Gödel's incompleteness theorems (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Gödel's incompleteness theorems" in English language version.

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12doi.org

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3semanticscholar.org

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1godelbook.net

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1digizeitschriften.de

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ams.org

mathscinet.ams.org

Franzén 2005, p. 112. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326.
Smith 2007, p. 24. Smith, Peter (2007). An introduction to Gödel's Theorems. Cambridge, U.K.: Cambridge University Press. ISBN 978-0-521-67453-9. MR 2384958. Archived from the original on 2005-10-23. Retrieved 2005-10-29.
Franzén 2005, p. 106. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326.
Shelah 1974. Shelah, Saharon (1974). "Infinite Abelian groups, Whitehead problem and some constructions". Israel Journal of Mathematics. 18 (3): 243–256. doi:10.1007/BF02757281. MR 0357114.
Franzén 2005, p. 73. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326.
Franzén 2005; Raatikainen 2005; Sokal & Bricmont 1999; Stangroom & Benson 2006. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326. Raatikainen, Panu (2005). "On the philosophical relevance of Gödel's incompleteness theorems". Revue Internationale de Philosophie. 59 (4): 513–534. doi:10.3917/rip.234.0513. S2CID 52083793. Sokal, Alan; Bricmont, Jean (1999). Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science. Picador. ISBN 0-312-20407-8. Stangroom, Jeremy; Benson, Ophelia (2006). Why Truth Matters. Continuum. ISBN 0-8264-9528-1.
Wang 1996, p. 179. Wang, Hao (1996). A Logical Journey: From Gödel to Philosophy. MIT Press. ISBN 0-262-23189-1. MR 1433803

ams.org

Davis 2006, p. 416; Jones 1980. Davis, Martin (2006). "The Incompleteness Theorem" (PDF). Notices of the AMS. 53 (4): 414. Jones, James P. (1980). "Undecidable Diophantine Equations" (PDF). Bulletin of the American Mathematical Society. 3 (2): 859–862. doi:10.1090/S0273-0979-1980-14832-6.

arxiv.org

Zach 2007, p. 418; Zach 2003, p. 33. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science. Vol. 5. Amsterdam: Elsevier. pp. 411–447. arXiv:math/0508572. doi:10.1016/b978-044451541-4/50014-2. ISBN 978-0-444-51541-4. OCLC 162131413. S2CID 291599. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1). Springer Science and Business Media LLC: 211–259. arXiv:math/0102189. doi:10.1023/a:1026247421383. ISSN 0039-7857. S2CID 16657040.

cairn.info

Franzén 2005; Raatikainen 2005; Sokal & Bricmont 1999; Stangroom & Benson 2006. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326. Raatikainen, Panu (2005). "On the philosophical relevance of Gödel's incompleteness theorems". Revue Internationale de Philosophie. 59 (4): 513–534. doi:10.3917/rip.234.0513. S2CID 52083793. Sokal, Alan; Bricmont, Jean (1999). Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science. Picador. ISBN 0-312-20407-8. Stangroom, Jeremy; Benson, Ophelia (2006). Why Truth Matters. Continuum. ISBN 0-8264-9528-1.

digizeitschriften.de

Finsler 1926. Finsler, Paul (1926). "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. doi:10.1007/bf01283861. S2CID 121054124.

