, totalization is no longer a neutral formal move. It becomes a structural overreach. What later appears as explosion is not an accidental defect of infinity, but the necessary consequence of allowing arbitrary predicates to operate over a fictionalized object as though a whole had already been legitimately secured. The central claim is simple: static writability is not dynamic completeness. Set theory can write the whole, name the whole, and manipulate the whole in symbolic form, yet none of this entitles it to genuine whole-closure. The problem is therefore not a missing technical patch, but a prior defect in the object-license chain. Power set expansion, cumulative hierarchy, self-reference, and infinite descent are not separate failures. They are different readouts of the same root permission. ZFC does not cure this source defect; it only acts as a local brake. The deeper verdict is that object fiction, once granted whole-forming license, leads mechanically to explosion.

Fields of Study & Subjects

Philosophy and Theoretical Science Philosophy and History of Science Qualitative Comparative Analysis Research

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
10 March 2026
Document type
Preprint