Papers by André H . Rodrigues
En un texto titulado "La extensión de la axiomática según Leonardo Polo", publicado en Studia Pol... more En un texto titulado "La extensión de la axiomática según Leonardo Polo", publicado en Studia Poliana 2 , Juan Fernando Sellés hace un intento explícito de dar mayor rigor filosófico al pensamiento poliano. En resumen, su esfuerzo consiste en extender (en la estela de L. Polo) el concepto de "axioma", tradicionalmente circunscrito a la esfera lógico-matemática, al campo de la metafísica, la antropología e incluso la ética. La intención declarada es atribuir a la filosofía la misma claridad y fuerza demostrativa que las matemáticas obtuvieron con Euclides y que la lógica obtuvo con Aristóteles. Sellés, siguiendo a Polo, entiende que los "primeros principios de la realidad", que se dice que son el de la "no contradicción" o el de la "prioridad del acto sobre el poder", pueden y deben ser considerados axiomas en sentido estricto, con la misma necesidad y evidencia que las proposiciones lógicas elementales. Sin embargo, este movimiento, si se mira más de cerca, ya revela un problema metodológico muy serio desde el principio. [Y aquí anticipamos, propiciamente, el comienzo de la parte propiamente crítica de este análisis]. El término "axioma" tiene una historia y una función técnica, vinculada a la estructura formal de los sistemas deductivos. Al extenderlo a la metafísica sin proporcionar una justificación conceptual clara, Sellés produce una ambigüedad de inmediato. Por un lado, habla de "axiomas" como proposiciones necesarias e indemostrables; por otro lado, los presenta como "actos reales", es decir, como principios metafísicos per se. Esta oscilación, sin embargo, es la que nos permite atribuir a las tesis de Pollyanna un cuestionable estatus de "autoevidencia" que, en la práctica, termina "blindando" la filosofía de Polo contra la crítica racional. Como veremos, el resultado es que la "axiomática metafísica" propuesta por Sellés se acerca más a una actitud de "legitimación retórica" que a un análisis/demostración filosófica riguroso. Lo que se anuncia como una extensión del método axiomático termina convirtiéndose en una simple postulación de principios supuestamente indubitables. Este es un punto sensible y absolutamente relevante, ya que la fuerza misma de cualquier filosofía depende de su apertura crítica, y no de la imposición de fundamentos dados por sentados sin mediación argumentativa. Y es precisamente esta tensión entre la promesa de rigor lógico y el riesgo de dogmatismo lo que este breve análisis crítico pretende examinar.
This work proposes a technical-conceptual analysis of the correspondence between the fundamental ... more This work proposes a technical-conceptual analysis of the correspondence between the fundamental physical/quantum structure, as described in contemporary theories of theoretical physics (especially quantum cosmology and quantum gravity), and the mathematical notion of structure developed by Bourbaki and deepened ontologically by Lorenz Puntel. It is argued that primordial physical reality is not composed of objects in a preexisting space-time, but rather of a functional relational campal structure, formalizable by the triple S = (C, R, Ψ), where C represents the fundamental physical configurations, R the dynamic relations between them, and Ψ the quantum state function that organizes and determines the evolution of the system. This formulation generalizes and dynamizes Bourbaki's classical mathematical structure E = (E, O, R), in that it replaces static operationswith a functional quantum state function, incorporating the principles of superposition, non-locality and emergence. It is concluded that the relational quantum structure represents not only a physical-mathematical model, but a fundamental ontology of the physical real, establishing a bridge between mathematical foundation, physical formalization and contemporary structural metaphysics.
The problem that will be the object of study throughout the development of this text can be summa... more The problem that will be the object of study throughout the development of this text can be summarized by presenting the following question: if everything is structure, and if structure is an upfold, and if the upfold is an ordered sequence of n elements, that is, a function whose domain is an ordered countable set, What does all this say about "reality"? The argument that follows basically consists of a long attempt to articulate a systematic and rigorous answer to this question.
