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== Bibliografi ==
 
=== Artikel tulisan Gödel ===
* 1931, ''Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.'' ''Monatshefte für Mathematik und Physik 38'': 173-98.
* 1931, ''Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.'' and ''On formally undecidable propositions of Principia Mathematica and related systems I'' in [[Solomon Feferman]], ed., 1986. ''Kurt Gödel Collected works, Vol. I''. Oxford University Press: 144-195. The original German with a facing English translation, preceded by a very illuminating introductory note by [[Kleene]].
** Hirzel, Martin, 2000, ''[http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf On formally undecidable propositions of Principia Mathematica and related systems I.]''. A modern translation by Hirzel.
* 1951, ''Some basic theorems on the foundations of mathematics and their implications'' in [[Solomon Feferman]], ed., 1995. ''Kurt Gödel Collected works, Vol. III''. Oxford University Press: 304-23.
 
=== Terjemahan makalah Gödel ke dalam bahasa Inggris semasa hidupnya ===
<!--None of the following agree in all translated words and in typography. The typography is a serious matter, because Gödel expressly wished to emphasize "those metamathematical notions that had been defined in their usual sense before . . ." (van Heijenoort 1967:595). Three translations exist. Of the first John Dawson states that: "The Meltzer translation was seriously deficient and received a devastating review in the ''Journal of Symbolic Logic''; "Gödel also complained about Braithwaite's commentary (Dawson 1997:216). "Fortunately, the Meltzer translation was soon supplanted by a better one prepared by Elliott Mendelson for Martin Davis's anthology ''The Undecidable'' . . . he found the translation "not quite so good" as he had expected . . . [but because of time constraints he] agreed to its publication" (ibid). (In a footnote Dawson states that "he would regret his compliance, for the published volume was marred throughout by sloppy typography and numerous misprints" (ibid)). Dawson states that "The translation that Gödel favored was that by Jean van Heijenoort" (ibid). For the serious student another version exists as a set of lecture notes recorded by Stephen Kleene and J. B. Rosser "during lectures given by Gödel at to the Institute for Advanced Study during the spring of 1934" (cf commentary by Davis 1965:39 and beginning on p.&nbsp;41); this version is titled "On Undecidable Propositions of Formal Mathematical Systems". In their order of publication:
-->
* [[B. Meltzer]] (translation) and [[R. B. Braithwaite]] (Introduction), 1962. ''On Formally Undecidable Propositions of Principia Mathematica and Related Systems'', Dover Publications, New York (Dover edition 1992), ISBN 0-486-66980-7 (pbk.) This contains a useful translation of Gödel's German abbreviations on pp.&nbsp;33–34. As noted above, typography, translation and commentary is suspect. Unfortunately, this translation was reprinted with all its suspect content by
:* [[Stephen Hawking]] editor, 2005. ''God Created the Integers: The Mathematical Breakthroughs That Changed History'', Running Press, Philadelphia, ISBN 0-7624-1922-9. Gödel's paper appears starting on p. 1097, with Hawking's commentary starting on p. 1089.
* [[Martin Davis]] editor, 1965. ''The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable problems and Computable Functions'', Raven Press, New York, no ISBN. Gödel's paper begins on page 5, preceded by one page of commentary.
* [[Jean van Heijenoort]] editor, 1967, 3rd edition 1967. ''From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931'', Harvard University Press, Cambridge Mass., ISBN 0-674-32449-8 (pbk).<ref>{{cite web|last=van Heijenoort|first=Jean|title=From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931|url=http://books.google.com/books?id=v4tBTBlU05sC&dq=ISBN+0-674-32449-8|work=This link goes to the Google Books page for the text.|publisher=The original print book was published by Harvard University Press in 1977 and is widely available from booksellers.|accessdate=9 April 2014}}</ref> van Heijenoort did the translation. He states that "Professor Gödel approved the translation, which in many places was accommodated to his wishes." (p.&nbsp;595). Gödel's paper begins on p.&nbsp;595; van Heijenoort's commentary begins on p.&nbsp;592.
* Martin Davis editor, 1965, ibid. "On Undecidable Propositions of Formal Mathematical Systems." A copy with Gödel's corrections of errata and Gödel's added notes begins on page 41, preceded by two pages of Davis's commentary. Until Davis included this in his volume this lecture existed only as mimeographed notes.
 