doi.org

Shelah 1974. Shelah, Saharon (1974). "Infinite Abelian groups, Whitehead problem and some constructions". Israel Journal of Mathematics. 18 (3): 243–256. doi:10.1007/BF02757281. MR 0357114.
Kleene 1943. Kleene, S. C. (1943). "Recursive predicates and quantifiers". Transactions of the American Mathematical Society. 53 (1): 41–73. doi:10.1090/S0002-9947-1943-0007371-8. Reprinted in Davis 1965, pp. 255–287
Shoenfield 1967, p. 132; Charlesworth 1981; Hopcroft & Ullman 1979. Shoenfield, Joseph R. (1967). Mathematical logic. Natick, Mass.: Association for Symbolic Logic (published 2001). ISBN 978-1-56881-135-2. Charlesworth, Arthur (1981). "A Proof of Godel's Theorem in Terms of Computer Programs". Mathematics Magazine. 54 (3): 109–121. doi:10.2307/2689794. JSTOR 2689794. Hopcroft, John E.; Ullman, Jeffrey (1979). Introduction to Automata Theory, Languages, and Computation. Reading, Mass.: Addison-Wesley. ISBN 0-201-02988-X.
Davis 2006, p. 416; Jones 1980. Davis, Martin (2006). "The Incompleteness Theorem" (PDF). Notices of the AMS. 53 (4): 414. Jones, James P. (1980). "Undecidable Diophantine Equations" (PDF). Bulletin of the American Mathematical Society. 3 (2): 859–862. doi:10.1090/S0273-0979-1980-14832-6.
Hellman 1981, pp. 451–468. Hellman, Geoffrey (1981). "How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism". Noûs. 15 (4 - Special Issue on Philosophy of Mathematics): 451–468. doi:10.2307/2214847. ISSN 0029-4624. JSTOR 2214847.
Priest 1984; Priest 2006. Priest, Graham (1984). "Logic of Paradox Revisited". Journal of Philosophical Logic. 13 (2): 153–179. doi:10.1007/BF00453020. Priest, Graham (2006). In Contradiction: A Study of the Transconsistent. Oxford University Press. ISBN 0-19-926329-9.
Shapiro 2002. Shapiro, Stewart (2002). "Incompleteness and Inconsistency". Mind. 111 (444): 817–32. doi:10.1093/mind/111.444.817.
Franzén 2005; Raatikainen 2005; Sokal & Bricmont 1999; Stangroom & Benson 2006. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326. Raatikainen, Panu (2005). "On the philosophical relevance of Gödel's incompleteness theorems". Revue Internationale de Philosophie. 59 (4): 513–534. doi:10.3917/rip.234.0513. S2CID 52083793. Sokal, Alan; Bricmont, Jean (1999). Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science. Picador. ISBN 0-312-20407-8. Stangroom, Jeremy; Benson, Ophelia (2006). Why Truth Matters. Continuum. ISBN 0-8264-9528-1.
Zach 2007, p. 418; Zach 2003, p. 33. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science. Vol. 5. Amsterdam: Elsevier. pp. 411–447. arXiv:math/0508572. doi:10.1016/b978-044451541-4/50014-2. ISBN 978-0-444-51541-4. OCLC 162131413. S2CID 291599. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1). Springer Science and Business Media LLC: 211–259. arXiv:math/0102189. doi:10.1023/a:1026247421383. ISSN 0039-7857. S2CID 16657040.
Finsler 1926. Finsler, Paul (1926). "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. doi:10.1007/bf01283861. S2CID 121054124.
Rodych 2003; Floyd & Putnam 2000; Priest 2004. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Priest, Graham (2004). "Wittgenstein's Remarks on Gödel's Theorem". In Max Kölbel (ed.). Wittgenstein's lasting significance. Psychology Press. pp. 207–227. ISBN 978-1-134-40617-3.
Floyd & Putnam 2000; Rodych 2003; Berto 2009. Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Berto, Francesco (2009). "The Gödel Paradox and Wittgenstein's Reasons". Philosophia Mathematica. III (17).

godelbook.net

Smith 2007, p. 24. Smith, Peter (2007). An introduction to Gödel's Theorems. Cambridge, U.K.: Cambridge University Press. ISBN 978-0-521-67453-9. MR 2384958. Archived from the original on 2005-10-23. Retrieved 2005-10-29.

ias.edu

math.ias.edu

Wigderson 2010. Wigderson, Avi (2010). "The Gödel Phenomena in Mathematics: A Modern View" (PDF). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.

jstor.org

Shoenfield 1967, p. 132; Charlesworth 1981; Hopcroft & Ullman 1979. Shoenfield, Joseph R. (1967). Mathematical logic. Natick, Mass.: Association for Symbolic Logic (published 2001). ISBN 978-1-56881-135-2. Charlesworth, Arthur (1981). "A Proof of Godel's Theorem in Terms of Computer Programs". Mathematics Magazine. 54 (3): 109–121. doi:10.2307/2689794. JSTOR 2689794. Hopcroft, John E.; Ullman, Jeffrey (1979). Introduction to Automata Theory, Languages, and Computation. Reading, Mass.: Addison-Wesley. ISBN 0-201-02988-X.
Hellman 1981, pp. 451–468. Hellman, Geoffrey (1981). "How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism". Noûs. 15 (4 - Special Issue on Philosophy of Mathematics): 451–468. doi:10.2307/2214847. ISSN 0029-4624. JSTOR 2214847.
Rodych 2003; Floyd & Putnam 2000; Priest 2004. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Priest, Graham (2004). "Wittgenstein's Remarks on Gödel's Theorem". In Max Kölbel (ed.). Wittgenstein's lasting significance. Psychology Press. pp. 207–227. ISBN 978-1-134-40617-3.
Floyd & Putnam 2000; Rodych 2003; Berto 2009. Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Berto, Francesco (2009). "The Gödel Paradox and Wittgenstein's Reasons". Philosophia Mathematica. III (17).

publicism.info

Hofstadter 2007. Hofstadter, Douglas R. (2007) [2003]. "Chapter 12. On Downward Causality". I Am a Strange Loop. Basic Books. ISBN 978-0-465-03078-1.

