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Gotowe bibliografie tematyczne / Godel's Incompleteness theorem

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Gotowa bibliografia na temat „Godel's Incompleteness theorem”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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Artykuły w czasopismach na temat "Godel's Incompleteness theorem"

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Katrechko, Sergey. "Goedel's Incomplete Theorem: Does it Say Something about the Incompleteness of Math." Respublica Literaria 4, no. 4 (2023): 82–87. http://dx.doi.org/10.47850/rl.2023.4.4.82-87.

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The report will propose some methodological approach (“method of eliminating monsters”) going back to Lakatos (“Proof and refutation”) to the analysis of Godel’s theorem, which shows that despite its mathematical correctness, Godel’s theorem is not applicable to mathematics (recursive arithmetic), since the Gödel expression is not a formula, but a formulaoid (Yesenin-Volpin), or a mathematical “monster” that must be eliminated from the field (language) of mathematics. This makes it possible to “remove” Godel's thesis about the incompleteness of mathematics, although it does not cancel the task

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Jech, Thomas. "On Godel's Second Incompleteness Theorem." Proceedings of the American Mathematical Society 121, no. 1 (1994): 311. http://dx.doi.org/10.2307/2160398.

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Moore, A. W. "What Does Godel's Second Incompleteness Theorem Show?" Noûs 22, no. 4 (1988): 573. http://dx.doi.org/10.2307/2215458.

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Gauker, C. "T-schema deflationism versus Godel's first incompleteness theorem." Analysis 61, no. 2 (2001): 129–36. http://dx.doi.org/10.1093/analys/61.2.129.

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Gauker, Christopher. "T-schema deflationism versus Godel's first incompleteness theorem." Analysis 61, no. 270 (2001): 129–36. http://dx.doi.org/10.1111/1467-8284.00282.

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Xie, Ling. "The Reason for the Incompleteness of Some Theorems in Modern Mathematics: Non Numbers Enter Mathematical Analysis or the Concept Definition Is Incomplete." European Journal of Theoretical and Applied Sciences 1, no. 3 (2023): 171–80. http://dx.doi.org/10.59324/ejtas.2023.1(3).19.

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The concept of non-number and number is found, and the concept of non-number and number is defined by symbols. The basic theory of number theory is solved; it is proved that {Godel's Incomplete Theorem} are incomplete. and it is also proved that the first number of natural number must be 1, not 0.

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Tselishchev, Vitaly V. "The truth of undecidable sentences in the perspective of Godel's first incompleteness theorem." Vestnik Tomskogo gosudarstvennogo universiteta, no. 421 (August 1, 2017): 53–58. http://dx.doi.org/10.17223/15617793/421/7.

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Lv, Sicheng. "Formalism in the History of Philosophical Mathematics: Beyond Logicism and Intuitionism." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 522–30. http://dx.doi.org/10.54097/ywkbwm53.

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An examination of the similarities and differences between these three schools may shed light on the richness and variety of mathematical philosophies, as well as the significance of such philosophies to the comprehension and growth of mathematics. Formalism, logicism, and intuitionism are the names of these schools. The purpose of this study is to investigate the three primary schools of thought within the philosophy of mathematics, examine the many ways in which these schools interpret and approach mathematics, and investigate the areas in which these schools share and diverge in their persp

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Franzén, Torkel. "Transfinite Progressions: A Second Look at Completeness." Bulletin of Symbolic Logic 10, no. 3 (2004): 367–89. http://dx.doi.org/10.2178/bsl/1102022662.

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§1. Iterated Gödelian extensions of theories. The idea of iterating ad infinitum the operation of extending a theory T by adding as a new axiom a Gödel sentence for T, or equivalently a formalization of “T is consistent”, thus obtaining an infinite sequence of theories, arose naturally when Godel's incompleteness theorem first appeared, and occurs today to many non-specialists when they ponder the theorem. In the logical literature this idea has been thoroughly explored through two main approaches. One is that initiated by Turing in his “ordinal logics” (see Gandy and Yates [2001]) and taken v

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Enderton, H. B. "Vladimir A. Uspensky. Godel's incompleteness theorem. A reprint of LV 889 with minor corrections. Theoretical computer science, vol. 130 (1994), pp. 239–319." Journal of Symbolic Logic 60, no. 4 (1995): 1320. http://dx.doi.org/10.1017/s0022481200018132.

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Rozprawy doktorskie na temat "Godel's Incompleteness theorem"

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St, John Gavin. "On formally undecidable propositions of Zermelo-Fraenkel set theory." Youngstown State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1369657108.

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Książki na temat "Godel's Incompleteness theorem"

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Uspenskii, Vladimir Andreevich. Gia to theōrēma mē-plērotētas tou Godel. Trochalia, 1998.

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Language and Godel's theorem. Shaker Publishing, 2008.

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Smullyan, Raymond M. Gödel's Incompleteness Theorems. Oxford University Press, 1992. http://dx.doi.org/10.1093/oso/9780195046724.001.0001.

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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with

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Franzen, Torkel. Godel's Theorem: An Incomplete Guide to Its Use and Abuse. A K Peters, Ltd., 2005.

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Smullyan, Raymond M. Godel's Incompleteness Theorems. Oxford University Press, Incorporated, 1992.

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Goldstein, Rebecca. Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries). W. W. Norton & Company, 2005.