== Referensi ==
{{reflist}}
 
== Pustaka tambahan ==
=== Artikel oleh penulis lain ===
* [[George Boolos]], 1989, "A New Proof of the Gödel Incompleteness Theorem", ''Notices of the American Mathematical Society'' v. 36, pp.&nbsp;388–390 and p.&nbsp;676, reprinted in Boolos, 1998, ''Logic, Logic, and Logic'', Harvard Univ. Press. ISBN 0-674-53766-1
* Arthur Charlesworth, 1980, "A Proof of Godel's Theorem in Terms of Computer Programs," ''Mathematics Magazine'', v. 54 n. 3, pp.&nbsp;109–121. [http://links.jstor.org/sici?sici=0025-570X%28198105%2954%3A3%3C109%3AAPOGTI%3E2.0.CO%3B2-1&size=LARGE&origin=JSTOR-enlargePage JStor]
* [[Martin Davis]], "[http://www.ams.org/notices/200604/fea-davis.pdf The Incompleteness Theorem]", in Notices of the AMS vol. 53 no. 4 (April 2006), p.&nbsp;414.
* [[Jean van Heijenoort]], 1963. "Gödel's Theorem" in Edwards, Paul, ed., ''Encyclopedia of Philosophy, Vol. 3''. Macmillan: 348-57.
* [[Geoffrey Hellman]], ''How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism.'' Noûs, Vol. 15, No. 4, Special Issue on Philosophy of Mathematics. (Nov., 1981), pp.&nbsp;451–468.
* [[David Hilbert]], 1900, "[http://aleph0.clarku.edu/~djoyce/hilbert/problems.html#prob2 Mathematical Problems.]" English translation of a lecture delivered before the International Congress of Mathematicians at Paris, containing Hilbert's statement of his Second Problem.
* {{Citation | last1=Kikuchi | first1=Makoto | last2=Tanaka | first2=Kazuyuki | title=On formalization of model-theoretic proofs of Gödel's theorems | mr=1326122 | year=1994 | journal=Notre Dame Journal of Formal Logic | issn=0029-4527 | volume=35 | issue=3 | pages=403–412 | doi=10.1305/ndjfl/1040511346}}
* [[Stephen Cole Kleene]], 1943, "Recursive predicates and quantifiers," reprinted from ''Transactions of the American Mathematical Society'', v. 53 n. 1, pp.&nbsp;41–73 in Martin Davis 1965, ''The Undecidable'' (loc. cit.) pp.&nbsp;255–287.
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* C. Smoryński, "The incompleteness theorems", in J. Barwise, ed., ''Handbook of Mathematical Logic'', North-Holland 1982 ISBN 978-0-444-86388-1, pp.&nbsp;821–866.
* Dan E. Willard (2001), "[http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jsl/1183746459 Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles]", ''Journal of Symbolic Logic'', v. 66 n. 2, pp.&nbsp;536–596. {{doi|10.2307/2695030}}
* {{Citation | author=Richard Zach|author-link=Richard Zach | title=The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program | url=http://www.ucalgary.ca/~rzach/static/conprf.pdf | publisher=[[Springer-Verlag]] | location=Berlin, New York | year=2003 | journal=Synthese | issn=0039-7857 | volume=137 | issue=1 | pages=211–259 | doi=10.1023/A:1026247421383}}
* {{Citation | author=Richard Zach| author-link=Richard Zach | year=2005 | chapter=Paper on the incompleteness theorems | editor=Ivor Grattan-Guinness|editor-link=Ivor Grattan-Guinness | title=Landmark Writings in Western Mathematics |publisher=Elsevier|pages=917-25 |doi=10.1016/B978-044450871-3/50152-2|url=http://www.sciencedirect.com/science/article/pii/B9780444508713501522}}
 
