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Diagonalização, Paradoxos e o Teorema de Löb

Diagonalização, Paradoxos e o Teorema de Löb

Paulo Guilherme Santos and Reinhard Kahle, “Diagonalização, Paradoxos e o Teorema de Löb,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1169–88, DOI 10.17990/RPF/2017_73_3_1169.

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Diagonalização, Paradoxos e o Teorema de Löb

Type Journal Article
Author Paulo Guilherme Santos
Author Reinhard Kahle
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1169-1188
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1169
Language Portuguese
Abstract Diagonalization is a transversal theme in Logic. In this work, it is shown that there exists a common origin of several diagonalization phenomena — paradoxes (the Liar, Curry's Paradox, and Russell's Paradox) and Löb's Theorem. That common origin comprises a common reasoning and a common logical structure. We analyse the common structure from a philosophical point-of-view and we draw some conclusions.
Date Added 17/01/2018, 17:50:12
Modified 17/01/2018, 19:35:34

Tags:

  • diagonalization,
  • liar,
  • Löb,
  • paradox

Notes:

  • Barwise, J. Handbook of Mathematical Logic (Oitava ed.). North-Holland, 1993.
    Beall, J. Curry's Paradox (Spring 2013 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2013/entries/ curry-paradox/.
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    Benthem, J. 'Four paradoxes'. Journal of Philosophical Logic 7 (1), (1978), 49–72.
    Bíblia Sagrada. Lisboa: Sociedade Bíblica de Portugal.
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    Moschovakis, Y. Notes on Set Theory (Segunda ed.). Springer, 2006.
    Smorynski, C. 'The Incompleteness Theorems'. In Handbook of Mathematical Logic, 821–865. North-Holland, 1977.
    Smullyan, R. M. . Diagonalization and Self-reference. Oxford Science Publications. Verbrugge, R. L. (2017). Provability Logic (Summer 2017 ed.). Metaphysics Research.
    Verbrugge, R. L., Stanford University. https://plato.stanford.edu/archives/sum2017/entries/ logic-provability/.
    Voltaire. Le dîner du comte de Boulainvilliers. https://books.google.pt/books?id=_GNOAAAAcAAJ&printsec=frontcover.

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