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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18524667 |
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Table of Contents:
- <p>This paper establishes a <em>generator–terminal</em> impossibility result for existence claims grounded in <em>universal properties</em>. It proves that no admissible system can generate or stabilize existence by appealing to universal mapping conditions without violating admissibility and standing conservation.</p> <p>The analysis exhausts categorical strategies that treat universal properties as existence guarantees. It shows that such moves presuppose illicit global quantification over morphisms, unrestricted comparison classes, or meta-level existence assumptions that cannot be licensed within the admissible interior. When made explicit, universal properties function as forbidden operators rather than legitimate foundations.</p> <p>The generator–terminal structure is decisive: if an object is not already admissibly fixed, there exists no admissible generator that can produce it via a universal property, nor any terminal state in which its existence becomes well-defined by universality alone. Universal-property-based repair and generation strategies are therefore terminally blocked.</p> <p>The result is strictly negative and non-constructive. The paper does not reject category theory as a tool, nor does it propose alternative existence principles. Its contribution is to demonstrate, by exhaustion, that universal properties cannot serve as generators of foundational legitimacy.</p> <p>This work forms part of the broader generator–terminal closure program, establishing hard limits on categorical abstraction and existence claims in admissible mathematics and physics.</p>