Have a personal or library account? Click to login
Negation and infinity Cover

References

  1. Aristotle. (1961). Physics. Lincoln: University of Nebraska Press. (Richard Hope, trans.)
  2. Béziau, J.-Y. (2002). Are paraconsistent negations negations? In W. A. Carnielli, M. E. Coniglio, & I. M. Loffredo D’Ottaviano (Eds.), Paraconsistency: the logical way to the inconsistent (pp. 465-486). New-York: Marcel Dekker. Retrieved from www.jyb-logic.org/papers12-11/paraconsistent%20negations.pdf
  3. Cantor, G. (1932). Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Mit Erl¨auterunden Anmerkungen sowie mit Erg¨anzungen aus den Briewechsel Cantor-Dedekind. Nebst einem Lebenslauf Cantors von A. Fraenkel (E. Zermelo, Ed.). Berlin, G¨ottingen: Verlag von Julius Springer. Retrieved from http://gdz.sub.uni-goettingen.de/dms/load/pdf/?PPN=PPN237853094&DMDID=DMDLOG0059&LOGID=LOG0059&PHYSID=PHYS0391 (Reprinted: Hildesheim 1962; 2nd ed. Springer, Berlin 1980 Mit erl¨auternden Anmerkungen sowie mit Erg¨anzungen aus dem Briefwechsel Cantor-Dedekind; reprint 2013. Available online)
  4. Carnielli,W., & Coniglio, M. E. (2016). Paraconsistent logic: Consistency, contradiction and negation (Vol. 40). Springer International Publishing.10.1007/978-3-319-33205-5
  5. Davis, M. (Ed.). (1965). The undecidable: Basic papers on undecidable propositions, unsolvable problems, and computable functions (1965, 2004 ed.). Hewlett, N.Y.: Raven Press. (An anthology of fundamental papers on undecidability and unsolvability, this classic reference opens with G¨odel’s landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by G¨odel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. 1965 edition.)
  6. Gentzen, G. (1936). Die Widerspruchsfreicheit der reinen Zahlentheorie. Mathematische Annalen, 112, 493-565. (Translated as The consistency of arithmetic, in (?, ?).)10.1007/BF01565428
  7. Gentzen, G. (1938). Neue Fassung des Widerspruchsfreicheitsbeweises f¨ur die reine Zahlentheorie. Forschungen zur Logik und Grundlegung der exakten Wissenschaften, 4, 19-44. (Translated as New version of the consistency proof for elementary number theory, in (?, ?).)
  8. Gentzen, G. (1969). The collected papers of Gerhard Gentzen (M. E. Szabo, Ed.). Amsterdam: North-Holland.
  9. Gerardy, T. (1969). Nachtr¨age zum Briefwechsel zwischen Carl Friedrich Gauss und Heinrich Christian Schumacher. G¨ottingen: Vandenhoeck u. Ruprecht.
  10. Gödel, K. (1931). ¨Uber formal unentscheidbare S¨atze der Principia Mathematica und verwandter Systeme I. Monatshefte f¨ur Mathematik und Physik, 38, 173-198. (Received: 17.XI.1930. Translated in: (?, ?, 144-195). Includes the German text and parallel English translation. English translations in (?, ?, 5-38), (?, ?, 595-616). Online version (translation by B. Meltzer, 1962): http://www.ddc.net/ygg/etext/godel/, PDF version (translation by M. Hirzel): http://nago.cs.colorado.edu/∼hirzel/papers/canon00-goedel.pdf)10.1007/BF01700692
  11. Gödel, K. (1934). On undecidable propositions of formal mathematical systems. ((mimeographed lecture notes, taken by S. C. Kleene and J. B. Rosser at the Institute for Advanced Study), Princeton; Reprinted in: (?, ?, 39-74))
  12. Gödel, K. (1986a). Collected works (Vols. 1 Publications 1929-1936; S. Feferman, J. Dawson, & S. Kleene, Eds.). New York: Oxford University Press.
