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Borges Meneses Ramiro Délio (Instituto Politécnico de Saúde do Norte, Gandra-Paredes, Portugal)
A Matemática como linguagem analítica em R. Carnap
Społeczeństwo i Edukacja. Międzynarodowe Studia Humanistyczne, 2014, nr 2, s. 15-35, bibliogr. poz.
Society and Education. International Humanist Studies
Logika, Matematyka, Nauka
Logic, Mathematics, Science
Logical empirism, which the metaphysical and seeks to discover the truth about the world exclusively through the natural sciences, owes its name two of its basic tenets, namely: the view that the solution of a philosophical problem requires a logical analysis of the languages in which the problem is stated, and that therefore logic plays a central role in philosophy, and the empiricist principle that any significant theory which is not of a purely logical or mathematical character must be testable by reference to empirical evidence. Carnap's work provides, among other thing, a precise elaboration of, and a broad theoretical basis for these tenets and it develops the technical tools for the pursuit of philosophy as logical analysis. R. Carnap shall see that he furnished instruments for deduction, that is, for the transformation of formulations of factual and contingent knowledge. However, logic and mathematics not only supply rules for transformation of factual sentences but they themselves contain sentences of a different non-factual kind. On this article I explain the linguistic sense to Mathematics, and the philosophical foundations. However the logic language plays a very important role to the logical foundations of mathematics and Mathematics is to analytic language according to R. Carnap(original abstract)
Full text
  1. R. Carnap - Autobiografía intelectual, tradugao do ingles, Barcelona, Ediciones Paidós, 1992, 90-91
  2. M. Schlick - Space and Time in Contemporary Physics, Oxford, At the University Press, 1920,16-34
  3. A. G. Manno - Filosofía della Matemática, Milano, Marzorati Editore, 1972,166-167
  4. R. Carnap - La costruzione lógica del Mundo, tradugao do alemao, Milano, Fratelli Fabbri Editori, 1966, 228-229
  5. R. Carnap - Meaning and Necessity, a Study in Semantics and Modal Logic, Chicago, The University Press, 1958, 205-207
  6. R. Carnap - Filosofía y Sintaxis Lógica, traduçâo do inglés, México, Centro de Estudos Filosóficos, 1963, 25
  7. D. Hilbert; P. Bernays - Die Grundlagen der Mathematik, Band I, Berlin, Springer-Verlag, 1934,10-49
  8. L. A. Cerqueira; A. Oliva - Introduçâoà Lógica, Riode Janeiro, Zahar Editores, 1980,25-26
  9. L. Hegenberg - Lógica Simbólica, tradugao do ingles, S. Paulo, Herder, 1966,10-46
  10. F. S. Barker - Filosofía da Matemática, tradugao do inglés, Rio de Janeiro, Zahar Editores, 1969, 46-100
  11. R. Carnap - Filosofía y Sintaxis Lógica, 34-35
  12. M. Cross - Modelos Matemáticos em Lingüística, Rio de Janeiro, Zahar Editores, 1976, 12-64; 65-69; 70-76
  13. L. D. Kudriavtsev - Curso de Análisis Matemático, 1, Moscú, Editorial Mir, 1983,141
  14. R. Carnap - Logical Foundations of Probability, Chicago, At the University Press, 1950,1-12
  15. G. Frege - Lógica e Filosofía da Linguagem, traduçâo do alemäo, S. Paulo, Edusr 1978, 16-39; 40-65
  16. W.V. Quine - Mathematical Logic, Cambridge, At University Press, 1974,19-48
  17. R. CARNAP - "Meaning and Synonymy in Natural Languages", in: Philosophical Studies, (New York, 1955) 33-46
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