Pythagoras

This article brings to light a complex ‘dynamic of errors’ which Albert, in his Commentary on Aristotle’s Physica, uses to elaborate on the problem of the void. In his analysis, the Dominican philosopher addresses issues such as the void’s definition, its existence, or its relationship to motion, while stating his own position on the matter, which heavily relies on Aristotle. Albert argues that the errors made by certain pre-Socratic philosophers (in particular, Anaxagoras, Leucippus, Democritus, Xuthus, and Pythagoras) contributed to the (...) formation of flawed doctrines in the Middle Ages, such as that of Avempace (alongside whom Albert mistakenly places Avicenna). By identifying and exposing ‘errors’ Albert creates a valuable vantage point to address the problem of the void, whilst emphasizing the significant role played by pre-Socratic thinkers in the emergence and evolution of scientific discourse on the issue. (shrink)

La explicación tradicional del concepto de "vacío" (τò κενóν) en la filosofía antigua lo sitúa como una invención del atomismo de Demócrito y Leucipo o, incluso, del eleático Meliso de Samos. De esta manera se ocultan las profundas razones que pudieron llevar a la necesidad y surgimiento de un tal concepto, y aparece como si hubiera sido creado ex nihilo. En este artículo se pretende descubrir tanto el principio mitológico como el origen racional del concepto de "vacío" en la filosofía (...) presocrática, que lo sitúa como anterior a las historias contadas hasta ahora. Mediante dos columnas que intentan aprehender lo mismo desde puntos de vista distintos, se llegará a la conclusión de que el concepto de "vacío" fue definido en el inicio como diferencia y repetición. En contra de una determinada visión de la historia de la filosofía que ve a los "clásicos" y a los "modernos" como dos compartimentos separados e incluso enfrentados, en el curso de esta interpretación se establecerá un diálogo entre la doxografía presocrática y la filosofía contemporánea de Schelling, Hegel, Nietzsche, Heidegger, Schmitt, Irigaray, Derrida o Deleuze. (shrink)

This chapter pursues an understanding of what Cicero thought 'Italic' philosophy to be, and proceeds to develop a broader account of how Cicero's version compares with the surviving textual evidence and testimonia from the Hellenistic period of the philosophy of the 'Italic' philosophers, including the Lucanians 'Ocellus', 'Eccelus', and 'Aresas/Aesara', and the Rudian Ennius. Special focus is placed on their theories of cosmology, psychology, and law. Collocation of 'Italic' with 'Pythagorean' philosophy of this era aids in building a more comprehensive (...) view of what Hellenistic Pythagoreanism may have looked like. Uploaded here is the pre-publication version; please email me for the printed version. (shrink)

This paper attempts to demonstrate that the conviction about the harmony and order of the world was a fundamental metaphysical principle of the Pythagoreans. This harmony and order were primarily sought in the structures of arithmetics, yet following the discovery of incommensurable magnitudes (irrational numbers, as we now call them), the Pythagoreans began to see geometrical structure as a fundamental part of the world. On the example of the Pythagoreans’ metaphysics and science, the paper shows the mutual relations between metaphysics (...) and science. It demonstrates— on the one hand—the necessity of the first as a guide for the latter, and—on the other—how our scientific research can change its basic metaphysical principles when these are found to be inappropriate. The paper also tries to show the need for a realistic approach in our scientific research by means of the same example of the Pythagoreans, that is, the need to discern something which is below the surface appearance. (shrink)

This is the formal capstone of the Cosmological Codas of the Principia Cybernetica 2025. Contemporary physics remains haunted by the apparent arbitrariness of nature’s fundamental constants: the fine-structure constant α⁻¹ ≈ 137, the baryon asymmetry ∼10⁻⁹, the MOND acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s², and the dark energy fraction ∼68%. Standard models treat these as free parameters—numerological inputs without causal explanation. This final entry of the Cosmological Coda series replaces numerology with geometric necessity, demonstrating that all constants emerge (...) from a single structural principle: the universe is a tetrahedral lattice in continuous self-organization. We posit that the vacuum is not a smooth continuum but a dynamical, pixelated geometry undergoing perpetual “Jitterbug” collapse from vector equilibrium to tetrahedral stability. This living lattice imposes two competing imperatives: perfect packing at the irrational golden angle (137.508°, solving the Thomson Problem) and quantization into rational harmonic closure (137.036°). The geometric strain between these angles—approximately α—becomes the fundamental incompleteness that manifests as physical phenomena. From this strain we derive: α⁻¹ ≈ 137 as the crystallized golden angle—the resonant closure of infinite potential into finite structure; the baryon asymmetry ∼10⁻⁹ as the exponential residue of chiral filtration through the lattice; dark energy (Ω_Λ ≈ 68.17%) as the tensegrity recoil of the lattice, geometrically fixed as 1 − 1/π; the MOND scale a₀ = c H₀ / 2π as the critical acceleration where inertial wavelengths exceed the cosmic cavity circumference; and gravity as the entropic cost of maintaining geometric strain, unifying Landauer’s principle with Hawking temperature. The framework resolves long-standing anomalies without new particles or fields: dark matter effects arise from holographic inertia below a₀; the Hubble tension reflects varying lattice strain in voids versus structures; the hierarchy problem is the scale gap between Planckian pixels and hadronic standing waves. Time itself is discrete, emerging as the “click rate” of the Jitterbug at the Planck frequency. We predict precise convergence of Ω_Λ to 1 − 1/π, a geometric origin for Chern–Simons terms in electroweak knots, and laboratory signatures of lattice thermodynamics. The constants are not random; they are the immutable signature of a universe wrestling infinite potential into finite, stable form—a cosmic geometry writing its own laws. (shrink)