  13. Gödel, K. (1986b). Collected works. Publications 1929-1936 (Vol. 1; S. Feferman, J. W. Dawson Jr., S. C. Kleene, G. H. Moore, R. M. Solovay, & J. van Heijenoort, Eds.). Oxford University Press Inc, USA.
  14. Granger, G. G. (1998). L’irrationnel. Paris: Odile Jacob.
  15. Heyting, A. (1930). Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der preusischen Akademie der Wissenschaften, phys.-math. Klasse, 42-56.
  16. Heyting, A. (1956). Intuitionism. an introduction (1st ed.). Amsterdam: North- Holland Publishing Co. (2nd edition 1966)
  17. Hilbert, D. (1928a). Die Grundlagen der Mathematik. Abhandlungen aus dem Seminar der Hamburgischen Universit¨at, 6, 65-85. (followed by Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag by H. Weyl, pp. 86-88, and Zusatz zu Hilberts Vortrag by P. Bernays, pp. 89-95; shortened version in (?, ?), 7th ed., pp. 289-312; English translation (by S. Bauer-Mengelberg and D. Follesdal) in (?, ?), pp. 464-479. On-line publication www.marxists.org/reference/subject/philosophy/works/ge/hilbert.htm)10.1007/BF02940603
  18. Hilbert, D. (1928b). ¨Uber das Unendliche. Mathematische Annalen, 95, 161-190. Retrieved from http://eudml.org/doc/159124 (Lecture given in M¨unster, 4 June 1925)10.1007/BF01206605
  19. Hilbert, D. (1998). The theory of algebraic number fields. Berlin: Springer Verlag.10.1007/978-3-662-03545-0
  20. Jaśkowski, S. (1936). Recherches sur le syst´eme de la logique intuitioniste. In Actes du Congr´es International de Philosophie Scientifique (Vol. 6, pp. 58-61). Paris.
  21. Jaśkowski, S. (1948). Rachunek zdań dla systemow dedukcyjnych sprzecznych. Studia Societatis Scientiarun Torunesis, 1(5), 55-77. (An English translation: (?, ?))
  22. Jaśkowski, S. (1949). O koniunkcji dyskusyjnej w rachunku zdań dla systemow dedukcyjnych sprzecznych. Studia Societatis Scientiarum Torunensis (Sectio A), 1(8), 171-172. (An English translation appeared as (?, ?))
  23. Jaśkowski, S. (1969). A propositional calculus for inconsistent deductive systems. Studia Logica, 24, 143-157. (An English translation of (Jaśkowski, 1948) (reprinted in (?, ?)))10.1007/BF02134311
  24. Jaśkowski, S. (1999). On the discussive conjunction in the propositional calculus for inconsistent deductive systems. Logic and Logical Philosophy, 7, 57-59. (An English translation of (Jaśkowski, 1949))10.12775/LLP.1999.004
  25. Japaridze, G. (2009). In the beginning was game semantics? In O.Majer, A. Pietarinen, & T. Tulenheimo (Eds.), Games: Unifying logic, language, and philosophy (Vol. 15, pp. 249-350). Springer Netherlands. Retrieved from https://www.researchgate.net/.../259202450 In the Beginning was Game Semantics10.1007/978-1-4020-9374-6_11
  26. Malec, A. (2001). Legal reasoning and logic. Studies in Logic, Grammar and Rethoric, 4(17), 97-101.
  27. Mathias, A. R. D. (1992). The ignorance of Bourbaki. The Mathematical Intelligencer, 14(3), 4-13. Retrieved from https://www.reddit.com/r/math/comments/24f8mp/the_ignorance_of_bourbaki_pdf/10.1007/BF03025863
  28. Nicholas of Cusa. (1985). On learned ignorance (de docta ignorantia) (2nd ed., Vol. 1; P. Wilpert, Ed.). Minneapolis, Minnesota: The Arthur J. Banning Press. Retrieved from www1.umn.edu/ships/galileo/library/cusa2.pdf (The translation of Book I was made from De docta ignorantia. Die belehrte Unwissenheit, Book I (Hamburg: Felix Meiner, 1970, 2nd edition), text edited by Paul Wilpert, revised by Hans G. Senger.)
