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  1.  26
    Mathematics and its Applications: A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Springer Verlag.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  2.  32
    Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - 2016 - Synthese 193 (6).
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  3.  24
    Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - 2016 - Synthese 193 (6):1925-1947.
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  4.  30
    Husserl's Two Notions Of Completeness.Jairo josé Da Silva - 2000 - Synthese 125 (3):417-438.
    In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic (...)
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  5.  66
    Husserl on Geometry and Spatial Representation.Jairo José da Silva - 2012 - Axiomathes 22 (1):5-30.
    Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical (...)
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  6. The Effectiveness of Mathematics in Empirical Science [La Efectividad de la Matemática En Las Ciencias Empíricas].Jairo José da Silva - 2018 - Disputatio. Philosophical Research Bulletin 7 (8).
    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 —mathematical domains in particular— whose formal structures bear relevant formal (...)
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  7. Mathematics and Its Applications, A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Springer.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  8. Husserl's Conception of Logic.Jairo José da Silva - 1999 - Manuscrito: Revista Internacional de Filosofía 22 (2):367-397.
     
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  9.  2
    The (Reasonable) Effectiveness of Mathematics in Empirical Science.Jairo José da Silva - 2018 - Disputatio 7 (8).
    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 —mathematical domains in particular— whose formal structures bear relevant formal (...)
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  10. Beyond Leibniz : Husserl's Vindication of Symbolic Knowledge.Jairo José da Silva - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
  11.  33
    The Road Not Taken. On Husserl's Philosophy of Logic and Mathematics.Claire Ortiz Hill & Jairo Jose da Silva (eds.) - 1997 - College Publications.
    For different reasons, Husserl's original, thought-provoking ideas on the philosophy of logic and mathematics have been ignored, misunderstood, even despised, by analytic philosophers and phenomenologists alike, who have been content to barricade themselves behind walls of ideological prejudices. Yet, for several decades, Husserl was almost continuously in close professional and personal contact with those who created, reshaped and revolutionized 20th century philosophy of mathematics, logic, science and language in both the analytic and phenomenological schools, people whom those other makers of (...)
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  12. Notes on Authors 379.Jairo Jose da Silva - 2000 - Manuscrito 23.
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  13.  14
    Godel and transcendental phenomenology.Jairo Jose da Silva - 2005 - Revue Internationale de Philosophie 4:553-574.
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  14.  52
    Structuralism and the Applicability of Mathematics.Jairo José da Silva - 2010 - Axiomathes 20 (2-3):229-253.
    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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  15.  64
    The Axioms of Set Theory.Jairo José Da Silva - 2002 - Axiomathes 13 (2):107-126.
    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 (...)
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  16. Imposturas intelectuais: algumas reflexões.Jairo José da Silva - 2004 - Human Nature 6 (1):87-99.
    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 the most (...)
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  17. Mathematics and the Crisis of Science.Jairo José da Silva - 2008 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 43 (91):37-58.
  18.  20
    Poincaré on Mathematical Intuition. A Phenomenological Approach to Poincaré's Philosophy of Arithmetic.Jairo José Da Silva - 1996 - Philosophia Scientiae 1 (2):87-99.
  19.  19
    Intentional objects and objective existence.Jairo José da Silva - 1991 - Trans/Form/Ação 14:155-164.
    In this paper I show the possibility of an ontology of mathematics that keeps some points in common with platonism and constructivism while diverging from them in other essencial ones. I understand that mathematical objects are simply the referential focus of mathematical discourse, I also understand that their existence is merely intentional but none the less objective, in the sense of being shared by all those who are engaged in the mathematical activity. However, the objective existence of mathematical entities is (...)
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  20.  7
    Phenomenology and the Formal Sciences.Jairo José Da Silva - 2002 - Veritas – Revista de Filosofia da Pucrs 47 (1):61-69.
    Este artigo procura mostrar que as idéias filosóficas de Husserl não apenas influenciaram o trabalho de alguns dos maiores matemáticos do século XX, mas foram decisivas para aproximarem uma epistemologia das ciências formais de uma fenomenologia do significado.
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  21.  9
    The Axioms of Set Theory.Jairo José Da Silva - 2002 - Axiomathes 13 (2):107-126.
    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 (...)
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  22.  26
    Husserl's Philosophy of Mathematics.Jairo José da Silva - 1993 - Manuscrito: Revista Internacional de Filosofía 16 (2):121-148.