Vítor Costa

ABSTRACT This philosophical article addresses the modeling of consensus and dissent in normative scientific communities, employing multi-agent epistemic logic. Grounded in a non-normal system with monotonic structure, aligned with Newton da Costa’s concept of “weak scientific justification,” the study defines different forms of scientific knowledge, emphasizing mutual, distributed, and common knowledge. By exploring normative groups, where general knowledge derives from specialized subgroups, the article examines the notions of scientific consensus and dissent. Specifically, dissent occurs when scientific knowledge among subgroups is in disagreement, while consensus emerges through the convergence of these knowledges. The formalism of multi-agent epistemic logic is demonstrated to capture this dichotomy without contradictions in distributed knowledge, providing a robust foundation for understanding the complex dynamics within normative scientific communities.

This work presents a structural gravitational model based on the relationship between gravity — which compacts formats — and energy. The model introduces three fundamental aspects of gravity: internal gravitational tension, structural global gravity, and observable external gravity. Gravitational tension is defined by the ratio between energy and structural volume: while global gravity and external gravity are described respectively by: and A comparative analysis of elementary particles, atoms, and molecules reveals two distinct structural regimes. In the first regime — corresponding to fundamental particles — structural compactness dominates gravitational behaviour. The proton emerges as a critical intermediate structure, characterised by extremely high gravitational tension and an abrupt increase in both global and external gravity. In the second regime — corresponding to atomic and molecular structures — a strong dilution of gravitational tension is observed due to structural volumetric growth. Stability becomes predominantly associated with geometric complementarity of formats and optimisation of energy distribution. The model suggests that gravity may be interpreted as an intrinsic property of the structural organisation of space‑time that generates energy, emerging at different scales under distinct forms of cohesion and gravitational projection.

My structural gravitational model is here applied to neutron stars and black holes. The calculations show that neutron stars reach gravitational tensions close to those observed at the hadronic scale, suggesting the existence of a common regime of structural compactification. The transition between neutron stars and black holes appears as a continuation of the gravitational compactification process. Since a black hole contains both extreme gravity in its core and enormous but dispersed internal gravity throughout its interior, th e fundamental discontinuity occurring at the level of the cores does not become observable. In fact, the analysis reveals that the exclusive use of the Schwarzschild radius leads to a progressive decrease in the average gravitational tension of more massive black holes, since the associated volume grows faster than the “confined energy”. To overcome this conceptual limitation, a distinction is introduced between an observational gravitational radius and a hypothetical energetic structural radius. The first describes observable external gravity, while the second attempts to attenuate the heterogeneity of internal gravity in black holes, which generates the discrepancy in observations. When calculations are performed using an energetic structural radius smaller than the Schwarzschild radius, significantly higher values are obtained for gravitational tension and global gravity, consistent with the hypothesis of extreme compactification of black‑hole cores. In this framework, black holes represent states of high gravitational re‑compactification, approaching the structural conditions of primordial energy. The model thus suggests the existence of two complementary levels of description for black holes: – an external level, associated with observable gravity and described by the Schwarzschild radius; – an internal level, associated with the energetic structure that sustains the object. This distinction establishes a link between the physics of compact objects, extreme gravity, and the states of maximum energetic compactification that characterise the origin and the fate of the universe.

This article presents the mathematical formulation that supports the unified vision developed throughout this series, in which gravity is the structuring principle of all existence — from the pre– Big Bang state to elementary particles, atoms, molecules, and extreme astrophysical objects. Here, gravity is no longer understood merely as the external space‑time curvature described by Einstein, but as the internal geometric expression of the formats that generate energy — the true origin of structural cohesion and motion. In the primordial state preceding the Big Bang, all the energy of the universe existed in a unified format of maximum gravitational compactness. The absolute homogeneity of these simple formats prevented any evolution: there was no complementarity, no reorganization, no time. Gravitational tension reached its maximum possible value, expressed by the unit: 1=E/V The Big Bang did not create energy; it broke this uniformity, allowing the emergence of new formats, new complementarities, and new gravitational tensions. With the appearance of elementary particles, energy began to be measured by E=mc 2 and the formats acquired their own volumes, enabling the structural reorganization that drives expansion. Global gravity — resulting from the aggregation of formats and their respective gravitational fields — intensifies with structural complexity, while external gravity emerges as the curvature that extends beyond the format and becomes observable. The distinction between gravitational tension, global gravity, and external gravity allows us to understand very different physical regimes: – in fundamental particles, structural compactness dominates; – in atoms and molecules, complementarity and energetic optimization prevail; – in neutron stars and black holes, gravitational tension becomes extreme again, leading to the collapse of complex formats. The article also introduces the energetic gravitational factor G`= G/ C 2 which establishes the equivalence between energy and gravity, allowing global gravity to be expressed as G global = G` * E 2/ R 3 This formulation unifies the description of gravity from the pre– Big Bang state to present‑day structures, showing that gravitational cohesion is always a function of total gravity (equivalent to total energy) and spatial compactness. Finally, minimum and maximum limits for energetic quanta are defined, associated respectively with a minimal relational frequency and the Planck frequency. These limits reflect the flexibility of dual formats — remnants of primordial energy — which sustain both electromagnetic energy and extreme compactification states. This article thus establishes the mathematical foundation of this unified theory, in which gravity derives from the internal geometry that structures energy, linking quantum mechanics, atomic physics, and extreme astrophysics through a single structural principle.

