Negation and infinity

Open access

Abstract

Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic issues will be considered.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Aristotle. (1961). Physics. Lincoln: University of Nebraska Press. (Richard Hope trans.)

  • 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

  • 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)

  • CarnielliW. & Coniglio M. E. (2016). Paraconsistent logic: Consistency contradiction and negation (Vol. 40). Springer International Publishing.

  • 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.)

  • Gentzen G. (1936). Die Widerspruchsfreicheit der reinen Zahlentheorie. Mathematische Annalen 112 493-565. (Translated as The consistency of arithmetic in (? ?).)

  • 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 (? ?).)

  • Gentzen G. (1969). The collected papers of Gerhard Gentzen (M. E. Szabo Ed.). Amsterdam: North-Holland.

  • Gerardy T. (1969). Nachtr¨age zum Briefwechsel zwischen Carl Friedrich Gauss und Heinrich Christian Schumacher. G¨ottingen: Vandenhoeck u. Ruprecht.

  • 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)

  • 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))

  • Gödel K. (1986a). Collected works (Vols. 1 Publications 1929-1936; S. Feferman J. Dawson & S. Kleene Eds.). New York: Oxford University Press.

  • 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.

  • Granger G. G. (1998). L’irrationnel. Paris: Odile Jacob.

  • Heyting A. (1930). Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der preusischen Akademie der Wissenschaften phys.-math. Klasse 42-56.

  • Heyting A. (1956). Intuitionism. an introduction (1st ed.). Amsterdam: North- Holland Publishing Co. (2nd edition 1966)

  • 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)

  • 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)

  • Hilbert D. (1998). The theory of algebraic number fields. Berlin: Springer Verlag.

  • 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.

  • Jaśkowski S. (1948). Rachunek zdań dla systemow dedukcyjnych sprzecznych. Studia Societatis Scientiarun Torunesis 1(5) 55-77. (An English translation: (? ?))

  • 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 (? ?))

  • Jaśkowski S. (1969). A propositional calculus for inconsistent deductive systems. Studia Logica 24 143-157. (An English translation of (Jaśkowski 1948) (reprinted in (? ?)))

  • 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))

  • 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 Semantics

  • Malec A. (2001). Legal reasoning and logic. Studies in Logic Grammar and Rethoric 4(17) 97-101.

  • 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/

  • 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.)

  • 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

  • Odintsev S. (2008). Constructive negations and paraconsistency (Vol. 26). Springer Netherlands.

  • 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)

  • 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.

  • 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-354

  • 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.

  • Szabό A. (1978). The beginnings of greek mathematics. Dordrecht: D. Reidel.

  • 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)

  • Thomas Aquinas. (1947). Summa theologica. Benziger Bros. Retrieved from http://dhspriory.org/thomas/summa/FP.html (Translated by Fathers of the English Dominican Province)

  • 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)

  • Weber H. (1893). Leopold Kronecker. Jahresbericht der Deutschen Mathematiker- Vereinigung 2 5-31. Retrieved from http://www.digizeitschriften.de/dms/resolveppn/?PPN=PPN37721857X0002.

Search
Journal information
Impact Factor


Cite Score 2018: 0.29

SCImago Journal Rank (SJR) 2018: 0.138
Source Normalized Impact per Paper (SNIP) 2018: 0.358

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 142 142 4
PDF Downloads 69 69 2