THE INVERTED FRACTAL UNIVERSE OF BLAIR D. MACDONALD: a critical–propositional analysis in confrontation with the modal axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of the Theory of Objectivity

This article presents a critical–propositional analysis of Blair D. Macdonald’s paper Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures (2024), in dialogue with the Theory of Objectivity (TO). Macdonald proposes that the universe may be understood not merely as containing fractal structures at certain scales, but as a growing inverted fractal whose internal observation can reproduce features associated with contemporary cosmology, including accelerated expansion, the Hubble–Lemaître law, large-scale smoothness, and structural differentiation across cosmic scales. The present study examines this hypothesis in confrontation with the modal axioms of the Theory of Objectivity, especially the axioms of boundary, infinity, recursive composition, observation, and transcendent informational substance. It also articulates Macdonald’s model with the phenomenic elements of TO, the Expansive and Reductive Inducer Effects, the cosmogonic theorem, and the cosmological Eras of the Theory of Objectivity. Particular attention is given to the possibility of reading fractal geometry as a later geometric-operational manifestation of recursive composition and boundary multiplication, rather than as an ultimate ontological foundation of the universe. The analysis argues that Macdonald’s inverted fractal model offers a strong field of dialogue with TO, especially because of its emphasis on recursion, internal observation, structured expansion, and the critique of absolute homogeneity and isotropy. However, the article also identifies important tensions: the absence of a modal ontology of Nothingness, the lack of a theory of the element, the absence of triadic observation, and the need for a deeper informational/radiative interpretation of transcendence. In TO, the transcendent element is interpreted as the knowledge or information produced in atomic relations, equivalent to atomic radiations. This analytical text received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Blair D. Macdonald; inverted fractal; fractal cosmology; modal ontology; cosmic expansion; Hubble–Lemaître law; cosmological principle; boundary; recursive composition; Inducer Effects; cosmogonic theorem; cosmological Eras; informational transcendence; atomic radiation; ChatGPT.