This paper proposes to present a (structural) ontology of the relationship from the articulation ... more This paper proposes to present a (structural) ontology of the relationship from the articulation between form, content and structure. Reexamining fundamental concepts of logic and semantics, such as proposition, meaning and truth, the text argues that form and content do not constitute autonomous domains, but functional moments of the same structural complex. Truth is conceived as an identity between logical operator, proposition and fact [ T(p) ⮂ F ], which implies an integration between the syntactic, semantic and ontological levels of language. Drawing inspiration from Bourbaki's (and Puntel's) notion of structure and developing a relational metaphysics, the essay argues that everything that can be thought, said, or known constitutes a relation. Form rules, content determines, and complex structures; Being thus manifests itself as a network of disjunctive metaphysical intervals between distinct terms. Logic, semantics, and ontology are not separated, but converge within a single relational network of the real.
This paper critically examines five key theoretical errors in Thomas Aquinas' philosophy, particu... more This paper critically examines five key theoretical errors in Thomas Aquinas' philosophy, particularly in his quinque viae (five ways) from the Summa Theologiae. The analysis begins with a discussion on translation issues regarding Aquinas' terminology, emphasizing the distinction between esse (being) and existence. The identified errors include: (1) the conflation of esse and essentia in God, leading to an incoherent notion of divine nature; (2) the contradiction arising from treating essence as distinct from being, rendering essence as "nothing"; (3) the presupposition of a dimension beyond God's being, undermining His ultimate condition; (4) the misidentification of God with the supreme being (maxime ens) in the quinque viae, rather than as ipsum esse subsistens; and (5) the failure of the five ways to truly demonstrate the "Being of God" rather than a mere supreme entity. The study also critiques Aquinas’ use of actus purus (pure act) and causality, suggesting that these categories improperly constrain the concept of God. Ultimately, it argues that Aquinas partially reaches an understanding of Being but remains entangled in outdated Scholastic frameworks, leading to conceptual and methodological inconsistencies.
To address the question "on what there is" raised by Quine, and to accomplish the task of compreh... more To address the question "on what there is" raised by Quine, and to accomplish the task of comprehending exhaustively the many ontological units that populate the great province of Being, we propose as an alternative to Puntel's ontology a new ontology designated as "Structural Ontology" (SO). Such ontology is based on systematic-structural theoretical foundations, but leads to a diverse view in which structured factual units, structural configurations (dynamics), as well as apparent ontological units (objects), all encompassed by the temporal subdimension that interconnects them, understood as an internal sub-dimension of the macrodimension of Being, co-subsist. In this sense, we begin by situating the ontological theme in current philosophical discussion from a Quinean perspective. We then present a concept of truth derived from our reading of puntelian philosophy, which will be the point of connection between language and the world. Subsequently, we show how from the concept of truth, after a brief foray into philosophical semantics, we arrive at the ontological field from the ontological categories of structure and ontological state. Finally, we outline, in its general features, our structural ontology, which includes its own ontological notions that give new directions to philosophical understanding of this great theme.
This article critically examines the concept of "Absolute Nothingness" from a rigorous logical-me... more This article critically examines the concept of "Absolute Nothingness" from a rigorous logical-metaphysical perspective. It is argued that Nothingness, as a negation of Being, cannot subsist as a primary, autonomous or positively articulable concept without incurring in a performative contradiction. Based on the thesis that Being is a necessary metaphysical-ontological condition of every proposition (S((T)(φ))), it is demonstrated that every attempt to enunciate absolute Nothingness inevitably converts it into linguistic or conceptual positivity, betraying its own definition. The text critically examines authors such as Heidegger, Hegel, Sartre, Graham Priest, and Alain Badiou, showing that any effort to positivize absolute Nothingness, whether ontologically, logically, or phenomenologically, collapses when it depends on Being itself for its formulation. It is concluded that absolute Nothingness is not ontologically thinkable, logically consistent, or linguistically referenceable, being only a negative limit that demarcates the impossibility of thought outside Being.