Il s'agit d'une exploration de l'idée ricoeurienne de mémoire heureuse en confrontation avec les notions de futurs passés, par Reinhart Koselleck, et de situations irréalisables, par Jean-Paul Sartre. Considérant que ces deux notions indiquent les limites d'un rapport angoissant à la temporalité et à son vécu, il s'agit de montrer comment la perspective de Ricœur, en pensant à partir de différents postulats anthropologiques, offre une voie d'expérience heureuse de la temporalité. Le parcours se déroulera à travers l'exposition des idées de Koselleck et de Sartre, ainsi qu'un bref exposé des idées du romancier Milan Kundera sur les faiblesses de la mémoire. Ensuite, les idées de Ricœur seront mobilisées tout en offrant des réponses aux problèmes posés par ces penseurs. Enfin, il s'agit de montrer que la littérature sur Ricœur offre des pistes interprétatives pour une conception plus narrativiste de la pensée de Ricœur, à travers lesquelles il semble possible de consolider une notion d'expérience heureuse comme analogue – et condition – de la mémoire heureuse.

My dear friends, Continuing the series of previously published articles, I now present the 5th article – Gravity and Energy – The Eternal Dance of Gravity and the Evolution of the Universe,. The articles already published, as well as those yet to come within this theme, collectively present a unified vision of the universe — from its essence to the vastness of the cosmos, from its birth to its death. However, only by reading them in the order in which they were conceived will it be possible to gain a full understanding of this vision. This article presents an alternative interpretation of gravity as the structuring force of the universe, sustained by the space–time geometry of formats in a dialectical interaction with cosmic expansion. We start from the notion that each format—whether individual or collective—generates its own gravitational field. Gravity manifests itself on two levels: the internal, which corresponds to the total force of gravitational field generated by the format, and the external, which corresponds to the part that extends beyond its boundaries. The idea is explored that gravitational fields grow in proportion to the aggregation of formats, reinforcing global gravity. It is also shown that their intensity decreases with distance, not only by dispersion but also under the effect of expansion. This dynamic balance between gravity and expansion explains the formation of stable structures, the gradual evolution of systems, and, conversely, extreme phenomena such as black holes. Finally, it is argued that elementary particles, as fundamental formats, cancel each other out in the final collapse of the universe, returning to the unified state of the Big Crunch/Big Bang, ensuring the cyclical continuity of existence.

This article, following the previous one, proposes a unifying vision of gravity and energy as an inseparable unity. From everyday examples to quantum and cosmological physics, it shows that energy only exists when there is a spatio-temporal geometric configuration that sustains it. It also suggests that energy can only exist between geometric configurations bounded by a minimum quantum (Planck ) and a maximum quantum (pre–Big Bang). Thus, energy is framed within these geometric boundaries. The idea is also developed that Einstein’s external gravity only manifests as a consequence of accumulated internal gravity, revealing its true origin. Einstein’s gravity, which manifests in the spacetime surrounding objects, has its root in their internal gravity—that is, in the spatial-temporal geometries of the objects’ constituents.

The theory of quasi-truth was developed by Newton da Costa and collaborators as a more realistic account of truth, encompassing the incompleteness and inconsistency of scientific knowledge. Intuitively, the idea is that truth is reached when consensus is established at the end of inquiry; until that is reached, we have something less than the whole truth, we have partial or quasi-truth. Formally, the view faces some challenges that have been recently addressed in the literature; they concern a mismatch between the offered formalism and the expected claims to be formalized. In this paper we use inspiration from quasi-truth theory to develop an account of consensus in science encompassing the notion of quasi-truth. We not only present the formal system capturing the idea of a scientific consensus, but also show how quasi-truth may be represented within it too. We compare the original quasi-truth approach to ours, and argue that the latter is able to face some of the difficulties that plagued the former.

Quasi-truth is a formal approach to a pragmatically-oriented view of truth. The basic plan motivating the framework consists in providing for a more realistic account of truth, accommodating situations where there is incomplete information, as typically happens in the practice of science. The historical sciences are a case in hand, where incomplete information is the rule. It would seem, then, that the quasi-truth approach would be the most appropriate one to deal with historical sciences, then. In this paper, we explore this possibility and use the historical sciences as a test case for the approach of quasi-truth. Our claim is that, on what concerns historical sciences, the quasi-truth approach fails in two basic senses; first, by misrepresenting some cases concerning incomplete information, and second, by falling short of accounting for many features of incomplete information peculiar to historical sciences. We conclude that, despite its stated goals, quasi-truth must be either amended or substituted if the goal of a more faithful representation of scientific practice is to be achieved.