semanticscholar.org

api.semanticscholar.org

Franzén 2005; Raatikainen 2005; Sokal & Bricmont 1999; Stangroom & Benson 2006. Franzén, Torkel (2005). Gödel's theorem : an incomplete guide to its use and abuse. Wellesley, MA: A K Peters. ISBN 1-56881-238-8. MR 2146326. Raatikainen, Panu (2005). "On the philosophical relevance of Gödel's incompleteness theorems". Revue Internationale de Philosophie. 59 (4): 513–534. doi:10.3917/rip.234.0513. S2CID 52083793. Sokal, Alan; Bricmont, Jean (1999). Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science. Picador. ISBN 0-312-20407-8. Stangroom, Jeremy; Benson, Ophelia (2006). Why Truth Matters. Continuum. ISBN 0-8264-9528-1.
Zach 2007, p. 418; Zach 2003, p. 33. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science. Vol. 5. Amsterdam: Elsevier. pp. 411–447. arXiv:math/0508572. doi:10.1016/b978-044451541-4/50014-2. ISBN 978-0-444-51541-4. OCLC 162131413. S2CID 291599. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1). Springer Science and Business Media LLC: 211–259. arXiv:math/0102189. doi:10.1023/a:1026247421383. ISSN 0039-7857. S2CID 16657040.
Finsler 1926. Finsler, Paul (1926). "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. doi:10.1007/bf01283861. S2CID 121054124.

stanford.edu

plato.stanford.edu

Raatikainen 2020 : "Assume $F$ is a consistent formalized system which contains elementary arithmetic. Then $F\not \vdash {\text{Cons}}(F)$ ." Raatikainen, Panu (2020). "Gödel's Incompleteness Theorems". Stanford Encyclopedia of Philosophy. Retrieved November 7, 2022.

ucalgary.ca

people.ucalgary.ca

Zach 2007, p. 418; Zach 2003, p. 33. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science. Vol. 5. Amsterdam: Elsevier. pp. 411–447. arXiv:math/0508572. doi:10.1016/b978-044451541-4/50014-2. ISBN 978-0-444-51541-4. OCLC 162131413. S2CID 291599. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1). Springer Science and Business Media LLC: 211–259. arXiv:math/0102189. doi:10.1023/a:1026247421383. ISSN 0039-7857. S2CID 16657040.

web.archive.org

Smith 2007, p. 24. Smith, Peter (2007). An introduction to Gödel's Theorems. Cambridge, U.K.: Cambridge University Press. ISBN 978-0-521-67453-9. MR 2384958. Archived from the original on 2005-10-23. Retrieved 2005-10-29.

worldcat.org

Hellman 1981, pp. 451–468. Hellman, Geoffrey (1981). "How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism". Noûs. 15 (4 - Special Issue on Philosophy of Mathematics): 451–468. doi:10.2307/2214847. ISSN 0029-4624. JSTOR 2214847.
Dawson 1997, p. 63. Dawson, John W. Jr. (1997). Logical dilemmas: The life and work of Kurt Gödel. Wellesley, Massachusetts: A. K. Peters. ISBN 978-1-56881-256-4. OCLC 36104240.
Zach 2007, p. 418; Zach 2003, p. 33. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science. Vol. 5. Amsterdam: Elsevier. pp. 411–447. arXiv:math/0508572. doi:10.1016/b978-044451541-4/50014-2. ISBN 978-0-444-51541-4. OCLC 162131413. S2CID 291599. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1). Springer Science and Business Media LLC: 211–259. arXiv:math/0102189. doi:10.1023/a:1026247421383. ISSN 0039-7857. S2CID 16657040.
Rodych 2003; Floyd & Putnam 2000; Priest 2004. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Priest, Graham (2004). "Wittgenstein's Remarks on Gödel's Theorem". In Max Kölbel (ed.). Wittgenstein's lasting significance. Psychology Press. pp. 207–227. ISBN 978-1-134-40617-3.
Floyd & Putnam 2000; Rodych 2003; Berto 2009. Floyd, Juliet; Putnam, Hilary (2000). "A Note on Wittgenstein's "Notorious Paragraph" about the Godel Theorem". The Journal of Philosophy. 97 (11). JSTOR: 624–632. doi:10.2307/2678455. ISSN 0022-362X. JSTOR 2678455. Rodych, Victor (2003). "Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein". Dialectica. 57 (3): 279–313. doi:10.1111/j.1746-8361.2003.tb00272.x. doi:10.1111/j.1746-8361.2003.tb00272.x Berto, Francesco (2009). "The Gödel Paradox and Wittgenstein's Reasons". Philosophia Mathematica. III (17).