=== Buku-buku mengenai teorema ===
* Francesco Berto. ''There's Something about Gödel: The Complete Guide to the Incompleteness Theorem'' John Wiley and Sons. 2010.
* Domeisen, Norbert, 1990. ''Logik der Antinomien''. Bern: Peter Lang. 142 S. 1990. ISBN 3-261-04214-1. [http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0724.03003 Zentralblatt MATH]
* [[Torkel Franzén]], 2005. ''Gödel's Theorem: An Incomplete Guide to its Use and Abuse''. A.K. Peters. ISBN 1-56881-238-8 {{MathSciNet|2007d:03001}}
* [[Douglas Hofstadter]], 1979. ''[[Gödel, Escher, Bach|Gödel, Escher, Bach: An Eternal Golden Braid]]''. Vintage Books. ISBN 0-465-02685-0. 1999 reprint: ISBN 0-465-02656-7. {{MathSciNet|80j:03009}}
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* [[Per Lindström]], 1997, ''[http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.lnl/1235416274 Aspects of Incompleteness]'', Lecture Notes in Logic v. 10.
* [[J.R. Lucas]], FBA, 1970. ''The Freedom of the Will''. Clarendon Press, Oxford, 1970.
* [[Ernest Nagel]], James Roy Newman, Douglas Hofstadter, 2002 (1958). ''Gödel's Proof'', revised ed. ISBN 0-8147-5816-9. {{MathSciNet|2002i:03001}}
* [[Rudy Rucker]], 1995 (1982). ''Infinity and the Mind: The Science and Philosophy of the Infinite''. Princeton Univ. Press. {{MathSciNet|84d:03012}}
* Smith, Peter, 2007. ''[http://www.godelbook.net/ An Introduction to Gödel's Theorems.]'' Cambridge University Press. [http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=AUCN&pg6=PC&pg7=ALLF&pg8=ET&s4=Smith%2C%20Peter&s5=&s6=&s7=&s8=All&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=2&mx-pid=2384958 MathSciNet]
* N. Shankar, 1994. ''Metamathematics, Machines and Gödel's Proof'', Volume 38 of Cambridge tracts in theoretical computer science. ISBN 0-521-58533-3
* [[Raymond Smullyan]], 1991. ''Godel's Incompleteness Theorems''. Oxford Univ. Press.
* —, 1994. ''Diagonalization and Self-Reference''. Oxford Univ. Press. {{MathSciNet|96c:03001}}
* [[Hao Wang (academic)|Hao Wang]], 1997. ''A Logical Journey: From Gödel to Philosophy''. MIT Press. ISBN 0-262-23189-1 {{MathSciNet|97m:01090}}
 
