Dismantling Infinity as a Metaphysical Category Error: With an Analog–Digital Reconstruction of 0, 1, and Unbounded Refinement
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901577245130752 |
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| author | Schutheis, Andreas |
| author_facet | Schutheis, Andreas |
| contents | <p>Modern mathematics and physics insist that the symbol ∞ is “not a number,” yet</p> <p>routinely assign it numerical behavior. Inequalities such as 0 < 1 < ∞ and 0 >−1 ></p> <p>−∞, together with comparisons like ∞> −∞, only make sense if ∞is treated as a</p> <p>member of an ordered magnitude space. The result is a category error that quietly</p> <p>imports metaphysical assumptions into ostensibly quantitative form.</p> <p> </p> <p>This paper dismantles that usage by returning to the ontological primitives reconstructed</p> <p>in Schultheis (2025).<span>1 </span>There, “something” is presence (represented by 1), “nothing” is</p> <p>conceptual absence (represented by 0, with no physical instantiation), and infinity is</p> <p>not a magnitude but unbounded refinement of presence. Here, those assignments are</p> <p>pushed further: infinity is shown to be an analog descriptor of continuous refinability,</p> <p>not a digital endpoint. The correct discrete representative of the maximal analog</p> <p>domain is 1, not ∞.</p> <p> </p> <p>The argument proceeds on three fronts. First, it clarifies endlessness as an inherently</p> <p>analog condition and shows why the numerical hierarchy 0 < 1 < ∞is conceptually</p> <p>illicit. Second, it exposes a structural contradiction: mathematics declares infinity</p> <p>non-numerical while using it as though it were numerical, and physics inherits this</p> <p>contradiction as singularities, divergences, and “infinite” densities or durations. Third,</p> <p>it traces the historical roots of actual infinity in the theological and cosmological</p> <p>motivations of Kronecker, Cantor, and early set theory, and examines the academic</p> <p>reflex to label such critiques as “intuitionist” or “constructivist” rather than engage</p> <p>their substance. The conclusion is blunt: the universe exhibits endless analog continuity,</p> <p>but it contains no infinite magnitudes. Unity, not infinity, is the correct digital</p> <p>representation of maximal presence.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17922034 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dismantling Infinity as a Metaphysical Category Error: With an Analog–Digital Reconstruction of 0, 1, and Unbounded Refinement Schutheis, Andreas infinity foundations of physics ontology limits calculus Analog vs discrete category error philosophy of mathematics philosophy of physics singularities endless symmetry principle <p>Modern mathematics and physics insist that the symbol ∞ is “not a number,” yet</p> <p>routinely assign it numerical behavior. Inequalities such as 0 < 1 < ∞ and 0 >−1 ></p> <p>−∞, together with comparisons like ∞> −∞, only make sense if ∞is treated as a</p> <p>member of an ordered magnitude space. The result is a category error that quietly</p> <p>imports metaphysical assumptions into ostensibly quantitative form.</p> <p> </p> <p>This paper dismantles that usage by returning to the ontological primitives reconstructed</p> <p>in Schultheis (2025).<span>1 </span>There, “something” is presence (represented by 1), “nothing” is</p> <p>conceptual absence (represented by 0, with no physical instantiation), and infinity is</p> <p>not a magnitude but unbounded refinement of presence. Here, those assignments are</p> <p>pushed further: infinity is shown to be an analog descriptor of continuous refinability,</p> <p>not a digital endpoint. The correct discrete representative of the maximal analog</p> <p>domain is 1, not ∞.</p> <p> </p> <p>The argument proceeds on three fronts. First, it clarifies endlessness as an inherently</p> <p>analog condition and shows why the numerical hierarchy 0 < 1 < ∞is conceptually</p> <p>illicit. Second, it exposes a structural contradiction: mathematics declares infinity</p> <p>non-numerical while using it as though it were numerical, and physics inherits this</p> <p>contradiction as singularities, divergences, and “infinite” densities or durations. Third,</p> <p>it traces the historical roots of actual infinity in the theological and cosmological</p> <p>motivations of Kronecker, Cantor, and early set theory, and examines the academic</p> <p>reflex to label such critiques as “intuitionist” or “constructivist” rather than engage</p> <p>their substance. The conclusion is blunt: the universe exhibits endless analog continuity,</p> <p>but it contains no infinite magnitudes. Unity, not infinity, is the correct digital</p> <p>representation of maximal presence.</p> |
| title | Dismantling Infinity as a Metaphysical Category Error: With an Analog–Digital Reconstruction of 0, 1, and Unbounded Refinement |
| topic | infinity foundations of physics ontology limits calculus Analog vs discrete category error philosophy of mathematics philosophy of physics singularities endless symmetry principle |
| url | https://doi.org/10.5281/zenodo.17922034 |