  29. Núũez, R. E. (2017). Conceptual metaphor and the cognitive foundations of mathematics: Actual infinity and human imagination. Retrieved from www.cogsci.ucsd.edu/∼nunez/web/SingaporeF.pdf
  30. Odintsev, S. (2008). Constructive negations and paraconsistency (Vol. 26). Springer Netherlands.10.1007/978-1-4020-6867-6
  31. Peters, C. A. F. (Ed.). (1860-1865). Briefwechsel zwischen C. F. Gaus und H. C. Schumacher. Altona-Esch. (Nachdruck Hildesheim: Olms 1975 in drei B¨anden I, II, III, wovon jeder Band des Nachdrucks 2 Bde. der Peters-Altona- Esch-Ausgabe enthält. Bd. 1 (1860): Briefe 1808-1825. Bd. 2: 1824/25- 02/1836. Bd. 3 (1861): 03/1836-12/1840. Bd. 4 (1862): 01/1841-04/1845. Bd. 5 (1863): 05/1845-09/1848. Bd. 6 (1865): 12/1848-11/1850. Trotz den Volumens ist der Briefwechsel nicht vollst¨andig: (?, ?). Zum Inhalt der Briefe: http://www.math.uni-hamburg.de/math/ign/gauss/register.htm)
  32. Presburger, M. (1929). ¨Uber die Vollst¨andigkeit eines gewissen Systems der Arithmetik ganze Zahlem, in welchem die Addition als einzige Operation hervortritt. In Comptes Rendus du I Congr´es de Math´ematiciens des Pays Slaves (pp. 92-101). Warsaw.
  33. Rucker, R. (2013). Infinity and the mind: The science and philosophy of the infinite. Princeton University Press. Retrieved from http://www.rudyrucker.com/infinityandthemind/#calibre link-35410.1515/9781400849048
  34. Russell, R. J. (2011). God and infinity: Theological insights from Cantor’s mathematics. In M. Heller & W. H.Woodin (Eds.), Infinity. New research frontiers (pp. 275-289). Cambridge: Cambridge University Press.10.1017/CBO9780511976889.015
  35. Szabό, A. (1978). The beginnings of greek mathematics. Dordrecht: D. Reidel.10.1007/978-94-017-3243-7
  36. Thomas Aquinas. (1920). Summa theologica. Online Edition Copyright c 2008 by Kevin Knight. Retrieved from http://www.newadvent.org/summa/index.html (Second and Revised Edition. Literally translated by Fathers of the English Dominican Province)
  37. Thomas Aquinas. (1947). Summa theologica. Benziger Bros. Retrieved from http://dhspriory.org/thomas/summa/FP.html (Translated by Fathers of the English Dominican Province)
  38. van Heijenoort, J. (Ed.). (1967). From Frege to G¨odel. A source book in mathematical logic 1879-1931 (1st ed.). Cambridge Mass.: Harvard University Press. (2nd ed., 1971, 3rd ed. 1976)
  39. Weber, H. (1893). Leopold Kronecker. Jahresbericht der Deutschen Mathematiker- Vereinigung, 2, 5-31. Retrieved from http://www.digizeitschriften.de/dms/resolveppn/?PPN=PPN37721857X0002.
DOI: https://doi.org/10.2478/slgr-2018-0021 | Journal eISSN: 2199-6059 | Journal ISSN: 0860-150X
Language: English
Page range: 131 - 148
Published on: Nov 16, 2018
Published by: University of Bialystok
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
Related subjects:

© 2018 Kazimierz Trzęsicki, published by University of Bialystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.