This article investigates the epistemological nature of the act of believing, aiming to clarify t... more This article investigates the epistemological nature of the act of believing, aiming to clarify to what extent belief can be considered a legitimate instance of knowledge or a mental state with epistemic value. The analysis begins with the conception of belief as a representational psychological disposition associated with a predicative proposition, whose validity and truth are presupposed by the subject. It is argued that, for a belief to possess full epistemic status, it must be properly justified and true, resulting from a cognitive process oriented toward reality. The implications of Gettier-style cases and Alvin Plantinga's approach to warrant are examined, confronting internalist and externalist perspectives on justification. It is concluded that believing, although psychologically necessary, is epistemically valid only when it is open to the rational and ontological scrutiny of truth, and may, under certain conditions, coincide with knowledge. Belief is thus conceived as a mental state that participates in the economy of knowledge, but whose epistemic value is conditional, graded, and dependent on its grounding in reality.
This work proposes a structural-ontological foundation for logic based on the principle of self-c... more This work proposes a structural-ontological foundation for logic based on the principle of self-contradicted identity, formulated as a relational tension within being itself. Rejecting both pragmatic and formalist approaches, the theory advances a second-order metalogical function, Φ, which operates on the set of relational structures over a given language and generates a class of stable configurations. Logic is not grounded in epistemic utility or inferential practices, but emerges from the iterability of a primary metaphysical contrariety, where identity and difference coexist as a generative tension. Through a formal definition of Φ and its convergence properties, the theory provides an account of logic as a manifestation of the structure of being, prior to any axiomatic system or linguistic articulation. The work engages with contemporary logical theories (e.g., Leitgeb, Da Costa) and classical foundations (e.g., Frege, Hilbert), offering a unified framework capable of encompassing both classical and non-classical logics. Ultimately, logic is redefined not as a tool of thought, but as an ontological-metaphysical necessity.
Quine's famous assertion that "to be is to be the value of a bound variable" translates, in synta... more Quine's famous assertion that "to be is to be the value of a bound variable" translates, in syntactic form, the way in which first-order formal logic correctly expresses existence, which can no longer be taken as a real predicate since Kant. However, this operation of quantification does not exhaust the metaphysical breadth of the theme of Being, involved by dragging through the use of the verb "to be". In particular, when it comes to mathematical objects, it is verified that quantification depends on the reality of non-empirical and non-mental domains, which support the truth of mathematical propositions. This work seeks to demonstrate that such domains must have an autonomous, independent, abstract and necessary way of being, which implies the adoption of mathematical Platonism in a strong sense, a position similar to that adopted by G. Frege in the proposition of his thesis of the "Third Kingdom" ("drittes Reich") in his famous article Der Gedanke.
Unpublished , 2024
Philosophy can never be separated from the rigorous pursuit of the foundations of science, where ... more Philosophy can never be separated from the rigorous pursuit of the foundations of science, where "science" is understood broadly as a body of rational knowledge organized into a systematic, self-founded discourse. Philosophy is, in a certain sense, the evolving metarationality, and only it is capable of advancing into the inquiry of ultimate presuppositions. 1 Undergraduate degree in Law (FADI), graduate degree in civil procedural law (Damásio Faculty of Law), philosopher with no institutional affiliation, independent researcher in philosophy, with an emphasis on the areas of metaphysics, metaphilosophy, and epistemology.
The article responds to Lorenz Puntel's criticism of the Hegelian dialectic, which he claims is u... more The article responds to Lorenz Puntel's criticism of the Hegelian dialectic, which he claims is unintelligible because it involves infinite regress, results in the absence of methodological metalevel and in arbitrary use of negativity. It is argued that these objections stem from an externalist reading, incompatible with the self-reference proper to Hegel's speculative method. The dialectical process is reinterpreted as convergent, self-legitimate, and productively contradictory. On the basis of our formal system, centered on the function Φ, the convergence criterion ConvΦ, and the self-contradicted identity A⮂ A, we demonstrate that dialectics can be reconstructed with logical precision, without losing its conceptual dynamism.
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Papers by André H . Rodrigues