=== Pustaka lain-lain ===
* Francesco Berto. "The Gödel Paradox and Wittgenstein's Reasons" ''[[Philosophia Mathematica]]'' (III) 17. 2009.
* [[John W. Dawson, Jr]]., 1997. ''Logical Dilemmas: The Life and Work of Kurt Gödel'', [[A. K. Peters]], Wellesley Mass, ISBN 1-56881-256-6.
* [[Rebecca Goldstein|Goldstein, Rebecca]], 2005, ''Incompleteness: the Proof and Paradox of Kurt Gödel'', W. W. Norton & Company. ISBN 0-393-05169-2
* Juliet Floyd and Hilary Putnam, 2000, "A Note on Wittgenstein's 'Notorious Paragraph' About the Gödel Theorem", ''[[Journal of Philosophy]]'' v. 97 n. 11, pp.&nbsp;624–632.
* [[David Hilbert]] and [[Paul Bernays]], ''[[Grundlagen der Mathematik]]'', Springer-Verlag.
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* Russell O'Connor, 2005, "[http://arxiv.org/abs/cs/0505034 Essential Incompleteness of Arithmetic Verified by Coq]", Lecture Notes in Computer Science v. 3603, pp.&nbsp;245–260.
* [[Graham Priest]], 2006, ''In Contradiction: A Study of the Transconsistent'', Oxford University Press, ISBN 0-19-926329-9
* Graham Priest, 2004, ''Wittgenstein's Remarks on Gödel's Theorem'' in Max Kölbel, ed., ''Wittgenstein's lasting significance'', Psychology Press, pp.&nbsp;207–227.
* Graham Priest, 1984, "Logic of Paradox Revisited", ''Journal of Philosophical Logic'', v. 13,` n. 2, pp.&nbsp;153–179
* [[Hilary Putnam]], 1960, ''Minds and Machines'' in [[Sidney Hook]], ed., ''Dimensions of Mind: A Symposium''. New York University Press. Reprinted in Anderson, A. R., ed., 1964. ''Minds and Machines''. Prentice-Hall: 77.
* {{Citation|last=Rautenberg|first=Wolfgang|authorlink=Wolfgang Rautenberg|doi=10.1007/978-1-4419-1221-3|title=A Concise Introduction to Mathematical Logic|url=http://www.springerlink.com/content/978-1-4419-1220-6/|publisher=[[Springer Science+Business Media]]|location=[[New York City|New York]]|edition=3rd|isbn=978-1-4419-1220-6|year=2010}}.
* Victor Rodych, 2003, "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein", ''Dialectica'' v. 57 n. 3, pp.&nbsp;279–313. {{doi|10.1111/j.1746-8361.2003.tb00272.x}}
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* [[Jeremy Stangroom]] and [[Ophelia Benson]], ''Why Truth Matters'', Continuum. ISBN 0-8264-9528-1
* George Tourlakis, ''Lectures in Logic and Set Theory, Volume 1, Mathematical Logic'', Cambridge University Press, 2003. ISBN 978-0-521-75373-9
* {{Citation
|chapterurl=http://www.math.ias.edu/~avi/BOOKS/Godel_Widgerson_Text.pdf
|authorlink=Avi Wigderson
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|title=Kurt Gödel and the Foundations of Mathematics: Horizons of Truth
|publisher=Cambridge University Press}} <!-- from Wigderson's home page, http://www.math.ias.edu/~avi/BOOKS/ -->
* [[Hao Wang (academic)|Hao Wang]], 1996, ''A Logical Journey: From Gödel to Philosophy'', The MIT Press, Cambridge MA, ISBN 0-262-23189-1.
* Richard Zach, 2006, [http://www.ucalgary.ca/~rzach/static/hptn.pdf "Hilbert's program then and now"], in ''Philosophy of Logic'', Dale Jacquette (ed.), Handbook of the Philosophy of Science, v. 5., Elsevier, pp.&nbsp;411–447.
 
== Pranala luar ==
* {{In Our Time|Godel's Incompleteness Theorems|b00dshx3|Godel's_Incompleteness_Theorems}}
* {{SEP|goedel|Kurt Gödel|Juliette Kennedy |July 5, 2011}}
* {{SEP|goedel-incompleteness|Gödel's Incompleteness Theorems|Panu Raatikainen|November 11, 2013}}
* MacTutor biographies:
** [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html Kurt Gödel.]
** [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Gentzen.html Gerhard Gentzen.]
** [http://podnieks.id.lv/gt.html What is Mathematics:Gödel's Theorem and Around] by ''Karlis Podnieks''. An online free book.
* [http://blog.plover.com/math/Gdl-Smullyan.html World's shortest explanation of Gödel's theorem] using a printing machine as an example.
* [http://www.radiolab.org/2011/oct/04/break-cycle/ October 2011 RadioLab episode] about/including Gödel's Incompleteness theorem
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