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15Structuralism and the Applicability of MathematicsGlobal Philosophy 20 (2-3): 229-253. 2010.In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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15A filosofia moral e política de Hobbes em duas tradições interpretativas do LeviatãInvestigação Filosófica 11 (1): 69. 2020.O objetivo do presente artigo é apresentar e confrontar os pressupostos de duas tradições interpretativas _Leviatã _de Thomas Hobbes. Pretendo demonstrar como, a partir dos pressupostos e dos critérios de interpretação de cada uma delas, teremos não apenas duas abordagens diversas, mas resultados e soluções distintas para problemas políticos e morais que o próprio Hobbes buscou solucionar com essa obra. Na primeira parte do artigo, apresentarei os aspectos inovadores da nova interpretação do _Le…Read more
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15On proofs in mathematicsManuscrito 31 (1): 185-196. 2008.In his book Chateaubriand points out some differences between the mathematical and the formal notions of proof. I argue here that the contrast between both cannot be exaggerated, and that the latter fails to represent essential aspects of the former. I also sketch a view of the nature of mathematics that can accommodate one particular feature of mathematical proofs the formal notion, by its very nature, cannot: their freedom.Em seu livro, Chateaubriand aponta algumas diferenças entre a noção for…Read more
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14The effectiveness of mathematics in empirical science [La efectividad de la matemática en las ciencias empíricas]Disputatio. Philosophical Research Bulletin 7 (8). 2018.I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains —math…Read more
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13The Axioms of Set TheoryGlobal Philosophy 13 (2): 107-126. 2002.In this paper I argue for the view that the axioms of ZF are analytic truths of a particular concept of set. By this I mean that these axioms are true by virtue only of the meaning attached to this concept, and, moreover, can be derived from it. Although I assume that the object of ZF is a concept of set, I refrain from asserting either its independent existence, or its dependence on subjectivity. All I presuppose is that this concept is given to us with a certain sense as the objective focus of…Read more
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12Husserl and WeylIn Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics, Springer Verlag. 2017.In this paper, I carry out a comparative study of the philosophical views of Edmund Husserl and Hermann Weyl on issues such as mathematical existence and mathematical intuition, the validity of classical logic, the concept of logical definiteness, the nature of symbolic mathematics, the role of mathematics in empirical science, the relation of scientific theories with perception, space representation and the philosophy of geometry, and intentional constitution in general. My main goal is not sim…Read more
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10A phenomenological inquiry into the concept of setManuscrito 28 (2): 291-316. 2005.The main concern of this paper is the justification of the axioms of Zermelo-Fraenkel set theory, either as true statements about a concept of set or, alternatively, as true statements about abstract objects . I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations . I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent object…Read more
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6Mathematics and the crisis of scienceDiálogos. Revista de Filosofía de la Universidad de Puerto Rico 43 (91): 37-58. 2008.
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2The (reasonable) effectiveness of mathematics in empirical scienceDisputatio 7 (8). 2018.I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains —math…Read more
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A Phenomenological Inquiry Into The Concept Of SetManuscrito 29 (2): 291-316. 2006.The main concern of this paper is the justification of the axioms of Zermelo-Fraenkel set theory, either as true statements about a concept of set or, alternatively, as true statements about abstract objects. I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations. I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent objects.…Read more
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Imposturas intelectuais: algumas reflexõesHuman Nature 6 (1): 87-99. 2004.Neste artigo, relato os aspectos mais salientes do affair Sokal-Bricmont - uma paródia que evoluiu para uma crítica articulada dos excessos de um certo pensamento pós-modernista - e analiso algumas das reações que suscitou em artigos publicados na Folha de S. Paulo. Termino com algumas reflexões sobre a nefasta negligência para com as ciências exatas na educação em geral e, em particular, na formação dos profissionais das áreas de filosofia e ciências humanas.In this paper I summarize some of th…Read more
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Husserl on the Principle of the Excluded MiddleIn Gary Banham (ed.), Husserl and the Logic of Experience, Palgrave-macmillan. 2005.
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Husserl and Weyl on the Constitution of SpaceIn Carlos Lobo & Julien Bernard (eds.), Weyl and the Problem of Space: From Science to Philosophy, Springer Verlag. 2019.
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |