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Thematische Bibliographien / Three paradoxes of set theory

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Auswahl der wissenschaftlichen Literatur zum Thema „Three paradoxes of set theory“

Autor: Grafiati

Veröffentlicht am 18. Mai 2024

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Zeitschriftenartikel zum Thema "Three paradoxes of set theory"

1

OMORI, HITOSHI. "REMARKS ON NAIVE SET THEORY BASED ONLP." Review of Symbolic Logic 8, no. 2 (2015): 279–95. http://dx.doi.org/10.1017/s1755020314000525.

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AbstractDialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there is a way to handle classical negation.

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WEBER, ZACH. "TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY." Review of Symbolic Logic 3, no. 1 (2010): 71–92. http://dx.doi.org/10.1017/s1755020309990281.

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This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the exist

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Kreis, Guido. "The Challenge of Paradox: Infinity and Contradiction in Western and Chinese Philosophy." Journal of Chinese Philosophy 44, no. 3-4 (2017): 193–211. http://dx.doi.org/10.1163/15406253-0440304008.

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Kant claimed that it is impossible for us to have a consistent notion of the infinite. I shall concentrate on three versions of the paradoxes of the infinite: Kant’s first antinomy, the paradoxes of Cantorian set theory, and applications of Cantorian arguments to the metaphysics of the world. I shall dare two side-glance looks at Ancient Chinese Philosophy, where analogies to the Western paradoxes can be found. I shall first discuss key passages from the Chinese sophists, and then consider the formulation of the Law of Non-Contradiction in the Moist Canons. I conclude that the paradoxes of the

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Xue, Yang. "Reflection on Set theory: Is the barber example a genuine illustration of Russell's paradox?" Journal of Education, Humanities and Social Sciences 8 (February 7, 2023): 427–32. http://dx.doi.org/10.54097/ehss.v8i.4283.

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Since the formulation of Russell’s paradox, many people have created more accessible models while trying to understand and solve the paradox. The Barber paradox is the most famous one, but it is not the case that this paradox was not proposed by Russell. This paper will demonstrate the nature of both paradoxes through truth-functional language and propose possible solutions (theory of types) for Russell’s paradox. The reason why the Barber paradox is a pseudo paradox will also be illustrated with a possible solution. There is a huge difference between the paradoxes due to the fundamental diffe

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Nescolarde-Selva, Josué-Antonio, José-Luis Usó-Doménech, Lorena Segura-Abad, Kristian Alonso-Stenberg, and Hugh Gash. "Solutions of Extension and Limits of Some Cantorian Paradoxes." Mathematics 8, no. 4 (2020): 486. http://dx.doi.org/10.3390/math8040486.

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Cantor thought of the principles of set theory or intuitive principles as universal forms that can apply to any actual or possible totality. This is something, however, which need not be accepted if there are totalities which have a fundamental ontological value and do not conform to these principles. The difficulties involved are not related to ontological problems but with certain peculiar sets, including the set of all sets that are not members of themselves, the set of all sets, and the ordinal of all ordinals. These problematic totalities for intuitive theory can be treated satisfactorily

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Swart, Barbara. "Fair pricing, and pricing paradoxes." South African Journal of Economic and Management Sciences 19, no. 2 (2016): 321–29. http://dx.doi.org/10.4102/sajems.v19i2.1136.

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The St Petersburg Paradox revolves round the determination of a fair price for playing the St Petersburg Game. According to the original formulation, the price for the game is infinite, and, therefore, paradoxical. Although the St Petersburg Paradox can be seen as concerning merely a game, Paul Samuelson (1977) calls it a “fascinating chapter in the history of ideas”, a chapter that gave rise to a considerable number of papers over more than 200 years involving fields such as probability theory and economics. In a paper in this journal, Vivian (2013) undertook a numerical investigation of the

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Kakkar, Shiva. "The goblet and two faces." Learning Organization 26, no. 4 (2019): 412–24. http://dx.doi.org/10.1108/tlo-04-2018-0052.

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Purpose Paradox theory looks at ambidexterity as a set of paradoxical yet interrelated demands. A form of response to such paradoxes is transcendence. Currently, there is limited understanding of the concept among researchers. Using concepts from the Indian philosophy of Advaita Vedanta, this paper aims to provide a deeper understanding of transcendence, highlight some of the epistemological challenges it presents and suggest ways in which the concept can be used by practitioners and ambidexterity researchers. Design/methodology/approach The paper uses concepts and theories from advaitic epist

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Niizato, Takayuki, Kotaro Sakamoto, Yoh-ichi Mototake, et al. "Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis." Entropy 22, no. 7 (2020): 726. http://dx.doi.org/10.3390/e22070726.

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Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system’s cause–effect structure from spatio-temporal grain and reveals the system’s irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed u

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Halabi, Dana L., and Mitra Saamira. "Paradoxes in Policy Practice: Signaling Postsecondary Pathways in the Rust Belt." Teachers College Record: The Voice of Scholarship in Education 114, no. 1 (2012): 1–34. http://dx.doi.org/10.1177/016146811211400106.

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Context Research increasingly suggests that the high school diploma has lost its meaning as a symbol of life preparation. Having faced economic struggles earlier and longer than most regions of the United States, the “Rust Belt” region offers important lessons for the broader nation regarding how high schools might prepare youth for stable futures. Much like in towns in India and China, communities in the United States’ Rust Belt experience a paradox of wanting youth to find successful careers but not leave the area. Focus of Study Recent research connections between high school and college ha

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VINCENT, THOMAS L. "THE G-FUNCTION METHOD FOR ANALYZING DARWINIAN DYNAMICS." International Game Theory Review 06, no. 01 (2004): 69–90. http://dx.doi.org/10.1142/s0219198904000083.

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Darwinian dynamics refers to the dynamical processes underlying natural selection that drives evolution. We are interested in the evolution of strategies used by biological entities. There are two dynamical processes involved, population dynamics (relationship between population density and the agents affecting density) and strategy dynamics (relationship between strategy values and the agents affecting these values). Darwinian dynamics is a total dynamic obtained through the coupling of these two processes, the modeling of which, involves dynamical systems, optimization, stability, and game t

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