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Goldstein, Rebecca. Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries). W. W. Norton, 2006.

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Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries). W. W. Norton & Company, 2005.

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Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries). W. W. Norton, 2006.

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Części książek na temat "Godel's Incompleteness theorem"

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Kaye, Richard. "Gödel incompleteness." In Models of Peano Arithmetic. Oxford University PressOxford, 1991. http://dx.doi.org/10.1093/oso/9780198532132.003.0004.

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Abstract This chapter is devoted to the proof of Godel’s first incompleteness theorem for recursively axiomatized theories extending PA−. Godel’s theorem is often considered because of its role in foundational issues in mathematics (in this context the first incompleteness theorem tells us that ‘arithmetic truth is not axiomatizable’). We shall be also interested in it for a different reason: the incompleteness theorem, in conjunction with the completeness theorem, equips us with a rich supply of interesting models. The techniques we employ, such as the representability of recursive functions

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"John W. Dawson, Jr. : The Reception of Gödel's Incompleteness Theorems." In Godel's Theorem in Focus. Routledge, 2012. http://dx.doi.org/10.4324/9780203407769-9.

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"Excursion Two: Godel's Incompleteness Theorems." In Infinity and the Mind. Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400849048.267.

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Feferman, Solomon. "Infinity in Mathematics: Is Cantor Necessary? (Conclusion)." In In The Light Of Logic. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195080308.003.0012.

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Abstract By Godel’s doctrine I mean the view first enunciated in footnote 48a of Godel (1931) that the “true reason” for the incompleteness phenomena is that “the formation of ever higher types can be continued into the transfinite,” both in systems explicitly using types and in systems of set theory such as ZF for which the (cumulative) type structure is implicit in the axioms. For, as Godel says, the “undecidable propositions constructed here become decidable whenever appropriate higher types are added.” Since the undecidable propositions are of finitary character, Godel ‘s doctrine says in

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Giaquinto, M. "Incompleteness, and Undefinability of Truth." In The Search for Certainty. Oxford University PressOxford, 2002. http://dx.doi.org/10.1093/oso/9780198752448.003.0020.

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Abstract Hilbert’s Programme placed formal systems at the centre of foundational research. This work was proceeding apace in the late 1920s in the direction that Hilbert envisaged. Then in 1931 a paper was published by Godel, then only 25, that was to change the landscape of foundational studies permanently. This paper contained a couple of theorems about formal systems of great significance, and presented a new and powerful technique for metamathematics (the study of formal systems). This chapter presents the first of these two theorems, plus a related theorem of Tarski, and then assesses the

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Feferman, Solomon. "Gödel’s Life and Work." In In The Light Of Logic. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195080308.003.0006.

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Abstract Kurt Godel’s striking fundamental results in the decade 1929 through 1939 transformed mathematical logic and established him as the most important logician of the twentieth century. His work influenced practically all subsequent developments in the subject as well as all further thought about the foundations of mathematics. The results that made Godel famous are the completeness of first-order logic, the incompleteness of axiomatic systems containing number theory, and finally, the consistency of the Axiom of Choice and the Continuum Hypothesis with the other axioms of set theory. Dur

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Gillies, Donald. "Do Godel’s Incompleteness Theorems Place a Limit on Artificial Intelligence?" In Artificial Intelligence and Scientific Method. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198751588.003.0006.

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Abstract So far in this book we have examined some of the implications which new results in artificial intelligence might have for old questions in the philosophy of science and philosophy of logic. I think it will be agreed that the results have been quite striking. Advances in machine learning have supported the Baconian inductivist view of scientific method against more modern alternatives. The development of PROLOG has provided arguments for the empiricist as opposed to a priori conception of logic, and logic programming has also suggested a new framework for logic within which it may be p

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Gurukkal, Rajan. "Science of Uncertainty." In History and Theory of Knowledge Production. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199490363.003.0006.

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This chapter virtually illuminates the invisible universe of subatomic dynamics through mathematical formalism and probability theory rather than empiricism based on instrumentation. A series of strange discoveries go into the making of the New Science and a discussion of the process constitutes the core of this chapter. Max Planck’s proposition of the Quanta, Niels Bohr’s discovery of objects’ non-observable and immeasurable complementary properties, Erwin Schrodinger’s interpretation of the object-subject split as a figment of imagination, Werner Karl Heisenberg’s enunciation of the Uncertai

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"5 Godel’s Incompleteness Theorem and the Downfall of Rationalism: Vindication of Kant’s Synthetic A Priori." In Quantification: Transcending Beyond Frege’s Boundaries. BRILL, 2012. http://dx.doi.org/10.1163/9789004224179_006.

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Gratzer, Walter. "The limits of logic." In Eurekas and euphorias. Oxford University PressNew York, NY, 2002. http://dx.doi.org/10.1093/oso/9780192804037.003.0131.

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Abstract In 1931, an intellectual bombshell exploded in the sheltered world of mathematics. The perpetrator of the outrage was a young German, Kurt Godel (1906-78), and the most illustrious of the casualties David Hilbert [11], doyen of German mathematicians. The Hilbert Project, as it was called, had the aim of establishing a complete system of axioms from which all of mathematics could eventually be rigorously developed. (Remote from everyday reality as such a preoccupation might appear, this, like other researches of Hilbert’s and Gödel’s, proved to have a profound bearing on topics in scie

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