Guardat en:
| Autor principal: | |
|---|---|
| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2026
|
| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.20158755 |
| Etiquetes: |
Afegir etiqueta
Sense etiquetes, Sigues el primer a etiquetar aquest registre!
|
Taula de continguts:
- <p>The representability reconstruction of Anselm's ontological argument turns existence into a priced universal-property claim. The formal question is not whether existence belongs to a maximal concept, but whether a coherent field of manifestations is represented by a universal source; the move from manifestation to source requires explicit smallness, solution-set, continuity, accessibility, descent, or geometric hypotheses. Directly stipulating those hypotheses risks making the ontological move look locally tailored. The central thesis of this paper is that general reflection principles, and especially Vopěnka-style reflection, offer a more principled test: they ask which parts of the representability price can be paid at the level of the ambient universe.</p> <p class="p1">Vopěnka's Principle is the guiding test case because its standard categorical consequences speak directly to those costs. In locally presentable and accessible settings, Vopěnka-level reflection can turn many proper-class-looking obstruction problems into set-generated, accessible, or reflective ones, provided the relevant functorial and ambient hypotheses are already in place. The resulting framework assigns to a weakened pro, Ind, local, stacky, or Tate horizon a target-indexed price region, a theorem-backed approximation of that region, and, when a least sufficient principle exists, a reflection price. These are calibration devices, not new ontological proofs. Large-cardinal reflection does not create representability ex nihilo, and no reflection principle erases ordinary categorical obstructions or supplies a source without compatible structure.</p> <p>The philosophical payoff is a collapse spectrum. Reflection may certify some tame horizons at object, stack, or horizon level; others remain unpaid relative to available theorems. Even successful certification is attribute-conservative: it can add an ambient sourcehood certificate without changing truth in the old fibrewise language of manifestations. Thus Vopěnka-style reflection does not vindicate the classical Anselmian inference. It shifts the debate from predicate-concept analysis to the admissible reflection principles by which sourcehood may be certified. In compressed form: <em>ineffability is the residue left after the reflection price is paid</em>.</p>